RANDOM thoughts

[Irieguy]

"My major hobby is teasing people who take themselves & the quality of their knowledge too seriously & those who don’t have the guts to sometimes say: I don’t know...." (You may not be able to change the world but can at least get some entertainment & make a living out of the epistemic arrogance of the human race). -- Nassim Nicholas Taleb

Nassim Nicholas Taleb is the author of a book called Fooled by Randomness, which I think is a must-read for any professional or aspiring professinal poker player. I read the book several years ago, but I think about it often as I continue to struggle to wrap my mind around the role of randomness in my results.

I am frequently reminded about the concepts explained in that book when I read posts on this forum, but lately it seems that randomness has become a particularly neglected concept. I think that understanding the role of randomness in the world is a key component to a sound world view and a happy, peaceful existence. Most people disagree with me.

The majority of people on this planet believe in ghosts. They believe that aliens pilot UFOs. They believe in their God at the exculusion of all other gods and believe that disagreeing with them may have dire consequences. They believe that everything happens for a reason. They believe in fate. They believe in destiny. Believing these things brings comfort to the majority of people on this planet... as ironic as it seems.

Now, there is another point of view regarding the laws of the universe. It is a point of view governed by science and reason. It is a minority viewpoint. It may or may not be any better or worse than the majority viewpoint, but it's easier to defend in a debate (using science and reason as the primary debate tactics, of course.)

What does this have to do with SNG poker? Well; smart, scientific, reasonable people get fooled by randomness all of the time. I'll let anyone interested read the book if they want some brilliant examples (including a nice discussion of the Monte Carlo simulator which made a brief but magnificent appearance on this forum a few months back.) In any event, I submit that we could all benefit from looking a little harder at the role of randomness in our results.

Somebody (read: practically everybody) will misinterpret this post as an assertion by me that so and so isn't as good as he thinks he is. This is not my point. I don't care how good so and so is. I just think that a concept as profoundly significant as randomness should make a more frequent appearance. An ample acknowledgement of randomness keeps egotism and idolatry in check. 5 billion people on this planet earn less than $10 per day. We need to be careful not to assume that the reason why we earn $10 per SNG is because we are smarter or better than the rest of the people on this planet. We are merely better served by randomness, that is all.

That doesn't mean that there isn't a correct way to play poker. There is. That doesn't mean that you can't become a winning poker player and make a lot of money. You can. Here's what it means:

Let's say that flipping coins became the next craze. MGM-Mirage decided to pay anyone that wanted to play even money if they could flip heads.(minus a fee, of course.) People love to do this, and pretty soon everybody is wagering everything they have trying to flip heads.

Let's say that a small percentage of people actually figure out how to use certain mechanics and weather conditions to improve the chances that they can flip heads. This select group of "professional flippers" averages heads 60% of the time. Some members of this elite group average more, some less. It's quite a hard skill to master... but worth the effort. But the rest of the public simply takes their 50-50 shot and pays the vig. Still, everybody is aware of this elite group, and many fancy themselves a member of this group... many more than actually belong.

So, eventually there's a group of 500,000 donkeys flipping coins and 25,000 professionals. Legend and lore builds, and the goal of every flipper is to make a "magic 9." A "magic 9" is 9 heads in a row. Only professionals are really capable of such a feat, legend has it, because the random odds of this happening are astronomical.

So everybody starts flipping. In the first 9 flips there will be close to 1000 "magic 9ers" from the random population and only 250 or so from the professional group. Clearly, anyone who makes a magic 9 will fancy themselves a professional, so there will be 1250 self-proclaimed professionals with the title of "magic 9er," while only 250 of those people are, in fact, professionals. Oh, and by the way, those 250 professionals are on quite a heater.

So, you can tweak the analogy anyway you'd like... but the bottom line is that as long as professionals comprise a small percentage of the total population of players in an endeavor where chance plays a role, the majority of successful individuals are going to be the beneficiaries of randomness. Furthermore, the most successful of the "skilled professional" group will also be beneficiaries of randomness to a much larger degree than they would like to admit.

My opinion is that by coming to terms with the statistical truism analogized above, it becomes easier to distinguish signal from noise in discussions about what to expect from the game of poker.

Or something.

Irieguy

[Freudian]

Many pokerplayers who do well do indeed have their magic 9 start. That gives them breething room to suck while learning to play properly since they now have a bankroll. For some that is not enough (que complaints about bad luck, cheating) to get them through. Most who quit poker never have their magic 9 at any point. It is just a stupid game where you lose money. And lastly we have those that have a bad start but since the signs that this thing can be beat are there keep trying and improving. They most likely will have their magic 9 sooner or later.

[Benholio]

But don't we talk about variance every day? I think most, or many at least, of us have a good idea of the role that variance plays in our results.

[Freudian]

[ QUOTE ]
But don't we talk about variance every day? I think most, or many at least, of us have a good idea of the role that variance plays in our results.

[/ QUOTE ]

If that was true, why is invariably most new posters talking about their ROI in their first post.

And why do the posters with experience only divulge their results after running good?

[The Yugoslavian]

[ QUOTE ]
But don't we talk about variance every day? I think most, or many at least, of us have a good idea of the role that variance plays in our results.

[/ QUOTE ]

Yeah, like maybe 5 people on this forum have any idea of the depth and profundity that is VARIANCE.

I'm serious btw. Oh and Giga is one of them I'd imagine. He's rolled like 9 magic 9s, /images/graemlins/tongue.gif.

Yugoslav

[GrekeHaus]

[ QUOTE ]
But don't we talk about variance every day? I think most, or many at least, of us have a good idea of the role that variance plays in our results.

[/ QUOTE ]

I think that it is almost like a buzzword for a lot of people. Someone post stats saying "I have a 50% ROI after 150 tournaments". Then well all say "Just wait for variance to kick in".

Meanwhile, the same poster who just posted the above statement about variance makes a seperate post saying "Look how well I did this month". His results are more reasonable and seemingly more attainable so we all say "Way to go" and assume that we should all aspire to have a 25% ROI at the 109s, or a 33% ROI at the 11s or whatever.

Meanwhile, the poster never posts the results of how well he did the other 11 months out of the year.

[Benholio]

Well, talking about your ROI doesn't mean you have no concept of variance. If you played 50 tournaments and you had an ROI of 50%, well, you had an ROI of 50%.

However, I'm not going to speak for, or defend, the new posters who come in here thinking they are 70% ITM, etc. I'm just speaking for the majority of the people who have read the forum for more than a day.

Basically, I'm just saying, did that big long post say something besides "variance variance you are running good blah", because if so, I'd like to be enlightened.

This isn't meant as a dig, as I've gotten plenty of insight from Irie's posts before. I am just trying to make sure there isn't some new nugget of knowledge buried in this one.

[DMACM]

You dont need to roll a magic 9 if you start with play chips and work your way up to .01-.02 nl and so on. I don't understand why everyone doesn't do that.

[Freudian]

[ QUOTE ]

I think that it is almost like a buzzword for a lot of people. Someone post stats saying "I have a 50% ROI after 150 tournaments". Then well all say "Just wait for variance to kick in".

[/ QUOTE ]

Also it is used to explain away losing streaks. Drop xx buyins. "It is just variance". Which is silly. For all we know it could have zero to do with variance and everything to do with poor play.

[Freudian]

[ QUOTE ]
You dont need to roll a magic 9 if you start with play chips and work your way up to .01-.02 nl and so on. I don't understand why everyone doesn't do that.

[/ QUOTE ]

Hehe, I always get confused by those that read three 2+2 books while playing with play money and then make their first deposit.

Those freaks scare me.

[DMACM]

fine be that way. /images/graemlins/tongue.gif

[SuitedSixes]

[ QUOTE ]
They believe in their God at the exculusion of all other gods and believe that disagreeing with them may have dire consequences. They believe that everything happens for a reason. They believe in fate. They believe in destiny. Believing these things brings comfort to the majority of people on this planet... as ironic as it seems.

[/ QUOTE ]

I am comforted by these things and I wonder, if as a doctor you have ever experienced anything that cannot be explained by simple randomness.

[Irieguy]

[ QUOTE ]

I am comforted by these things and I wonder, if as a doctor you have ever experienced anything that cannot be explained by simple randomness.

[/ QUOTE ]

Randomness is far from simple.

Irieguy

[Benholio]

[ QUOTE ]
[ QUOTE ]

I am comforted by these things and I wonder, if as a doctor you have ever experienced anything that cannot be explained by simple randomness.

[/ QUOTE ]

Randomness is far from simple.

Irieguy

[/ QUOTE ]

What isn't simple about it? Or do I just need some puffs on the peace pipe to go with my alcohol tonight...

[microbet]

[ QUOTE ]
Somebody (read: practically everybody) will misinterpret this post as an assertion by me that so and so isn't as good as he thinks he is.

[/ QUOTE ]

You wrote this whole essay just to say how much I suck. Nice.

[valejo]

I certainly agree with the OP that the 2+2 approach would benefit from more science and less pride and/or emotion.

Part of applying a scientific approach to poker is to understand variance and it's roll. But variance doesn't have to be a parlor word around here. We can study the extent to which randomness can explain events. Statistics gives us a boatload of tools to help identify patterns in seemingly random data.

Yes, up and down swings can happen by random chance. However, if my data shows that I have 40% ROI over 100 tournaments, that is enough to be about 99% confident that I am a winning poker player if I continue to utilize the same strategies. Similarly, if I have 15% ROI over 10,000 tournaments but I've run at -20% ROI for the past 100, the probability is high that I've been playing poorly and I need to revisit my strategy.

2+2 should spend more time understanding and modeling the random walks of poker careers.

One easy model is to use one-sided hypothesis testing to predict the lowest possible ROI a given player can expect long run based on their current sample.* A second useful tool is confidence intervals for players with a huge database of tournaments to help them detect when they might be playing badly.

* Of course, we can only measure this to a specified degree of confidence; we can never be 100% sure we aren't just lucky.

[SuitedSixes]

Nice post.

[Gramps]

Newton said for every action there is a reaction. He broke things down into a measurable, predictable, mechanical science. Individualism and Western Society developed out of these sorts of ideas (or something). We're comfortable with these concepts.

Screw Quantum Physics. Heisenberg is full of sh-t, God does not play dice (One of greatest f-ing quotes of all-time BTW). If I average 6 BB/100 for 2,000 hands of limit poker or a 40% ITM for 100 higher level SNGs, I am a genius brilliant player.

If I go on a horrid losing streak, internet poker is rigged, and when I go another another heater it is because the "Party rigging switch" has been flipped back to off, and everything is right in the universe...

[Bigwig]

Weird.

If you're not trying to say that some results are based on luck, then what are you trying to say?

I understand your point in general, but it's relation to SNG poker is slim at best, complete gibberish at it's worst.

Whatever.

[microbet]

Seriously, interesting post. I'll check out the book, although he's probably preaching to the choir with me.

[bugstud]

read the mid/high limit DERB thread lately?

[vinyard]

[ QUOTE ]

I understand your point in general, but it's relation to SNG poker is slim at best, complete gibberish at it's worst.

Whatever.

[/ QUOTE ]

[treeofwisdom7]

hey guys interesting post. i have been running very good with a 25% ITM and 10% ROI over 95 games.. i think this is good but is it enuf to tell if im a winning player or not?




