how good can you be at tournament poker?

[Paul Phillips]

I don't feel like point-by-point addressing the problems with many of the statements in this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=tv&Number=1029465&page=0&v iew=collapsed&sb=5&o=14&fpart=all) and it'll be clearer this way anyway.

Almost everyone believes there is more skill in tournament poker than there actually is. One of the reasons is that it's so easy to buy into the seductive fallacy that if someone achieves multiple impressive results over a period of time, it must be because of skill. When more than one person wins multiple bracelets at the 2004 WSOP, we think, wow! Those guys must be playing great, and it's nice to have confirmation that skill wins out in the end.

This line of thinking illustrates a lack of understanding regarding the manifestations of variance and the certainty of clumping among chance results. If a guy wins one tournament we have no problem chalking it up to variance. After all, somebody had to win, maybe he was just the luckiest guy that day. But somehow the minute somebody has a few good results in quick succession, it's because of skill. The fact is that out of a large population of tournament players, it is absolutely inevitable that some will turn out to be much, much luckier at critical moments than others: not just in single tournaments, but over the course of a month, a year, and even a lifetime.

When someone has a great year, people conclude that those results illustrate how good it is possible to be. BUT NOBODY IS ANYWHERE NEAR AS "GOOD" AS YOU WOULD CONCLUDE FROM THOSE RESULTS. And this is where people go off the beam.

Since I know most people still won't believe any of this, here's how we settle things gambler-style. QUANTIFY your beliefs about how good players are. Decide who you think the very best tournament players are and make specific predictions about their results. Now bet on it. It's so easy to reach the end of the WSOP, find a lot of well-known players have won bracelets, and then say "yep, it's skill!" But were those the specific well-known players you predicted, or are you fitting the data to the hypothesis? There are many more poker players you've heard of than you may realize until you attempt to make forward-looking predictions.

Here are some ideas for possible proposition bets involving verifiable predictions. There is nothing that encourages clarity of thought quite so much as having to put your money where your mouth is. Post your ideas on these subjects in this thread, I imagine it'll be revealing.

* dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

* Two tournament players each play 100 large field tournaments. In the end, player A has averaged a profit of 0.5 buyins/tournament and player B has averaged 1.5 buyins/tournament. With what percentage confidence can you say that player B was actually playing with higher EV than player A? Alternately: what line would you place on player B winning more than A over the next 100 tournaments as well? What if B had averaged 3 buyins per tournament?

Here is one of the great articles ever written about tournament variance, almost five years old but as relevant as ever: Question Authority by Tom Weideman (http://www.google.com/groups?hl=en&lr=&ie=UTF-8&selm=LOG94.6060%24PZ3.313867%40tw12.nn.bcandid.c om). If you have a serious interest in the subject this is required reading.

There is a risk-free fortune to be made for the industrious proposition bet seeker by exploiting the gap between perceptions and reality. Go forth and wager!

[Easy E]

Flame away!

* dan harrington - What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

<font color="blue"> 1/600, based on regression to the mean. Based on pure skill (meaning, talent, experience, intangibles) I'd put Dan H at 1/250. I would put him higher, but I think his somewhat less aggressive style will make it less likely that he'll catch the lucky hands in big pots to give him the chips to survive.

* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?
2000 of the players that I feel were most likely to win (i.e be above average, so with a chance between 1/250 and 1/167) based on a field of 5000.
I still don't think I'd be a "favorite" but I'll take that as close enough to bet on.... not for big money however.

* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

I'll say 1 1/3 X of the average player... and that's a gamble.

* Two tournament players each play 100 large field tournaments. In the end, player A has averaged a profit of 0.5 buyins/tournament and player B has averaged 1.5 buyins/tournament. With what percentage confidence can you say that player B was actually playing with higher EV than player A?

None. Besides needing a lot more information, it's too short-term (assuming 1 year duration here) to come up with a meaningful number in my opinion.

