RANDOM thoughts

[jcm4ccc]

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

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

Regards
Brad S

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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:

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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.



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

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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).


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

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


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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]

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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.

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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? [img]/images/graemlins/wink.gif[/img]

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]

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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.

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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]

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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?)


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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.