AHHHHAAAAHHAAAAAAHAAAAA *do the raptor **GASP** * AHHHHAHHAAAHHHHHHHAAAAA

YOU CAN BE MY BABY IT DONT MATTER IF YOUR BLACK OF WHITE

[SumZero]

I think it was (or at least could become) a more constructive response to "Part-time SnG grinders" (thread link (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2734620&page=0&view=c ollapsed&sb=5&o=14&fpart=1)).

I mean even ignoring the amazing drjnightowl there were several posters who have a hard time understanding randomness.

And that isn't surprising seeing people in general have a hard time with probability. And not just random calculations (What are the chances of the flopped four flush giving me the flush be the river?) but especially the intuition to reason properly with math especially under uncertainty (and I think it is funny that Irieguy mentions "Fooled by Randomness" as that is on my queue of books to read and I'll probably get to it after HOH2 and HP6). I mean I post a little in General Gambling/Probability and look at two common questions people ask:

- Why doesn't a Martingale roulette strategy work (bet $1 on black, if you lose double your bet until you win and start over again)?

- The Monty Hall/Let's make a deal problem (choose from 3 doors randomly (one of which has a prize behind it), after you pick the host (who knows what's behind what door) will show you one of the rooms that you didn't pick that has no prize and then offer you to keep your pick or switch to the unpicked and unopened room).

The first is obviously a problem understanding how fast exponential growth is and figuring out how to calculate the expectation in the face of that. And what's worth even when people can't calculate the expectation they can't even inuitively reason why it doesn't work.

The second is but one of many examples that most people just don't get conditional probability and also can't logically reason the answer very well. I have two favorite examples of conditional probability that, when I ask them to many smart people, they can't figure out the right answer (or even worse "figure out" a wrong answer).

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)

The second one of my questions (and I think I may be cribbing it from "There Are Two Errors in the the Title of This Book*: A Sourcebook of Philosophical Puzzles, Paradoxes and Problems" by Robert M. Martin which is also a fantastic read) ties directly in to what Irieguy was getting at with the coin-flipping analogy (although coin-flipping is a bad analogy because one really can "flip" coins in an unfair way as often coins don't flip but actually wobble which only looks like flipping and one can practice this). But first the question:

Question 2 (a different flavor of the false positive health test question):
Assume that we are on an Island with 100 taxis. On the Island 95 taxis are yellow and 5 taxis are green on the Island. Police know that eyewitnesses are 80% accurate (that is they will correctly identify the color of a taxi 80% of the time and the other 20% of the time they will say that the taxi was the opposite color from what it was - and that this eroor rate is idependent and unrelated to the actual color of taxi). There is a hit and run involving a taxi. The only eyewitness says that the taxi was green. What is the probability that the taxi involved was actually a green taxi?

The very high number of people who think that it doesn't matter if you switch in the Montey Hall problem because it is 50/50 that you'll win or that the answer to question 1 above is 5 or that the answer to question 2 is 80% is astonishing.

So to repharse Irieguy's analogy as it applies to SNG (and this is the important point):

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

Irieguy's secondary point:

"Furthermore, the most successful of the 'skilled professional' group will also be beneficiaries of randomness to a much larger degree than they would like to admit" is worth remembering too (and has Daniel Negreanu's name all over it, for one).

[valejo]

[ QUOTE ]
hey guys interesting post. i have been running very good with a 25% ITM and 10% ROI over 95 games.. i think this is good but is it enuf to tell if im a winning player or not?




AHHHHAAAAHHAAAAAAHAAAAA *do the raptor **GASP** * AHHHHAHHAAAHHHHHHHAAAAA

YOU CAN BE MY BABY IT DONT MATTER IF YOUR BLACK OF WHITE

[/ QUOTE ]

Based on the stated sample, there's 70.5% confidence that you are ROI >= 0.

[jcm4ccc]

[ QUOTE ]

The very high number of people who think that it doesn't matter if you switch in the Montey Hall problem because it is 50/50 that you'll win . . . is astonishing.



[/ QUOTE ]

Oh yes, let's discuss Monty Hall.

Because it is 50/50. Marilyn vos Savant was wrong.

[elrudo]

I think this little essay is brilliant.

However, there is a small flaw in it.
There would be some real lucky flipdonkeys who performed a 'magic 9' yet wouldnt claim to be a pro.

Not that the real pros would notice.
A lucky poker player

[skipperbob]

[ QUOTE ]
I am just trying to make sure there isn't some new nugget of knowledge buried in this one.

[/ QUOTE ]

Irie doesn't dispense knowledge in nugget-sized parcels; it's more like "pixie dust" /images/graemlins/smirk.gif

[AleoMagus]

[ QUOTE ]
Because it is 50/50. Marilyn vos Savant was wrong.

[/ QUOTE ]

Given her assumptions, she was correct. it is NOT 50/50 if the host always offers the switch.

Regards
Brad S

[AleoMagus]

Very good post.

I actually doubt that many who should be paying attention to this will really get it. Bayesian reasoning is just so counter-intuitive to so many.

Regards
Brad S

[jcm4ccc]

[ QUOTE ]
[ QUOTE ]
Because it is 50/50. Marilyn vos Savant was wrong.

[/ QUOTE ]

Given her assumptions, she was correct. it is NOT 50/50 if the host always offers the switch.

Regards
Brad S

[/ QUOTE ]

yep, but why did she make that assumption? Did she watch every episode of "let's make a deal?"

What if you assume that the producers of the show are cheap (probably a more reasonable assumption)? They only offer the switch when you choose the car. Then you are certain to lose the car if you switch.

Statistics should reflect the real world, not the other way around.

Marilyn vos Savant is an idiot with an IQ of 200. Not mutually exclusive things.

[AleoMagus]

I think that when you contrast the accepted opinion, as summarized by valejo:

[ QUOTE ]
One easy model is to use one-sided hypothesis testing to predict the lowest possible ROI a given player can expect long run based on their current sample.* A second useful tool is confidence intervals for players with a huge database of tournaments to help them detect when they might be playing badly.



[/ QUOTE ]

with what SumZero later says in this thread about bayesian implications on our usual confidence assumptions

[ QUOTE ]
So to repharse Irieguy's analogy as it applies to SNG (and this is the important point):

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

Irieguy's secondary point:

"Furthermore, the most successful of the 'skilled professional' group will also be beneficiaries of randomness to a much larger degree than they would like to admit" is worth remembering too (and has Daniel Negreanu's name all over it, for one).


[/ QUOTE ]

then yes, I think that something interesting is being said in Irie's post. Unfortunately, it seems to be being missed by many.

[ QUOTE ]
I understand your point in general, but it's relation to SNG poker is slim at best, complete gibberish at it's worst.


[/ QUOTE ]

So no, I don't think you do understand. And I don't think it is gibberish. Though I suppose It's relation is no more specific to SNGs than to any other kind of poker.

Regards
Brad S

[AleoMagus]

I have a question now... especially seeing as I'm the one who first injected confidence interval calculations into this forum with my confidence calculator and later spreadsheets.

What effect does this have on our actual winning confidence? If I calculate a winning confidence of 95% based on the assumptionthat (say) 2/3 of all players are really losers, how does this sway the chance that I am a winner, given the additional info I now have about the rest of the population? What if 90% are losers?

I actually think I can answer this, but the question has just hit me, and you seem well versed.

How do I determine this new confidence % based on the rest of the population? (I may need to update the confidence calculator)

Regards
Brad S

[jcm4ccc]

[ QUOTE ]

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

[/ QUOTE ]

That's interesting. I'll stick some numbers on it to make it clearer.

Suppose we have 1000 players. 950 of these players are losing players, and 50 players are winning players.

After 500 tournaments, 10% of the losing players have a positive ROI, and 100% of the winning players have a positive ROI. This means that 95 of the losing players have a positive ROI, and 50 of the winning players have a positive ROI. If you are one of the 1000 players and have a positive ROI, are you more likely to be a winning player or a losing player?

[45suited]

Irieguy, you just have to kick over the ant hill every so often, don't you? /images/graemlins/wink.gif

Your post leads me to something that I think about alot regarding my own circumstances:

It came up a while back when a player who had an ROI of like 8% on the 11s (after 500 games) was asking if he should move up. He wanted to know how other people did on the 11s. I answered that I have well over 1000 games on the 11s with an ROI over 30%. I was immediately criticized (Flyingmoose, I believe) and asked if I was the most "cashout happy person in the world". My resonse is that I do throw in the occassional 22 with good results and that soon I will move up to that level. But I want to get 1000 games in at each level (as a winner) before moving up. Wherever I struggle is where I will stop (and try to learn) and that my ego will not get in my way - if I hit the 55s some day and lose, I will move back down.

I made the point that if someone is only beating the 11s at an 8% rate, the last thing they should do is move up and multi-table. He should improve his game, learn, and wait until he can beat the 11s at a higher rate. My belief is tht if you simply play solid poker and let your opponents beat themselves (and know how to play the bubble, of course), anyone should be able to beat the 11s for (pick a number) 15% ROI at least.

So, basically, the "randomness" idea (which I agree with in general) loses some of its power at the lower levels, since the terrible play of your opponents is not random, but entirely predictable and expected. Their bad play alone is enough to make you a winner in the long run.

My point is that I find it interesting that most of us (myself included) agree with you in general about "randomness" (or variance or whatever else you wish to call it) but at the same time, I believe that so many people move up in limits too quickly. Many players routinely give what I think is dangerous advice to noobs advising them to do so. This is in spite of the fact that GOOD players regularly post horror stories of bad runs ruining their bankrolls after moving up.

Personally, I have no ego when it comes to poker. TONS of players are better than me and I have no problem admitting it. I have lots to learn. But in the meantime, I have no shame winning at the lower levels until I can determine that I am ready to move up.

[Hood]

Surely the problem with this model is it makes the assumption "assuming you're one of the 1000 players". This isn't a fair assumption. If you're a regular here, read and post threads, read 2+2 material, study your HHs and really try and understand the game, you are not part of the general distribution of the 1000 players.

Infact, it could work in the opposite way: say 95% of 1000 2+2 posters (who spend a good amount of time trying to really learn and study the game) have an average ROI of 10% over 500 SNGs, yet your ROI is -5%, what's the chance you are a winning player?

Keep in mind that we have a famous thread here on 2+2 which lays out clearly and exactly how to play to 'beat the 10+1s'.

[Mr_J]

Well the problem is these probability tests are for a 'random' player. Someone who just plays, wins and then posts X% after 100 sngs is likely just lucky. Someone who works on their game and achieves the same X% after 100 sngs is more likely to be a winning player than the former, but if you ran a test the numbers would be the same.

It's like when I was running tests for sportsbetting. If you seached for patterns and found something that was a 1 in 10k event, it's still meaningless. But if you have developed your hypothesis first and then tested and achieved the same results then it means a WHOLE lot more.

[wulfheir]

<-- waiting and working on my "M9"

[PrayingMantis]

[ QUOTE ]
So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI.

[/ QUOTE ]

I'm not a mathematician, but I think this isn't very correct. If you so insist on the importance of conditional probablity to understanding results in this game, you can't ignore "deeper levels" of conditional probability. For some reason, you seem to ignore them completely, IMO.