**Alternately: what line would you place on player B winning more than A over the next 100 tournaments as well? What if B had averaged 3 buyins per tournament?

3:1 against. 9:1 against with the buyins.

[leykis]

Wow, nice post. It is always funny to me that even players who have a complete understanding of the statistical nature of the game believe that the statistics should hold true no matter how small the sample size. Of course if it wasnt for luck I would win every tournament. /images/graemlins/wink.gif

[djack]

[ QUOTE ]
* dan harrington - What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

1/600, based on regression to the mean. Based on pure skill (meaning, talent, experience, intangibles) I'd put Dan H at 1/250.

[/ QUOTE ] I think you're wrong here. Each main event is more or less an independent event, so there is no regression to the mean.

[Dominic]

Crap. I have no idea what "regression to the mean" even means!

[BobboFitos]

[ QUOTE ]
Since I know most people still won't believe any of this, here's how we settle things gambler-style. QUANTIFY your beliefs about how good players are. Decide who you think the very best tournament players are and make specific predictions about their results. Now bet on it. It's so easy to reach the end of the WSOP, find a lot of well-known players have won bracelets, and then say "yep, it's skill!" But were those the specific well-known players you predicted, or are you fitting the data to the hypothesis? There are many more poker players you've heard of than you may realize until you attempt to make forward-looking predictions.

[/ QUOTE ]

I made a bet with a friend concerning this World Series. Here's what happened: We both got to draft a "team," akin to fantasy football, of 12 players. (I drafted Dan Harrington in the later rounds, actually) If any player on the either team won the event, the bet was over, and that person won. In the likely event that no one won, we simply had total cash payout to each team, and the best cash team won the bet.
He had Chris Ferguson, so in the end it came down to a pretty exciting bet. (When we followed it while it happened through pokerpages and other sites)
I suggest to readers that a fantasy football style draft is the way to go. It was fun.
Phil Hellmuth was the 3rd overall pick, I believe, but I'm sure his stock has slipped. I picked Daniel Negreanu first, he picked Phil Ivey second. We both believe those two players are the two best in the world, but hey, what do we know!

[ QUOTE ]
* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

[/ QUOTE ]

In a weak field, where blinds increase very slowly, (the structure most accomodating to players, such as the Championship at the Plaza) I believe the best player has a "5x" buyin on average. This is pretty much just picking a number without using math, but I see no reason why in a low blind, weak field, a player (such as Negreanu) to cash more than 10% of the time, and when cashing, finishing much higher than an average finish.



All in all, I think your post was very thought provoking... And of your mentioned bets, I think they all would seem like fun. Wanna bet on 2005? /images/graemlins/wink.gif

[BobboFitos]

[ QUOTE ]
* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?
2000 of the players that I feel were most likely to win (i.e be above average, so with a chance between 1/250 and 1/167) based on a field of 5000.
I still don't think I'd be a "favorite" but I'll take that as close enough to bet on.... not for big money however.


[/ QUOTE ]

I may be misreading what Paul wrote, but I belief when he said "winning a bracelet in 2005," he meant from any event, not just the championship event.

In that regard, 2000 would be an insanely high number, as some events (i.e. no limit 2-7 lowball) still draw just 47ish players. (And ace to five only drew slightly more than 100 I think)

However, the numbers increased heavily from 2003 to 2004, and I do not see why this trend will not continue, but if Paul did in fact mean "from any event," I would take this bet if I could pick 12 players. I would feel great about my chances if I could pick 15. If I could pick 20, I would feel foolish to lose.

I could be waaaaay wrong here though.

[rjc199]

Was Tradesports.com offering bets for this year's WSOP?

Dan Harrington to make the final table at next year's WSOP - 50:1.


I need 7 players to get me even money to win a bracelet (Daniel N. is about 2:1 himself to win a bracelet next year). As a matter of fact I'm making my list right now. Daniel N., Men the Master, Ted Forrest, Phil Ivey, Scott Fishman, Barry Greenstein, Howard Lederer.