If you state in the beginning of this example, that we're talking about a player who "has done the heavy lifting of the math" involved here, it's only natural to assume this player is not picked up randomly from the non-uniform distribution of SNG players, but rather that he is placed in a "higher" point on this graph to begin with, AT LEAST with regard to his mathematical abilities, which, as we know, play a very important part in playing SNGs. And so, using some conditional probability reasoning, it makes sense to conclude that there IS something along the lines of 80% confidence (or even more!) that this is indeed a winning player.

[Dr_Jeckyl_00]

[ QUOTE ]

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)


[/ QUOTE ]

I believe that x=5 is a fair game (on average both people break even). 6:1-6:5 = 5 ways, 6:6=1 way any other outcome is irrelevent...

maybe I should have finished reading thread before posting, but if it is not 5, then what is the answer? Certainly over the short term you may rarely or frequently see 6:6, but over long term x should = 5, if not please explain why not.

[Daliman]

Blackjack diety Arnold Snyder wrote a very similar, but much more fleshed-out example for a Blackjack Forum atricle called "Swami Pastrami" or something like that. looking around online for it.

[jcm4ccc]

[ QUOTE ]
[ QUOTE ]

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)


[/ QUOTE ]

I believe that x=5 is a fair game (on average both people break even). 6:1-6:5 = 5 ways, 6:6=1 way any other outcome is irrelevent...

maybe I should have finished reading thread before posting, but if it is not 5, then what is the answer? Certainly over the short term you may rarely or frequently see 6:6, but over long term x should = 5, if not please explain why not.

[/ QUOTE ]

Nope. It took me a while to figure this out. The fair number is 11.

Here are the 12 different ways the dice can come up:

61
16
62
26
63
36
64
46
65
56
66

1 out of these 12 is 66.

[junkmail3]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)


[/ QUOTE ]

I believe that x=5 is a fair game (on average both people break even). 6:1-6:5 = 5 ways, 6:6=1 way any other outcome is irrelevent...

maybe I should have finished reading thread before posting, but if it is not 5, then what is the answer? Certainly over the short term you may rarely or frequently see 6:6, but over long term x should = 5, if not please explain why not.

[/ QUOTE ]

Nope. It took me a while to figure this out. The fair number is 11.

Here are the 12 different ways the dice can come up:

61
16
62
26
63
36
64
46
65
56
66

1 out of these 12 is 66.

[/ QUOTE ]

There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[jcm4ccc]

[ QUOTE ]
There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[/ QUOTE ] Yeah, didn't think it through. But I was thrilled to come up with the semi-right answer. It's a pretty tricky question, I think.

[freemoney]

i understand and appreciate your post but i think the idea of seeing significant mistakes your opponents make that you do not continually make allows you to gauge your ability to beat/compete at a certain level just as much as playing 124234 SnGs.

[Dr_Jeckyl_00]

[ QUOTE ]
[ QUOTE ]
There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[/ QUOTE ] Yeah, didn't think it through. But I was thrilled to come up with the semi-right answer. It's a pretty tricky question, I think.

[/ QUOTE ]

Damn it! I thought I was good at this stuff, how could I screw that up... thanks for the answer

[Irieguy]

[ QUOTE ]



So to repharse Irieguy's analogy as it applies to SNG (and this is the important point):

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

Irieguy's secondary point:

"Furthermore, the most successful of the 'skilled professional' group will also be beneficiaries of randomness to a much larger degree than they would like to admit" is worth remembering too (and has Daniel Negreanu's name all over it, for one).

[/ QUOTE ]

Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

[jcm4ccc]

[ QUOTE ]

Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

[/ QUOTE ]

I think the vast majority of people on this forum are quite intelligent and can understand arguments and analogies when they are presented well. Is your argument "invisible to most" because the message is obscure or the messenger is obscure?

[Dr_Jeckyl_00]

[ QUOTE ]
[ QUOTE ]

Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

[/ QUOTE ]

I think the vast majority of people on this forum are quite intelligent and can understand arguments and analogies when they are presented well. Is your argument "invisible to most" because the message is obscure or the messenger is obscure?

[/ QUOTE ]

I have to admit I am confused by OP's message. Sounds like he is saying if you're profitable, it is most likely due to randomness and nothing to do with skill... I think we all agree that no matter how good your hand is, it can be beaten (except for one hand) but when you play correctly, your hand will be beaten less often then when you play poorly. So randomness affects all of us, but if affects certain people less because they take steps to mitigate the effects of randomness... Is this what OP is saying???

[SumZero]

I think what you want to do is treat it similar to a maximum likelihood calculation. But rather than merely solving for p-hat you solve for what is the probability that p is > 0.

So basically you need to have the distribution of the population (not just the number below 0, although you could guess that it might be scew-normal centered on a -rake ROI and set the sd based on your number below 0 who are losers) and then for every point (say X ROI) on the distribution curve multiply the probability that someone random is this quality by the probability that they could produce the observed behavior given they are of that X ROI [really you want to do this for the continuous population density function, but with computers you can approximate it by testing discrete points, say every 0.1% ROI from say -50% ROI to 40% ROI). Then at the end you will have a new distribution and can see what percentage of the distribution (area under the new curve) is above 0.

[SumZero]

I agree that you are better off when you take the deeper numbers into account (I.e., if you can get a better model for you distribution than "random player" you should take it). But in my example I meant that someone ELSE had done the heavy lifting. And that Player X was a 2+2 noob who was making his first post after playing his first 500 SNG and having found the conventional wisdom of the confidence interval from someone else. You are right that this still doesn't make him a total random player because he's at least searching about poker or thinking about his game as he found 2+2 and he is also tracking his results to know how well he did after 500 SNG, but still he is closer to the random player than most people's math leave. (Perhaps the biggest flaw in my assumption is that a noob would wait even 500 SNG before talking about their ROI). /images/graemlins/smile.gif

[Slim Pickens]

[ QUOTE ]
Newton said for every action there is a reaction. He broke things down into a measurable, predictable, mechanical science. Individualism and Western Society developed out of these sorts of ideas (or something). We're comfortable with these concepts.

Screw Quantum Physics. Heisenberg is full of sh-t, God does not play dice (One of greatest f-ing quotes of all-time BTW). If I average 6 BB/100 for 2,000 hands of limit poker or a 40% ITM for 100 higher level SNGs, I am a genius brilliant player.

If I go on a horrid losing streak, internet poker is rigged, and when I go another another heater it is because the "Party rigging switch" has been flipped back to off, and everything is right in the universe...

[/ QUOTE ]

I like this quote from Terry Pratchett

"God does not play dice with the universe. He plays an ineffable game of His own devising, which might be compared, from the perspective of any of the other players [i.e. everybody], to being involved in an obscure and complex variant of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won't tell you the rules, and who smiles all the time."

[Slim Pickens]

[ QUOTE ]
(I.e., if you can get a better model for you distribution than "random player" you should take it)

[/ QUOTE ]

This information is the magic key for SNG simulation. If I had access to Party's servers for one hour, the second thing I'd take is all their player results data (after the RNG seed). I've decided not to attempt any more of this simulation nonsense until this information is available. If we could figure out Poker Prophecy, that would be good enough.

SlimP

[gumpzilla]

[ QUOTE ]
If I had access to Party's servers for one hour, the second thing I'd take is all their player results data (after the RNG seed).

[/ QUOTE ]

The second thing is probably more valuable to you than the seed, considering that if Party does it like most of the other places, any seed you pick up is going to be antiquated quite quickly within a matter of seconds thanks to the mighty entropy stream.

[Irieguy]

[ QUOTE ]
i understand and appreciate your post but i think the idea of seeing significant mistakes your opponents make that you do not continually make allows you to gauge your ability to beat/compete at a certain level just as much as playing 124234 SnGs.

[/ QUOTE ]

I disagree... but not in the way you might think. Statistical analysis of results is a horrible method for evaluating the skill level of a player. It's the method most commonly discussed here, but it's horrible. There are other ways to tell if you, or anybody else, are any good at this game.

Irieguy

[freemoney]

so arent we agreeing in the sense that results after X SnGs regardless how big X is, is not the most effective way to judge an individual?

[Gramps]

[ QUOTE ]
"God does not play dice with the universe. He plays an ineffable game of His own devising, which might be compared, from the perspective of any of the other players [i.e. everybody], to being involved in an obscure and complex variant of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won't tell you the rules, and who smiles all the time."

[/ QUOTE ]

Me likey very much.

Bust that quote out to your average poker player, and see what reaction you get...

[jcm4ccc]

[ QUOTE ]
Statistical analysis of results is a horrible method for evaluating the skill level of a player. It's the method most commonly discussed here, but it's horrible.

[/ QUOTE ]

It's not perfect, but it is the best method. The ROI is without a doubt the best method for evaluating the skill level of a player, just as the won/loss record of a baseball team is the best method for calculating the skill level of a baseball team. I suppose you would look at the way they played the game, rather than their results. I would say that that is ass-backwards.

You have 2 players. They have both played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. I don't have to see one damned hand to know who is better.

[jcm4ccc]

[ QUOTE ]
so arent we agreeing in the sense that results after X SnGs regardless how big X is, is not the most effective way to judge an individual?

[/ QUOTE ] I'm definitely not agreeing. If the sample size is big enough, then ROI is the best method for judging an individual's abilities at SnG (of course, you want to judge them at the same level, etc).

[45suited]

[ QUOTE ]
so arent we agreeing in the sense that results after X SnGs regardless how big X is, is not the most effective way to judge an individual?

[/ QUOTE ]

You guys are bordering on mental masturbation if you really believe this. Kind of like Sklansky always talking about how smart he is (which he obviously is) while trying to belittle the results of players who perform better than him.

Results over the long haul (ROI, bracelets, however you want to keep score using objective criteria) are what matter.

[valenzuela]

[ QUOTE ]


You have 2 players. They have both played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. I don't have to see one damned hand to know who is better.

[/ QUOTE ]
Yes you do.

[jcm4ccc]

[ QUOTE ]
[ QUOTE ]


You have 2 players. They have both played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. I don't have to see one damned hand to know who is better.

[/ QUOTE ]
Yes you do.

[/ QUOTE ]

Really? How many hands would you have to see to convince yourself that the 10% ROI player is better than the 20% ROI player. 1? 2? 10? 100?

What if they played 1000000 SnGs? Would you still need to see how they played to know who is best? Because if your argument is a sample size argument, I'll grant you that 5000 SnGs might not be enough. But somewhere along the line, there would be enough SnGs to tell you who is the better player, SOLELY on the basis of their ROI.

Also, don't forget that our estimation of a person's hand is influenced by what we know about him. Look at Gigabet's posted hands. Anyone else, we would call him a stupid fish. But since we know his success rate, we judge him differently.

[Degen]

i love sucking out

[Slim Pickens]

P(poster who posts Giga-style hand is actually good)=?
P(poster who posts Giga-style hand is actually good given Giga's ROI)=?

Rev. Bayes to the rescue.

[mosdef]

[ QUOTE ]
You have 2 players. They have both played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. I don't have to see one damned hand to know who is better.

[/ QUOTE ]

you're missing the point. all you can do is build a model and then, given the assumptions in your model, calculate a probability that one player is better than the other. you can never say with 100% certainty which player is better unless you subject them both to a controlled test set of identical SNGs and calculate which player performed better in producing a higher expected ROI given what he/she actually did. of course this is impossible to do.

but the statement that a higher ROI over 5000 SNGs absolutely and conclusively PROVES that player A is better than player B is exactly the incorrect reasoning that irie is shooting down. it is just not so.

[45suited]

[ QUOTE ]
You have 2 players. They have both played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. I don't have to see one damned hand to know who is better.

[/ QUOTE ]


--------------------------------------------------------------------------------


[ QUOTE ]
Yes you do.

[/ QUOTE ]

So at what point is someone's results at all meaningful? Has Scott Fischman played enough poker to say he's a winning player based strictly on his results? Doyle Brunson? Anybody?

I guess at the WS they should just go back to the old days and have a vote on who played the best and let you guys vote on it... Come on.

[jcm4ccc]

[ QUOTE ]
the statement that a higher ROI over 5000 SNGs absolutely and conclusively PROVES that player A is better than player B is exactly the incorrect reasoning that irie is shooting down. it is just not so.

[/ QUOTE ]

Of course it doesn't. I was using hyperbole.

So Irieguy makes this obscure statement that statistical analysis is a HORRIBLE method for comparing the skill levels of players. Do you agree? Let's say you have 2 players who have played 5000 SnGs. One has an ROI of 20%. One has an ROI of 10%. You think it is HORRIBLE to use the ROI to make probability statement about their skill levels? Do you have a better (and practical) method for comparing their skill levels, because I'd love to hear it.

[45suited]

[ QUOTE ]
Do you have a better (and practical) method for comparing their skill levels, because I'd love to hear it.

[/ QUOTE ]

Me too

[pokerlaw]

[ QUOTE ]

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)

The second one of my questions (and I think I may be cribbing it from "There Are Two Errors in the the Title of This Book*: A Sourcebook of Philosophical Puzzles, Paradoxes and Problems" by Robert M. Martin which is also a fantastic read) ties directly in to what Irieguy was getting at with the coin-flipping analogy (although coin-flipping is a bad analogy because one really can "flip" coins in an unfair way as often coins don't flip but actually wobble which only looks like flipping and one can practice this). But first the question:

Question 2 (a different flavor of the false positive health test question):
Assume that we are on an Island with 100 taxis. On the Island 95 taxis are yellow and 5 taxis are green on the Island. Police know that eyewitnesses are 80% accurate (that is they will correctly identify the color of a taxi 80% of the time and the other 20% of the time they will say that the taxi was the opposite color from what it was - and that this eroor rate is idependent and unrelated to the actual color of taxi). There is a hit and run involving a taxi. The only eyewitness says that the taxi was green. What is the probability that the taxi involved was actually a green taxi?


[/ QUOTE ]

w/o looking at other answers, here is what i got:

1) If you pay me $11 when double-six hits, i will play your game (can i 2,000 table it?).

2) roughly 17.39% of the time that someone says green, it is a green cab, i think.

[raptor517]

craig when i get to vegas, i expect a brand new copy of this book waiting on the floor where i will be stepped on while reading. np btw. i been waiting for something like this.. holla

[gumpzilla]

Another interesting point to consider is that trying to identify who plays well by how they play is sort of begging the question, in a sense. How so? Well, we need some metric to determine whether a player's play is good or not. If we're not using his results, the best we can do (I think) is see how he matches up against other good players, or some theoretical model. But how do we know that the model is accurate, or that the other good players are actually good, if the only things that we can compare them to are other players or other models? Chains of comparison like this can't go back forever. You ultimately need to ground them in something else, and results seem like the only other thing to me. (There are certainly some hands and plays that will be clear mathematical mistakes, even taken in isolation. But I think these will be quite rare.)

That said, I tend to agree that examining the thought processes of a player is probably going to be a more productive and accurate way to determine their skill than looking at short/middle term results. But, over a very large sample size, I think statistical analysis starts to look pretty good. Which is nice, because it's the whole point of the statistical analysis in the first place.

[The Yugoslavian]

[ QUOTE ]
craig when i get to vegas, i expect <font color="red">some buck nekkid big bootay scrippa scrips</font> waiting on the floor where i will be stepped on while <font color="red">crushing</font>. np btw. i been waiting for something like this.. holla

[/ QUOTE ]

FYP

Yugoslav

[valenzuela]

matt walker already explained why on another thread.
Im jimmy, I saw Sam Farha on TV and he was really cool so I decided to play online poker, on my first 1000 sngs I lost 2000 but then I decided to get better and checked out moneymaker how to beat sngs stuff and I even became a winner player !! After 3000 sngs I was breaking-even( considering my previous losses( jimmy doesnt mention that he was on a heater for the first 500 sngs after reading the moneymaker guide)Then I came to two-plus-two, worked on my game and kicked ass, a nice 25 ROI during 2000 sngs!!!So I ended up with a ROI of 10% after 5000 sngs.
Hi Im andy I came to twoplustwo looking for the WPT forum and by accident ended up on the SNG forum, and I realized that all I had to do is fold early and push late!!! So I tried the thing , my first 1000 sngs I had 5% ROI and I was really disapointed , I just figured it was variance I played another 1000 and ended up with 25 ROI, hahaha now things were right, then I 8 tabled on the 11s and ended up with a total 20% ROI.

[West]

To further clarify:

When the host always offers the switch (whether your initial guess is right or not), it's not 50/50 so long as when your initial guess was wrong, the host always reveals the other wrong door (switching right 2/3 of time).

For it to be 50/50 to switch, when your initial guess is wrong, the procedure would have to be that the host randomly chooses one of the remaining doors to reveal, and if he reveals the prize, then the game always starts over from the beginning.

[mosdef]

[ QUOTE ]
You think it is HORRIBLE to use the ROI to make probability statement about their skill levels? Do you have a better (and practical) method for comparing their skill levels, because I'd love to hear it.

[/ QUOTE ]

no, i don't necessarily think it's HORRIBLE, as irie said. i also don't have a better and practical measure for comparing players. i was only pointing out that your hyperbolic statement was just 100% wrong. i did not intend to infer that irie's murky statements are 100% right.

[SuitedSixes]

So how do we compare ourselves to other poker players? (http://www.carlspackler.com/sounds/030.wav)

I'm 6'1"

[revots33]

[ QUOTE ]
So everybody starts flipping. In the first 9 flips there will be close to 1000 "magic 9ers" from the random population and only 250 or so from the professional group. Clearly, anyone who makes a magic 9 will fancy themselves a professional, so there will be 1250 self-proclaimed professionals with the title of "magic 9er," while only 250 of those people are, in fact, professionals. Oh, and by the way, those 250 professionals are on quite a heater.

[/ QUOTE ]

This is very interesting. I am lousy at statistics so bear with me.

If you carry this analogy further, out of the 1000 random "magic 9ers", there will likely be some tiny number that are "magic 18ers", then perhaps even a miraculous "magic 27er", based purely on the flukes of statistical randomness.

If you follow this out to its conclusion, my question is this: is it possible that a poker player, who SHOULD be an overall loser based on his actual skill level, can play his entire life and still be a winner, based only on the randomness of results? In other words, in isolated cases can randomness account for success, even over a span all would agree constitutes the "long run"?

I've thought about this sometimes as I watch the World Poker Tour. Often, Sexton will start raving about a player's incredible "feel" or "ability to read" when he makes a great call that most players would never make. But how can you know if it's really skill, or randomness that just happened to reward an incorrect play that particular time?

[pokerlaw]

[ QUOTE ]
So how do we compare ourselves to other poker players? (http://www.carlspackler.com/sounds/030.wav)

I'm 6'1"

[/ QUOTE ]

at 6'1" as well, i'm no slouch myself /images/graemlins/smile.gif

[PrayingMantis]

[ QUOTE ]
you can never say with 100% certainty which player is better unless you subject them both to a controlled test set of identical SNGs and calculate which player performed better in producing a higher expected ROI given what he/she actually did. of course this is impossible to do.


[/ QUOTE ]

Yes, well, that's why we use COMMON SENSE. COMMON SENSE is a very helpful tool. I believe you can download it somewhere, I forgot the URL.

Anyway, COMMON SENSE is very helpful when you need to make a reasonable assessment regarding who is a better player, X or Y, when both played, say 1000 SNGs at the same site and level. Of course you can't know that with 100% certainty, but who the hell looks for 100% certainty? in ANY field of life?

So If player X is on 20% ROI, and Y is on 10%, and both give you a different (sincere) advice about a certain hand, who would you listen to? COMMON SENSE tells you you'll listen to player X. A model, or a way of thinking, or a statistical concept, or an idea about randomness, that tells you that you can't be really sure who to listen, is flawed in the most practical, realistic way.

[Rduke55]

So what's the taxi answer?
Is it 76%?

[benfranklin]

[ QUOTE ]


COMMON SENSE is a very helpful tool. I believe you can download it somewhere, I forgot the URL.

[/ QUOTE ]

Common Sense (http://www.ushistory.org/paine/commonsense/)

[pokerlaw]

[ QUOTE ]
So what's the taxi answer?
Is it 76%?

[/ QUOTE ]

I got 17.39%. here's why:

The question asked "There is a hit and run involving a taxi. The only eyewitness says that the taxi was green. What is the probability that the taxi involved was actually a green taxi?"

So, we know that the answer the eyewitness said is green. So how often is "green given?"

Take a RANDOM car crash:

1) 5% of the time it IS a green cab in the accident. 80% of the time it is a green one, someone will say green. So 4% of total accidents will be when a green car hits something and is CORRECTLY identified as a green car (.05*.8 = .04 = 4%).

2) 95% of the time, it IS a yellow cab in the accident. 20% of the time a yellow cab hits something, someone will say green (since 80% of the time, they will correctly say yellow). So 19% of total accidents will be when a yellow cab hits something and is INCORRECTLY identified as a green cab (.95*.20 = .19 = 19%).

SO, we add the two (19+4) and find out that a green cab will be identified in a random accident 23% of the time. of that sample, 4/23 is the ratio of times the eyewitness will be correct and 19/23 is the ratio of times the eyewitness will be incorrect.

Therefore, 4/23, or 17.39%, is the frequency that a green car will be correctly identified.

[SumZero]

recall:

[ QUOTE ]

Question 2 (a different flavor of the false positive health test question):
Assume that we are on an Island with 100 taxis. On the Island 95 taxis are yellow and 5 taxis are green on the Island. Police know that eyewitnesses are 80% accurate (that is they will correctly identify the color of a taxi 80% of the time and the other 20% of the time they will say that the taxi was the opposite color from what it was - and that this eroor rate is idependent and unrelated to the actual color of taxi). There is a hit and run involving a taxi. The only eyewitness says that the taxi was green. What is the probability that the taxi involved was actually a green taxi?


[/ QUOTE ]

The correct answer is:

p(Green|Green said) = 4/(19+4) = 4/23 ~ 17.4%

Consider 100 different instances of the island accident, one with each taxi. And have one eyewitness. In the 5 times there really was a green taxi at fault 4 of them you'll get witness saying "green". In the 95 times there was a yellow taxi at fault you'll get 19 witnesses saying "green". So you'll have 23 different "green" senarios, only 4 of which are true positive green taxis.