2+2 should have an unoffical pool for tournaments. You get to pick 5 guys and get points for highest combined finish. The winner gets something.

The rest of the stuff I don't care about.

[Nate tha' Great]

Is there anywhere to get a complete lists of players and placements for both the 2003 and 2004 WSOP main event? If so, it seems to me that you could get somewhere toward answering this question by taking a simple correlation of placements in each of the two years. I guess that it would be somewhere in the neighborhood of .2, or perhaps a little lower.

[Tosh]

[ QUOTE ]
Almost everyone believes there is more skill in tournament poker than there actually is.

[/ QUOTE ]

Remove the word 'tournament', and add 'in the short term' at the end of the sentence. Anyone can lose in any given short term period; cash games or tournaments. It is not till we begin to see a long term trend that we get an idea. There are daily posts on the strategy forums of this board along the lines of 'I am losing over 10k hands, I don't know what to do'. The answer is generally play more hands if you believe you should be beating the game, until your sample size is relevant.

Getting long term results in cash games, whilst playing multiple tables online, is hard enough but IMO long term tournament results don't even exist; with the size of WPT events these days you would surely need to play many 1000s before getting a sample size of any relevance at all. Noone is ever going to play enough, so how can we ever know who the best players are from results alone?

[ QUOTE ]
When someone has a great year, people conclude that those results illustrate how good it is possible to be. BUT NOBODY IS ANYWHERE NEAR AS "GOOD" AS YOU WOULD CONCLUDE FROM THOSE RESULTS. And this is where people go off the beam.

[/ QUOTE ]

Couldn't agree more. I also think its a bad idea for any poker pro to just play tournaments as a means of support, without a very large cushion for variance.

[blackaces13]

[ QUOTE ]
1/600, based on regression to the mean.

[/ QUOTE ]

WHAT!!? Am I missing something or is this like saying it makes sense to bet black in roulette after 5 consecutive reds? Its a myth.

[Tosh]

[ QUOTE ]
* dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

[/ QUOTE ]

Any answer is obviously a guess, for all we know Dan's odds of making the final table are 1000/1.

[ QUOTE ]
* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

[/ QUOTE ]

Well I think the sizes of the tournaments next year is the big unknown that makes it impossible, but I am sure the magic number is more than most think.

[ QUOTE ]
* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

[/ QUOTE ]

I really have no idea, and I don't believe anyone can either. Maybe that was your point.

[ QUOTE ]
* Two tournament players each play 100 large field tournaments. In the end, player A has averaged a profit of 0.5 buyins/tournament and player B has averaged 1.5 buyins/tournament. With what percentage confidence can you say that player B was actually playing with higher EV than player A? Alternately: what line would you place on player B winning more than A over the next 100 tournaments as well? What if B had averaged 3 buyins per tournament?

[/ QUOTE ]

This can obviously be calculated, but my stats days are over.

[Easy E]

So, Dan can be expected to make every final table from here on in?

Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[Easy E]

[quote
I may be misreading what Paul wrote, but I belief when he said "winning a bracelet in 2005," he meant from any event, not just the championship event.


[/ QUOTE ]

<font color="blue">dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000 </font>

He is clearly referring to the $10K championship event (unless you expect a different tournament to have a chance of hitting 5,000 entrants)

[BobboFitos]

[ QUOTE ]
[quote
I may be misreading what Paul wrote, but I belief when he said "winning a bracelet in 2005," he meant from any event, not just the championship event.


[/ QUOTE ]

<font color="blue">dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000 </font>

He is clearly referring to the $10K championship event (unless you expect a different tournament to have a chance of hitting 5,000 entrants)

[/ QUOTE ]

Actually, I did not:

I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

Thats what I was referring to.