[valenzuela]

the taxi answer is 80% do you see why? LOL, i figured the answer myself actually, I never understood what was the other question about.

[PrayingMantis]

This could be maybe a bit more relevant...

Common sense (http://www-formal.stanford.edu/leora/commonsense/)

[Nottom]

Question 1:

Any roll without a 6 is essentially a don't care so we can ignore them.

There are 11 possible rolls with a 6:
1-6, 2-6, 3-6, 4-6, 5-6, 6-5, 6-4, 6-3, 6-2, 6-1 and 6-6
So winning $10 should make this a fair game

Question 2:
I could be off on this, but if you look at a random Taxi you have a 95% chance of it being yellow and 5% chacne of it being green.

Now of the yellow ones, 20% of the time you will think it was green. Of the green ones 80% of the time you will think it was green.

5%(80%) = 4% and 95%(20%) = 19%

So there is a 4/(4+19)= 17.4% chance the taxi was actually green.

(The obvious conclusion even if my math is a little off is that when the chance of error is large compared to the chance that a low frequency event actually took place, the chance that it was an error is quite high)

OK, gonna read the rest of the thead now.

[GrekeHaus]

[ QUOTE ]
Do you have a better (and practical) method for comparing their skill levels, because I'd love to hear it.

[/ QUOTE ]

The method in theory is simple, but in practice is difficult. All you have to do is watch them play and determine which one makes more/bigger mistakes and which one forces their opponent to make more/bigger mistakes.

What makes this difficult to do is that whoever is doing the evaluation of the playing will generally have to be much better than at least one of the players he's evaluating and if the players are very similar, it can be even more difficult (or even impossible) to determine which one is better.

For instance, suppose there's a player who calls or checks everytime it's his turn but never folds or raises. Now if you watch me play and watch this guy play it wouldn't take long for anyone on the forum to identify me as the better player. (Yes, I'm just that good)

Now, suppose you're comparing me to Zen. Most people on this forum would probably not be able to clearly identify him as the better player if the didn't already know. The reason is that they do not know the game well enough to understand the subtle intricacies of what he is doing that makes him a better player than me. Of course, someone like Irie would be able to make this judgement rather quickly.

So to answer your question. Get really good and it will just be obvious.

[mosdef]

[ QUOTE ]
[ QUOTE ]
you can never say with 100% certainty which player is better unless you subject them both to a controlled test set of identical SNGs and calculate which player performed better in producing a higher expected ROI given what he/she actually did. of course this is impossible to do.


[/ QUOTE ]

Yes, well, that's why we use COMMON SENSE. COMMON SENSE is a very helpful tool. I believe you can download it somewhere, I forgot the URL.

Anyway, COMMON SENSE is very helpful when you need to make a reasonable assessment regarding who is a better player, X or Y, when both played, say 1000 SNGs at the same site and level. Of course you can't know that with 100% certainty, but who the hell looks for 100% certainty? in ANY field of life?

So If player X is on 20% ROI, and Y is on 10%, and both give you a different (sincere) advice about a certain hand, who would you listen to? COMMON SENSE tells you you'll listen to player X. A model, or a way of thinking, or a statistical concept, or an idea about randomness, that tells you that you can't be really sure who to listen, is flawed in the most practical, realistic way.

[/ QUOTE ]

i know. i didn't say you need to be 100% certain. but the poster in front of me said that if someone has a 20% ROI and someone else has a 10% ROI then the 20% ROI guy is a better player, end of story, there's nothing else to be said. I replied saying that this is incorrect. and it is incorrect. i didn't say anything else.

and if a person with a 10% ROI and a person with a 20% ROI are giving you advice, don't you want to listen to both and decide which person makes more sense? don't you want to know what the probability is that the 20% really is better than the 10% guy? COMMON SENSE, my friend, tells you that it is more likely that the 20% ROI is correct if the two have differing opinions, but there are degrees of likelihood.

[skipperbob]

[ QUOTE ]
Now, suppose you're comparing me to Zen. Most people on this forum would probably not be able to clearly identify him as the better player if the didn't already know

[/ QUOTE ]

Have you no shame Greke?...Just admit you made a bad bid on Zen &amp; are praying somebody more stupid will take you off /images/graemlins/confused.gif

[gumpzilla]

[ QUOTE ]

The method in theory is simple, but in practice is difficult. All you have to do is watch them play and determine which one makes more/bigger mistakes and which one forces their opponent to make more/bigger mistakes.

[/ QUOTE ]

What's your metric for determining what is or isn't a mistake?

[PrayingMantis]

[ QUOTE ]
and if a person with a 10% ROI and a person with a 20% ROI are giving you advice, don't you want to listen to both and decide which person makes more sense?

[/ QUOTE ]

Of course I'd like to listen to both, but that doesn't have much to do with it. I also like to listen to complete fish with -65% ROI, you can learn a lot from them and from how they view this game. And I'm very serious.

But the more interesting question is, what exactly do you mean by "makes more sense"? Did giga's "blocks" post make any sense? I, quite like the huge majority of people here, know actually very little about how giga is playing. However, we know A LOT about how he is doing, his results, his stats. My point here is obvious, I think.

[ QUOTE ]
don't you want to know what the probability is that the 20% really is better than the 10% guy?

[/ QUOTE ]

Well, of course I'd like to know. But this doesn't change the essense of what I'm saying here.

[ QUOTE ]
COMMON SENSE, my friend, tells you that it is more likely that the 20% ROI is correct if the two have differing opinions, but there are degrees of likelihood.

[/ QUOTE ]

Surely I'm not disagreeing with you about the existence of degrees of likelihood. But when you have to act, and by acting I mean making a decision at the poker table, or judging who's the better player (let's say "betting on who's the better player", and by that, listening to HIS advice), you'll too often be wrong/paralysed if you sit and wait for your "confidence level" to get to a high enough spot, where-ever it is.

[GrekeHaus]

[ QUOTE ]
[ QUOTE ]
Now, suppose you're comparing me to Zen. Most people on this forum would probably not be able to clearly identify him as the better player if the didn't already know

[/ QUOTE ]

Have you no shame Greke?...Just admit you made a bad bid on Zen &amp; are praying somebody more stupid will take you off /images/graemlins/confused.gif

[/ QUOTE ]

Shut up Skipper...you're blowing my cover. /images/graemlins/wink.gif

[GrekeHaus]

[ QUOTE ]
[ QUOTE ]

The method in theory is simple, but in practice is difficult. All you have to do is watch them play and determine which one makes more/bigger mistakes and which one forces their opponent to make more/bigger mistakes.

[/ QUOTE ]

What's your metric for determining what is or isn't a mistake?

[/ QUOTE ]

You can easily analyze what is and what isn't a mistake if you know the hole cards of both people and by just doing the math. There's nothing fancy about it, just simple arithmetic.

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

The method in theory is simple, but in practice is difficult. All you have to do is watch them play and determine which one makes more/bigger mistakes and which one forces their opponent to make more/bigger mistakes.

[/ QUOTE ]

What's your metric for determining what is or isn't a mistake?

[/ QUOTE ]

You can easily analyze what is and what isn't a mistake if you know the hole cards of both people and by just doing the math. There's nothing fancy about it, just simple arithmetic.

[/ QUOTE ]

Have you been taking those magical 'Sklansky pills' I warned you about. This sounds straight outta TOP, how dare you!!! Let's call the metric Sklansky $, every heard of that?

Obviously COMMON SENSE is useless....for going over HHs or going over stats.

Since it's all 'bout the chedda, COMMON SENSE, is such a relative term that very few really possesses it (myself included) or are even on the right path.

Oh, and yes, Zen is way better than you....No0B!

Yugoslav
<font color="white"> Thankfully we can all tell a smokin' 100% BeefCakey approved big booty buk nekkkkid scrippalillla, ship it batches!?!?!?!</font>

[gumpzilla]

[ QUOTE ]

You can easily analyze what is and what isn't a mistake if you know the hole cards of both people and by just doing the math. There's nothing fancy about it, just simple arithmetic.

[/ QUOTE ]

Knowing the hole cards of both people is not representative of actual poker situations. It's obviously not a mistake when I open push KK from the button with 5 BBs PF and the BB turns over AA. So this isn't right.

Also, while I think mistakes are probably easier to identify in cash games from a purely mathematical standpoint, in a tournament I think the story is somewhat different. Some kind of model of tournament equity is needed if you want to come up with a mathematically clear exposition of what is and isn't a mistake. And how do we justify it? If the answer is to match up with what good players think of it - which is pretty much why ICM is used, if I understand correctly - then we're back in the same kind of circular argument that I mentioned earlier in the thread.

[PrayingMantis]

[ QUOTE ]
Obviously COMMON SENSE is useless....for going over HHs or going over stats.

Since it's all 'bout the chedda, COMMON SENSE, is such a relative term that very few really possesses it (myself included) or are even on the right path.

[/ QUOTE ]

Yes, there are many subtle decision for which mere COMMON SENSE is not very useful, I agree. That's part of the reason why people read and post here. However, my COMMON SENSE comment was in regard to the ability to judge who is a better player, a 10% or a 20% ROI player, who have both played what you might call a "reasonable sample" of SNGs (we can argue what reasonable is, of course), at the same levels and conditions. If you say something like "you just can't tell, stats are only stats, there's randomness, variance, hot runs, cold runs, blah blah", then you really really need some immidiate update of your COMMON SENSE tool. /images/graemlins/grin.gif

[GrekeHaus]

[ QUOTE ]
Oh, and yes, Zen is way better than you....No0B!

[/ QUOTE ]

Didn't I already make this clear? I just said that most people here wouldn't be able to make the distinction.

And don't call me a noob. Just look at the reged dates, I've been around longer than you [censored]!

[GrekeHaus]

[ QUOTE ]
Knowing the hole cards of both people is not representative of actual poker situations. It's obviously not a mistake when I open push KK from the button with 5 BBs PF and the BB turns over AA. So this isn't right.

[/ QUOTE ]

If you knew your opponent had AA, would you have open pushed here? Of course not, so it's a mistake. Just because it's a mistake that everybody would make doesn't mean it's not a mistake.

[SumZero]

Nottom explained them both pretty well but the first question was:

[ QUOTE ]
Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)

[/ QUOTE ]

So the idea is that you roll two dice until one of them is a 6. If you ask most people what are the chances that you rolled double sixes when you stop, in my experience, the vast majority say 1/6. This would be the right answer if what you did was have two dice, a red and a green, and you kept rolling both dice until the red one had a 6 on it. Now there are six possible outcomes (green 1, green 2, green 3, green 4, green 5, or green 6). But the question was until either dice has a six on it. If you make a 6 by 6 grid with the possible dice outcomes you'll have all 36 possible rolls. And you'll see that 11 of them involve one of the dice having a 6 in it and only 1 is double 6 so the chance that means the probability of winning the game is only 1/11. If you offered to pay people 8 to 1 for when they win (end on double sixes) most people would be willing to play the game and you'd be very +EV to play them.

Bonus question for reasoning:

Consider two players Alice and Bob. They are going to play a fair coin flipping game. But instead of one winning on heads and the other on tails they decide to add drama and win only if they get their triplet of result first. Bob chooses to win if he gets THH. Alice chooses to win if she gets HTH. They keep flipping until one of them wins.

I.e.,

If they flipped TTTHH then Bob would win [because TTT is no one's, TTH is no one's, but THH is Bob's]. If they flipped HHTH then Alice would win. Are Alice and Bob playing a fair game?

[gumpzilla]

[ QUOTE ]

If you knew your opponent had AA, would you have open pushed here? Of course not, so it's a mistake. Just because it's a mistake that everybody would make doesn't mean it's not a mistake.

[/ QUOTE ]

No, it's not a mistake, any more than it's a mistake when you get your money in with your opponent holding QQ and they flop a Q. This is exactly the wrong kind of results-oriented to be.

I think what you mean is that it is a mistake according to Sklansky's Fundamental Theorem of Poker. But that doesn't mean that it's an incorrect play - or are you suggesting folding KK PF when it has been folded to you is correct? Also, I don't believe that the Fundamental Theorem applies to tournament play very cleanly, because there are many situations where your opponent can make a mistake according to the Fundamental Theorem but you still lose equity by having them call you. Bubble play is full of situations like this.

[SuitedSixes]

FIRE!

[johnnybeef]

[ QUOTE ]
FIRE!

[/ QUOTE ]

Is that you Bevis?

[SuitedSixes]

[ QUOTE ]
[ QUOTE ]
FIRE!

[/ QUOTE ]

Is that you Bevis?

[/ QUOTE ]

No, Butthead, it's not.

[johnnybeef]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
FIRE!

[/ QUOTE ]

Is that you Bevis?

[/ QUOTE ]

No, Butthead, it's not.

[/ QUOTE ]

huh huh huh huh.......cool

[SuitedSixes]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
FIRE!

[/ QUOTE ]

Is that you Bevis?

[/ QUOTE ]

No, Butthead, it's not.

[/ QUOTE ]



huh huh huh huh.......cool

[/ QUOTE ] http://htomc.dns2go.com/anim/anim/bevbutt2.gif

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]

If you knew your opponent had AA, would you have open pushed here? Of course not, so it's a mistake. Just because it's a mistake that everybody would make doesn't mean it's not a mistake.

[/ QUOTE ]

No, it's not a mistake, any more than it's a mistake when you get your money in with your opponent holding QQ and they flop a Q. This is exactly the wrong kind of results-oriented to be.

I think what you mean is that it is a mistake according to Sklansky's Fundamental Theorem of Poker. But that doesn't mean that it's an incorrect play - or are you suggesting folding KK PF when it has been folded to you is correct? Also, I don't believe that the Fundamental Theorem applies to tournament play very cleanly, because there are many situations where your opponent can make a mistake according to the Fundamental Theorem but you still lose equity by having them call you. Bubble play is full of situations like this.

[/ QUOTE ]

There can be different kinds of mistakes depending on context. It certainly is one kind of mistake to not realize this, /images/graemlins/shocked.gif.

I believe you understand GrekeHaus but for some reason are interested in focusing on how he could incorrectly be using a term ('mistake') rather than making your focal point that Fundamental Theorem type thinking can't apply to STTs well.

On that subject, while the Theorem doesn't apply directly to tournament play, I'm not really sure how you can't mathematically tell who is making better decisions if you have a certain number of HHs and can see everyone's hole cards. It will be trickier, perhaps, than for a limit ring game, but it should still work.

Yugoslav

[gumpzilla]

[ QUOTE ]

I'm not really sure how you can't mathematically tell who is making better decisions if you have a certain number of HHs and can see everyone's hole cards. It will be trickier, perhaps, than for a limit ring game, but it should still work.

[/ QUOTE ]

a) Even in this instance, how do you propose to do this? Are you aware of a mathematically provably correct way of moving from tournament standings to equity?

b) You guys appear to be talking about a kind of mistake that is not particularly relevant to the context of determining who plays well, which was what this thread and discussion was about, which is why I'm harping on it. We'll all agree that correct SNG play involves substantial amounts of PF pushing late, frequently with any two in the right situations. Yet you guys are saying that it we can determine mistakes from a hand history if I push and my opponent happens to pick up AA. This isn't a mistake, it's bad luck.

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]

I'm not really sure how you can't mathematically tell who is making better decisions if you have a certain number of HHs and can see everyone's hole cards. It will be trickier, perhaps, than for a limit ring game, but it should still work.

[/ QUOTE ]

a) Even in this instance, how do you propose to do this? Are you aware of a mathematically provably correct way of moving from tournament standings to equity?

b) You guys appear to be talking about a kind of mistake that is not particularly relevant to the context of determining who plays well, which was what this thread and discussion was about, which is why I'm harping on it. We'll all agree that correct SNG play involves substantial amounts of PF pushing late, frequently with any two in the right situations. Yet you guys are saying that it we can determine mistakes from a hand history if I push and my opponent happens to pick up AA. This isn't a mistake, it's bad luck.

[/ QUOTE ]

Btw...this thread didn't start out being about making good plays. However, the OP has written like a bajillion other posts on that topic.

What you're saying applies to cash games too...so I'm not really sure what your point is. I don't see how you can't do for tournaments what you can do for ring games via FTOP. The idea is that one can play perfectly if seeing everyone's hole cards. While the best tournament strategy varies very differently from how you'd play if you could literally see everyone's hole cards, so do ring games. Also, in both structures one may even choose to make a 'bad' play even if seeing his/her opponent's hole cards due to metagame reasons....practically speaking, you are playing against imperfect players and so you must take their imperfections into account in your decisions. So if you're saying that the fundamental theorem is largely correct but not always...well, ok. Greke most likely will agree that practically there are situations one should abandon a strictly mathematical calculation based on perfect information, due to external imperfect information.

However, with perfect information, ring game and STT decisions both can be reduced to relatively simple math....which I think is what Greke is trying to say.

Yugoslav

[gumpzilla]

[ QUOTE ]

Btw...this thread didn't start out being about making good plays. However, the OP has written like a bajillion other posts on that topic.

[/ QUOTE ]

This is true, but it has spawned a lengthy subdiscussion on how to identify good players if you believe that statistical analysis of results is "horrible."

[ QUOTE ]
I don't see how you can't do for tournaments what you can do for ring games via FTOP.

[/ QUOTE ]

Villain pushes an 8 BB stack from MP. It's folded to you in the BB with AdKd. Villain accidentally shows you that he's holding two black sixes. You're getting 9.5:7 (or better) odds to call, and you're a 52:48 dog. In a cash game, this is clearly a correct call with no further information. However, in a tournament situation, there are so many other variables to consider: how close are we to payout? How big is my stack? How big is everybody else's stack? Are the blinds going up soon? etc. Now how do we take these variables into account?

The point is that the $ EV in a tournament is much more fundamentally linked to the situation of everybody else at the table and to what those situations will be like in the future than in a cash game. This is the same reason why the Fundamental Theorem doesn't really work in a tournament; even when there are only two of you in a pot, equity can be transferred to players other than yourselves.

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]

Btw...this thread didn't start out being about making good plays. However, the OP has written like a bajillion other posts on that topic.

[/ QUOTE ]

This is true, but it has spawned a lengthy subdiscussion on how to identify good players if you believe that statistical analysis of results is "horrible."

[ QUOTE ]
I don't see how you can't do for tournaments what you can do for ring games via FTOP.

[/ QUOTE ]

Villain pushes an 8 BB stack from MP. It's folded to you in the BB with AdKd. Villain accidentally shows you that he's holding two black sixes. You're getting 9.5:7 (or better) odds to call, and you're a 52:48 dog. In a cash game, this is clearly a correct call with no further information. However, in a tournament situation, there are so many other variables to consider: how close are we to payout? How big is my stack? How big is everybody else's stack? Are the blinds going up soon? etc. Now how do we take these variables into account?

The point is that the $ EV in a tournament is much more fundamentally linked to the situation of everybody else at the table and to what those situations will be like in the future than in a cash game. This is the same reason why the Fundamental Theorem doesn't really work in a tournament; even when there are only two of you in a pot, equity can be transferred to players other than yourselves.

[/ QUOTE ]

Ah yes, this is the type of post I was hoping for.

I agree wholeheartedly. One would have to adopt an equity model to do these strict calculations...ICM should work very, very well here (especially if a few short stack/position relative to blinds scenarios are optimized). And I think doing this calculation with perfect information would show exactly who is better. I don't think we'd get weird situations where we decided a worse player was better than a superior player.

Yugoslav

[gumpzilla]

[ QUOTE ]

I agree wholeheartedly. One would have to adopt an equity model to do these strict calculations...ICM should work very, very well here

[/ QUOTE ]

Now this is where my argument is. I agree that ICM probably does work very well here. That said, what is our justification for using ICM? We do not have proof that the results of ICM correspond to true tournament equity, and I think it's actually pretty obvious that it can't, since it leaves out so much information.

That said, most 2+2 STT regulars will agree that we should trust ICM. Why? Because it seems to mesh well with the advice of good, respected players. Why do we think those players are good? Because they win, ultimately. My argument is that if one says a good method for figuring out who is good at tournaments is to see how many mistakes they make, you need to talk about mistakes compared to what. And whether it's another good player or a mathematical model, it ultimately needs to be grounded in winning. I don't really see how you can talk about a player as being good if they are a long-term loser.

Irie's original point - that given large populations, even over pretty long stretches you'll find people who aren't so great doing well - is a good one, and is the reason why people make so much noise about sample size for looking at your ROI. But to go from there to saying that "statistical analysis of results is a horrible method of evaluating the skill level of a player" is a stretch, in my opinion. Practically, looking at their game and seeing how they play will be a faster method, but that's only because we have people whose opinions on how to play tend to be backed up by results, i.e. winning. And combining the two - looking at thought processes while getting some kind of short/middle-term statistical information - is better still, in my opinion.

EDIT: I also still think that the perfect information stipulation is kind of bogus. We don't have that kind of information in a game, and it's definitely possible to make moves that look correct from that standpoint that are wrong according to what we were thinking in a game, and vice versa. For an obviously extreme example of what I'm talking about, say I raise with JJ PF and somebody pushes over me, leaving me with 3:2 odds. Let's say that I put them on QQ-AA, AK. Calling here if I put them on that range is pretty bad, but let's say I do it anyway and they turn over 83. I've made a pretty gross series of mistakes - putting them on a range that is way too tight, calling against a range I shouldn't - but in Perfect Information land I look like a genius.

[GrekeHaus]

[ QUOTE ]
Now this is where my argument is. I agree that ICM probably does work very well here. That said, what is our justification for using ICM? We do not have proof that the results of ICM correspond to true tournament equity, and I think it's actually pretty obvious that it can't, since it leaves out so much information.

That said, most 2+2 STT regulars will agree that we should trust ICM. Why? Because it seems to mesh well with the advice of good, respected players. Why do we think those players are good? Because they win, ultimately.

[/ QUOTE ]

The reason people trust ICM is because of it's base in a solid mathematical foundation. It starts with the assumption that if two players of equal skill are heads up, each person's chance of winning is in direct correlation with the number of chips he has (an assumption that has recently been challenged but is probably relatively accurate). From there, we are able to calculate the approximate percentage of times that each players will finish in each position and hence, determine his expect percentage of the prize pool. Its limitations seem to lie in the fact that it doesn't account for differences in skill level or strategical advantages gained or lost by having a chip stack of different sizes. For something like SNGs however, this model seems to be relatively accurate and a good general indicator of whether or not you should call or raise in a given situation. Mason Malmuth gives an example of how to do a simple version of these calculations in Gambling Theory and Other Topics.