[Easy E]

Same statement as I made above. "Knowing" that Dan is 2/500 to make the final table of the 2005, 5000 entrant $10K tournament... AND knowing he made the final table in 2003 and 2004... I'd give you a better bet than 249:1 that he wouldn't do it again in 2005.

Don't waste your time asking me to do it- I'd want the chance to win $100 or more and there's no way I'm covering a four-figure loss, much less a $30K losing bet. /images/graemlins/tongue.gif

[fnurt]

[ QUOTE ]
So, Dan can be expected to make every final table from here on in?

Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]

If Paul's intent in posting this thread was looking for players to gamble with, I think he just found one.

[djack]

[ QUOTE ]
So, Dan can be expected to make every final table from here on in?

Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]

You have a bad grasp of the concepts involved in statistics and probability theory. I don't want to be mean, but it's true. What you are saying is a fallacy, and a common fallacy at that.

[NLfool]

FYI Raymer was about 500 to 1 this year. As were just about any non name player.

[Duke]

[ QUOTE ]
He is clearly referring to the $10K championship event (unless you expect a different tournament to have a chance of hitting 5,000 entrants)

[/ QUOTE ]

He was thinking total number of buy-ins, and figured that Daniel would rebuy in the $1k rebuy event about 4,000 times next year.

~D

[CrisBrown]

Hi EasyE,

[ QUOTE ]
Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

[/ QUOTE ]

Actually, all other things being equal, if you flip heads 50 times in succession, there's a significant possibility that the coin is somehow weighted -- albeit perhaps in ways you can't easily detect -- and I'd be expecting a greater than 50% of heads over the next N (very large) tosses.

Cris

[Big O]

Very nice post. I agree with you on this. Tournaments have one other function besides winning a boat loads of cash is Fame and Fame only. People dream (I know I do) about winning a Major. But my odds are not good because the fields are so large. For a Pro to make to the final table next year will be near to imposible. Look at this years 6+ players won their seat through the internet. DH the only real major Pro headliner there.

I feel players plucking down $10k to play are insane no matter how good you are (or think you are for that matter) are really throwing your money away. Maybe you'll make the money and get your money back, but why not put the $10k in a NL ring game. You have a better shot to double or triple you buyin.

I think the only time playing in a big tourney for a Rec. Player like myself is to win it though a Super. One that pays a vacation or something like the UB Aruba tourney. Now that is a great Vaca, free, and you play poker, Yehaaaaaaaaaa!!!

Paul I think you make great points and keep these coming.

Big O

[Daliman]

I, for one, am honored to have both started the initial thread that got PP going on this topic, AND for riling him up with my deadly hack math!

Once again, I agree with 99% of what you say,(hell, i'm experincing the bad side of luck in my game right now..), but your post seems to insinuate that results don't matter that much, except for long term(right?). Well, PH had long term results. Maybe it's an aberration. Hell, for that matter then, maybe Doyle's whole career is an aberration of a lifetime of good luck. I don't know

What I do know is what my new fantasy sport is! I will be tailoring a points system for this if one is not already made for next year's WSOP.

[CrisBrown]

Hi Paul,

I think most people significantly overestimate the skill difference between winners and losers, in almost every kind of sporting endeavor.

For example, consider the end-of-season scoring averages for PGA tour pros. In most years, the difference between the scoring leader and the 126th player will typically be right around two strokes per round. The scoring leader will often (although not always) be the money leader for that year. The 126th player will probably have lost his tour card and go back to Q-School.

Similarly, consider the effect of just one or two injuries on an NFL football team. With only 16 games in the season, one or two significant injuries will take the "best" team in the league out of playoff contention, because the skill difference between the "best" and "worst" teams just isn't all that great. For most of the also-rans, the difference between making and missing the playoffs comes down to five or six key plays over the course of a season: a touchdown pass dropped in this game, a blown coverage that gives up a touchdown in that one, a missed field goal here, a fourth-quarter drive-killing penalty there. The margin really is that small.