[ QUOTE ]
EDIT: I also still think that the perfect information stipulation is kind of bogus. We don't have that kind of information in a game, and it's definitely possible to make moves that look correct from that standpoint that are wrong according to what we were thinking in a game, and vice versa. For an obviously extreme example of what I'm talking about, say I raise with JJ PF and somebody pushes over me, leaving me with 3:2 odds. Let's say that I put them on QQ-AA, AK. Calling here if I put them on that range is pretty bad, but let's say I do it anyway and they turn over 83. I've made a pretty gross series of mistakes - putting them on a range that is way too tight, calling against a range I shouldn't - but in Perfect Information land I look like a genius.

[/ QUOTE ]

The point you seem to be making has to do with a strategical notion of mistake rather than a mathematical one. A sound strategy in any poker game is one that will minimize your own mathematical mistakes while maximizing your opponents mathematical mistakes.

In the example where you have KK UTG and you open push 5xBB. You know at the moment you push that you're making a mathematical mistake if any of your opponents hold AA. However, you are making the correct play in all other circumstances, so you're willing to live with the shortcoming of your strategy because you know that its pros outweight its cons much more than in a strategy where for instance you open fold KK every time you get it.

In the above example you give, your opponent is trying to make a mistake by raising which will force you to make a bigger mistake by folding the best hand most of the time. Of course, if you actually do fold here and your opponent flips over 83o, then you realize that there was a shortcoming in your strategy because of the fact that you failed to accurately assess the situation. Of course, if you feel that your opponent will only make a play like this every million hands and the rest of the time he actually will have AK or QQ+, then your strategy is fine. If he's making this play half the time, your strategy is terrible because it is forcing you to make mathematical blunder after mathematical blunder.

Even if you're going to talk about the strategical notion of a mistake, it still all comes down to math.

[gumpzilla]

[ QUOTE ]
For something like SNGs however, this model seems to be relatively accurate

[/ QUOTE ]

I think that this statement implicity suggests "because it suggests winning play," which ties in with results again. There are mathematical underpinnings for ICM, but it is an approximation and much more open to question than doing similar calculations in cash games, obviously.

[ QUOTE ]
The point you seem to be making has to do with a strategical notion of mistake rather than a mathematical one.

[/ QUOTE ]

Well, yes, because strategical mistakes are what's relevant to determining whether or not you're playing well.

Expanding the math further in the KK example, when you take into account how rarely he'll have AA, it becomes clear that it would be a mathematical mistake not to push. I dislike using the term mistake to mean "he turned over AA" and the like because it suggests that the play was wrong. If you push with KK in that situation, you're not making a mathematical mistake - you're theoretically gaining x BB, occasionally winning more and occasionally losing to AA, but on average there's some gain.

[The Yugoslavian]

[ QUOTE ]

I don't really see how you can talk about a player as being good if they are a long-term loser.


[/ QUOTE ]

If they are making profitable decisions..then yes, they'd still be a good player.

Some of the players who actually have very good stats will have a much different skill level. So, some of these players will actually be good, some will be ok, and a few will actually be bad. This is just the beginning of the problem when interpreting posted stats....I have no beef with the stats themselves (even though it may seem like I do sometimes), they just are what they are. However, I find that the ones public on this forum are *very* problematic, to the point of actually being close to worthless.

I'd much rather look at HHs from players in order to gauge their skill level than look at a snapshot of their stats.

Yugoslav

[gumpzilla]

[ QUOTE ]

If they are making profitable decisions..then yes, they'd still be a good player.

[/ QUOTE ]

Profitable decisions will eventually correspond to results, if you play long enough (otherwise how are we showing profit?). Obviously luck is a huge factor, and it takes a while, but if you play 5000 SNGs and are at an ROI of -20%, the odds of you actually being a winning/good player are very, very poor. At the very least your game selection would need some work.

[GrekeHaus]

[ QUOTE ]
[ QUOTE ]

If they are making profitable decisions..then yes, they'd still be a good player.

[/ QUOTE ]

Profitable decisions will eventually correspond to results, if you play long enough (otherwise how are we showing profit?). Obviously luck is a huge factor, and it takes a while, but if you play 5000 SNGs and are at an ROI of -20%, the odds of you actually being a winning/good player are very, very poor. At the very least your game selection would need some work.

[/ QUOTE ]

Right. This is at the heart of what Irie and Yugo are trying to get at. It's highly unlikely that a player with a -20% ROI after 5,000 SNGs is a winning player. However, when was the last time you read a post saying "Here are the results for my last 5,000 SNGs"?

Of course, part of the problem with assessing your play based on statistics is that you will very rarely have a large enough sample size to do so. Even if you do, a sample size that large will take a while to accumulate. During that time, the players in your game will be changing and your game might be improving or degenerating. So even if you have an ROI of 20% after your first 5,000 SNGs, it doesn't mean that you're currently playing at a 20% ROI clip or even that you're currently playing winning poker.

[gumpzilla]

[ QUOTE ]

Right. This is at the heart of what Irie and Yugo are trying to get at. It's highly unlikely that a player with a -20% ROI after 5,000 SNGs is a winning player. However, when was the last time you read a post saying "Here are the results for my last 5,000 SNGs"?

[/ QUOTE ]

You don't see those, no. But, then again, how often do you see people who haven't already established themselves as good players get a favorable response to "Here's my ROI after 500 SNGs"? I think people are generally reasonably aware of the sample size issue when dealing with unknowns.

[PrayingMantis]

[ QUOTE ]
I'd much rather look at HHs from players in order to gauge their skill level than look at a snapshot of their stats.

[/ QUOTE ]

I agree completely. But that doesn't minimize the significance of the data one can find in _big_ sample size stats (results, that is).

Anyway, I think it is a very interesting theroetical discussion, that is getting to different paths from the issues discussed in the OP. It has a lot to do with the big question of being / not being "results oriented": we hate and despise "results oriented" thinking in this game, but we just can't ignore the fact that "results oriented" thinking has still a lot to do with the ability of any player to learn and improve. So it's kind of a paradox, that I'm always thinking about.

[The Yugoslavian]

[ QUOTE ]

I agree completely. But that doesn't minimize the significance of the data one can fine in _big_ sample size stats (results, that is).

[/ QUOTE ]

Yeah, I just don't trust almost any of the stats posted on this site in measuring a player's ability. It's very hard for me to look at posted statistical results as a useful guideline in any way. I'd rather look at HHs.

I definitely agree that having a fairly large to large data sample is a good thing. This is why I'm finally back to keeping my STT stats. /images/graemlins/wink.gif. Besides, I believe I got everything I could out of not keeping stats. It wasn't the true obstacle of my growth as a poker player.

Yugoslav

[Moonsugar]

Read the book a few years ago. It is good.

As long as you are reading financial books, there are some books by behavioral economists that will blow away (or confirm) your ideas on the average person's risk acceptance v. risk aversion. News flash: People are dumb! Thaler, et. al.

[Wacken]

science is not sure yet about randomness.

If you flip a coin, it is influenced by many factors that will decide what it ends up like. All those factors are also influenced by other factors. Etc.
All those things not random at all /images/graemlins/smile.gif

However, if we have one atom of a substance with a half value time of 10 minutes, what will have happened to that atom after 10 minutes? We don't know if this is random or not.

Not that this all is very important, but for this very reason i do not at all discard the idea that everything might be predetermined and nothing random at all. And i am not religious or otherwise supersticious at all.

[jgunnip]

BUMP

[ QUOTE ]
Bonus question for reasoning:

Consider two players Alice and Bob. They are going to play a fair coin flipping game. But instead of one winning on heads and the other on tails they decide to add drama and win only if they get their triplet of result first. Bob chooses to win if he gets THH. Alice chooses to win if she gets HTH. They keep flipping until one of them wins.

I.e.,

If they flipped TTTHH then Bob would win . If they flipped HHTH then Alice would win. Are Alice and Bob playing a fair game?


[/ QUOTE ]

Alice and Bob would be playing a fair game IF each separate game constituted three flips of the coin. However, in this particular game where they play until one person wins, and then start over and play again, Bob is at a disadvantage because unless the first flop is T his needed sequence of coin flips to win is actually T[b]THH because when the flop is HTHH, Alice of course wins with HTHH.

[bearly]

a couple points: para 1) who is 'science'? para 2. i imagine it's shape will be called 'pretty worn out' at the end. para 3) you could say this about anything, ie. why is the football player still sitting on the bench, and where will he be 10 mins from now? para 4) little work on the spelling here. now to the meat, i believe this to be one of the finest of irie's or anyone else's posts. wish it could be stickied for a week......h

[tjh]

I think that the hidden gem of insight that I get from this post is that.

People believe in strange unscientific things. Given the effects of "random" events in poker, other players can do and will continue to do stupid things.

Using the power of science and reason we can play better than these folks. In the long run we will make money. In the short term we can also be fooled by random events.

I disagree with the opinion that results are meaningless.
One SNG is significant, and means more than 0 sng's. The more you play the more significant your results become.

I also disagree that a "good" player can watch a game and decide who is playing well and who isn't. We are playing a game of incomplete information against highly unpredictable opponents. There is no "one correct way" to beat SNG's. Aggression is good but can be dangerous, tighness is good but can be overdone. TAG is supposedly the best but within that there are various playing styles.

As for Daniel Negreaneu (sp?) being lucky and not talented... I don't know. Surely his style of play might not work at our level but at other levels it just might. Also the highly publicized plays of his may or may not being indicitave of his playing style overall. Each game has different weaknesses that we can take advantage of.

In my opinion results do matter. It may not be a perfect measure but it is a close as we can get.



--
tjh

[bearly]

hi. i think these will prove to be very prescient observations, both by irie and eastbay. i wish they would take a moment and expound further. i know i could pm them but i feel this material is very important for all those who are studying sngs in particular and on-line poker in general; especially as it relates to the profit possibilities of both. tia guys...........h

[AliasMrJones]

[ QUOTE ]
The reason people trust ICM is because of it's base in a solid mathematical foundation. It starts with the assumption that if two players of equal skill are heads up, each person's chance of winning is in direct correlation with the number of chips he has (an assumption that has recently been challenged but is probably relatively accurate). From there, we are able to calculate the approximate percentage of times that each players will finish in each position and hence, determine his expect percentage of the prize pool. Its limitations seem to lie in the fact that it doesn't account for differences in skill level or strategical advantages gained or lost by having a chip stack of different sizes. For something like SNGs however, this model seems to be relatively accurate and a good general indicator of whether or not you should call or raise in a given situation. Mason Malmuth gives an example of how to do a simple version of these calculations in Gambling Theory and Other Topics.

[/ QUOTE ]

This isn't entirely true. A chip equity=prize money equity model also starts with the above assumption. We don't use a chip equity model, however, we use ICM which is a chip-as-lottery-ticket model.

Back to the original Irie post. It seems to me to be a restatement of a previous post in which he talked about reviewing the results of many players, max long-term attainable ROI, etc. and basically said that most players on the forum aren't as good as they think they are because it takes so long to play enough SnG's to get any kind of precision/confidence interval. Plus self-reporting/selective memory... If you think about how few major tournaments there are every year and then think about how much stock people put into who won the WSOPME this year or who won 3 WPT events you're starting to get the picture.

[AliasMrJones]

[ QUOTE ]
I think that the hidden gem of insight that I get from this post is that.

People believe in strange unscientific things. Given the effects of "random" events in poker, other players can do and will continue to do stupid things.

I disagree with the opinion that results are meaningless.
One SNG is significant, and means more than 0 sng's. The more you play the more significant your results become.


[/ QUOTE ]

I think you're missing the real point of his post. The fact that poker often rewards mistakes and thus will encourage many players who don't understand this to make bad plays that good players can take advantage of is fairly well understood.

What isn't is to what extreme randomness-caused variance can play a role in what many people think is somewhat long-term. Unless you're a pro multi-tabling full time it maight take 10 years to get enough games under your belt to be able to say that you are a very good player. Yet virtually noone has played that long because internet SnG's haven't been around (or at least played by very many people) for long enough. So -- if you're not a full-time multi-tabler, you might never really know if you're any good. And, those pros you hear about all the time, have a fair chance of not being nearly as good as is generally accepted. Yet, people on the forum often take as gospel things put forward people because viewed as "long term winners."

[rydazzle]

This thread has left me with a nagging question:

1) Can a poker hand be characterized by random variables?

Wait, take a second to think about that. Consider bluffs, varying styles, human error and emotion, number of players, chance of seeing all cards on the board, etc, etc, etc.

Suppose yes: there should be some "normal" variance based on the combination of these random variables. How would our variance relate to this "normal" variance? What would it mean to have a variance above or below "normal"; would that reflect skill levels? Does this suggest the smaller the variance the better the player?

[GrekeHaus]

[ QUOTE ]
This thread has left me with a nagging question:

1) Can a poker hand be characterized by random variables?

Wait, take a second to think about that. Consider bluffs, varying styles, human error and emotion, number of players, chance of seeing all cards on the board, etc, etc, etc.

[/ QUOTE ]

The answer to this for me is a clear "yes". Suppose you're playing against a player who will always call to the river no matter what his hand, then bluffing is always wrong. On the other hand, suppose you're playing a player who never calls without the nuts, then bluffing is always correct.

Most players will fall somewhere in the middle. If you can accurately assess the range of hands that a player would have played in the manner that he played them, calculate the probabilities that he has each of those hands, and calculate the chances that he will call a bluff with each of those hands, you can mathematically predict if a bluff is the correct play. It's true that a player might call or fold on a whim, but you can still use percentages to predict each of these events.

[ QUOTE ]
Suppose yes: there should be some "normal" variance based on the combination of these random variables. How would our variance relate to this "normal" variance? What would it mean to have a variance above or below "normal"; would that reflect skill levels? Does this suggest the smaller the variance the better the player?

[/ QUOTE ]

Generally the ammount of variance a player has is determined by the game he is playing. In MTTs for example, a good player will have a much higher variance because he will be winning the tournaments much more frequently. STTs are the same, but less extreme. If you know that a place will place 14%/13%/12%/61% (1st/2nd/3rd/OOTM), then you can easily calculate that persons variance, and in general, it will be higher because of the fact that he's getting more firsts than average.

Many people confuse variance with the number of winning/losing sessions a player has, but this is incorrect. A player with a 20% ROI will have greater variance than a player with a 10% ROI. However, the player with a 10% ROI will have more losing sessions (assuming the same number of tournaments per session). Variance only refers to the deviation from the mean, so even though a player with a higher ROI will have fewer losing sessions, he will have a lot of sessions which are below average, but still winning.

[Misfire]

[ QUOTE ]
How many hands would you have to see to convince yourself that the 10% ROI player is better than the 20% ROI player. 1? 2? 10? 100?

What if they played 1000000 SnGs? Would you still need to see how they played to know who is best? Because if your argument is a sample size argument, I'll grant you that 5000 SnGs might not be enough. But somewhere along the line, there would be enough SnGs to tell you who is the better player, SOLELY on the basis of their ROI.

[/ QUOTE ]

Certainly as # of SNG's approaches infinity, the confidence in saying how good the player is based solely on his results approaches 100%.

I would suspect that as we increase the number of SNG's, the probability of a bad player maintaining a good ROI would drop exponentially. Like coin flipping, although the odds of winning and losing are the same per trial, the odds of maintaining the same lucky result time after time decline sharply. The more times you flip the coin, the less likely your overall results are to deviate from your true ROI (0% in this case)...that is, of course, unless you have some kind of coin-flipping skill.

In poker, after a certain point, the odds that the player's ROI can be attributed to "luck" have got to be so small that they're not even worth arguing over.

[Misfire]

[ QUOTE ]
Of course you can't know that with 100% certainty, but who the hell looks for 100% certainty? in ANY field of life?

[/ QUOTE ]

...especially poker.

[Al P]

It all comes down to sample size.

A casino never went broke because they offered a game with a house advantage.

[RedManPlus]

[ QUOTE ]

Unless you're a pro multi-tabling full time it maight take 10 years to get enough games under your belt to be able to say that you are a very good player. Yet virtually noone has played that long because internet SnG's haven't been around (or at least played by very many people) for long enough. So -- if you're not a full-time multi-tabler, you might never really know if you're any good. And, those pros you hear about all the time, have a fair chance of not being nearly as good as is generally accepted. Yet, people on the forum often take as gospel things put forward people because viewed as "long term winners."

[/ QUOTE ]

This is the statistical equivalent...
Of constantly warning people...
That they could be hit by an asteroid in the next 10 minutes.

What would motivate someone to push this stuff?
Why does it make him feel better?

rm+

/images/graemlins/cool.gif /images/graemlins/cool.gif /images/graemlins/cool.gif

[DMACM]

[ QUOTE ]
[ QUOTE ]

Unless you're a pro multi-tabling full time it maight take 10 years to get enough games under your belt to be able to say that you are a very good player. Yet virtually noone has played that long because internet SnG's haven't been around (or at least played by very many people) for long enough. So -- if you're not a full-time multi-tabler, you might never really know if you're any good. And, those pros you hear about all the time, have a fair chance of not being nearly as good as is generally accepted. Yet, people on the forum often take as gospel things put forward people because viewed as "long term winners."

[/ QUOTE ]

This is the statistical equivalent...
Of constantly warning people...
That they could be hit by an asteroid in the next 10 minutes.

What would motivate someone to push this stuff?
Why does it make him feel better?

rm+

/images/graemlins/cool.gif /images/graemlins/cool.gif /images/graemlins/cool.gif

[/ QUOTE ]

Amen to that, couldnt have said it better myself.

Furthermore, do we play these games with our eyes shut and open them up to find out how we did at the end? There are theories about what works that are grounded in probability. If my friend designed a program and refused to tell me what it did then maybe id need 10 years multitabling to test it and be sure it worked. In the real world let me play 50 games and post tons of hands and Ill know exactly where I stand. Successful people in aggregate play tons of games and there is huge consensus on how to beat low buy in games. Not only is there consensus on correct plays argumentation can be provided for them. Is whether or not we have a mathematical edge based on theory and experienced advice, or have been lucky to all this time with incorrect plays that in aggregate would be equivalent in probability to winning the lottery supposed to be a serious question? This might sound like a rant but I think misusing statistics like this is a terrific way to cause an experianced player to doubt himself every time he takes an inevitable downswing, plus I think its illogical.

[bearly]

i really think irie should respond to the 'crapola' part (he could do a damn good job). so, i will be the simple stimulant..............just think "10% rake".and think, and think.............h

[AliasMrJones]

[ QUOTE ]
[ QUOTE ]

Unless you're a pro multi-tabling full time it maight take 10 years to get enough games under your belt to be able to say that you are a very good player. Yet virtually noone has played that long because internet SnG's haven't been around (or at least played by very many people) for long enough. So -- if you're not a full-time multi-tabler, you might never really know if you're any good. And, those pros you hear about all the time, have a fair chance of not being nearly as good as is generally accepted. Yet, people on the forum often take as gospel things put forward people because viewed as "long term winners."

[/ QUOTE ]

This is the statistical equivalent...
Of constantly warning people...
That they could be hit by an asteroid in the next 10 minutes.

What would motivate someone to push this stuff?
Why does it make him feel better?

rm+

/images/graemlins/cool.gif /images/graemlins/cool.gif /images/graemlins/cool.gif

[/ QUOTE ]

Again you don't know what you're talking about. This is the exact opposite. Many people think they are excellent poker players because they have "won a lot". In effect saying they will be hit by an asteroid. Irie is saying for most people, even those that think they've looked through the telescope and seen the asteroid bearing down on them, it isn't true.

[RedManPlus]

OK...
Since stirring up this controversy...
I've gone back to my freshman stats...
Taken the last 20 SNGs from 5 different Leaderboard players...
And done a "quick and dirty" SNG variance analysis...
** Specifically ONLY for guys doing about 20% SNG ROI **.
(I'm not interested in any other group).

http://www.pathcom.com/~gzt/SNGVariance.jpg

So 100 games is worthless...
Even 500 is the bare threshold for evaluating long-term performance...
But 1000 is more realistic...
Giving you a ROI +/- 10% range.

For a true 20% ROI SNG player...
To lose money over 1000 tournies or roughly one month...
Is 4 SD away from the mean...
You know... asteroid territory.

On the other hand...
This is all very dire stuff for marginal players...
Like a zero to 5% ROI player.

The level of variance while quite manageable for a Leaderboard guy...
Pretty much what you would encounter in any business...
Is a level that cannot be sustained by a marginal player.

Basically...
Leaderboard guys no problem...
Marginal players...
You should get the hell out and do something else.

AliasMrJones is more or less right...
But only in terms of marginal players...
Which is about 90% of the posters at 2+2.

rm+

/images/graemlins/cool.gif /images/graemlins/cool.gif /images/graemlins/cool.gif

[AliasMrJones]

OK, so you're saying that all but 20 people in the world should stop playing STT's?

And, even at 2,000 STT's, your leaderboard guy is +/- 8 percentage points of ROI. So, your 20% guy may actually be a 12% guy. Do you think people in the forum would pay more attention to what a 20% ROI guy says than a 12% ROI guy? Now are you starting to get the point? How many WPT-type pros do you think play 2,000 tournaments a year?

The STT forum guys have run the simulations over very long periods of time and looked at all the 100 game and 1,000 game intervals. For a 15% ROI player, which is a very good ROI at the real money STT's ($11 STT's don't really count), &gt;30 buy-in drops are entirely within the realm of possibility. Yes, they will most likely be back to even after a couple of hundred STT's, that but doesn't mean the 30 buy-in drop didn't happen.

You keep talking about these "marginal" players. Do you put ZeeJustin in the "marginal" category? Irie? Giga?

Look STT's are my bread and butter. There are reasons why I play the STT"s and low variance compared to limit ring games and MTT's is definitely among them. But, you're basically saying that there are players who don't experience the not insignificant variance that IS there in STT's and you're just plain wrong.

[bearly]

what? the possible 'marginality' of a player is figured after the fact of 'varience' is assumed (a hypothesis, so to speak). i can't read irie any other way.......but i am usually 'wrong'..............irie?????.............h