The same is true in tournament poker. While I won't go to the same extent as Tosh and say that there's no way to draw any conclusions on less than 1000 tournaments, neither do I agree with the "results speak for themselves" crowd.

Chaos and statistical theory predict a substantial clumping factor in random events. If you roll a six-sided die often enough, sooner or later you'll roll a streak of 6s. If you see only a small sample containing that streak, you might conclude that 6 is the "best" number. A poker tournament, by nature, takes a tiny sample of the players' careers. In most tournaments, the finalists will play fewer than 500 hands from start to finish. Even in this year's WSOP Main Event, I doubt that was much greater than 2000 hands. That is a tiny sample in poker.

So yes, I agree that the luck factor is significantly underrated in tournament outcomes. The good players need a bit less "luck" than the poor players, but every tournament winner will have gotten lucky to win.

Cris

[Paul Phillips]

[ QUOTE ]
Actually, all other things being equal, if you flip heads 50 times in succession, there's a significant possibility that the coin is somehow weighted -- albeit perhaps in ways you can't easily detect. I'd be expecting a greater than 50% of heads over the next N (very large) tosses.

Cris

[/ QUOTE ]

Why require N to be very large? You have a pretty freaking good bet on the 51st flip alone.

Once you accept there's a nonzero chance that the coin is unfair, then: either it IS unfair, or you've just witnessed a one in 562-trillion odds event: like winning a one in 24-million lottery twice in a row. I think you can inch your estimation of the likelihood of another heads a tad up from 50%.

Seriously, forget about the math. If you knew you weren't being set up or hustled somehow and saw a coin flipped the same way fifty times in a row, wouldn't you be willing to give some pretty freaking long odds that it's going the same way next time too? I should hope so! There are a lot of potential gambling fallacies swirling around this subject matter, but predicting the future based on the past is only a fallacy when the events are actually random. In "real life" you're supposed to be somewhat results oriented -- otherwise known as the scientific method.

[jwvdcw]

[ QUOTE ]
So, Dan can be expected to make every final table from here on in?

Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]

I'll take you up on this wager. I know of a site with a simulated online dice roll...we could set the die to only two numbers..and when it came up one of the two numbers comes up many times in a row, we could then make the bet for the next several rolls. What odds exactly are you willing to lay? With this online simulator, we can run thousands of rolls per day. We can transfer all money either through Party, Stars, or through an online service like paypal. Up for it?

[blackaces13]

[ QUOTE ]
If you knew you weren't being set up or hustled somehow and saw a coin flipped the same way fifty times in a row, wouldn't you be willing to give some pretty freaking long odds that it's going the same way next time too? I should hope so!

[/ QUOTE ]

If we accept your parameter that "we're not being hustled" (ie. its a 50/50 shot on each individual flip of eother heads or tails), then the second part of your statement makes no sense.

[MicroBob]

[ QUOTE ]
I feel players plucking down $10k to play are insane no matter how good you are (or think you are for that matter) are really throwing your money away.

[/ QUOTE ]


Not really.
Consider that many of the top-name players finished in the money and at least got their buy-in back (or maybe a little more).

Anyone who finished in the top 225 got their buy-in back I think.
If you finished high enough to 'only' got $10-$20k, well, that still isn't THAT bad for a week's work.

Plus the excitement of being involved in the biggest poker event EVER.

I just think it's wrong to assume that not reaching the final-table constitutes failure.


Other thoughts -

Paul - thanks for a very insightful post. I will also be checking out the linked article.

Cris - Great post regarding other sports. right on the money. The line between great and mediocre is much closer in most sports then many people imagine.
look at all the 95 win teams in baseball compared with all the 91 win teams.
etc etc etc. Your golf example is good too and probably slightly closer to the poker-tournament construct.



My own situation - As some of you know, last week I decided to enter a $50k guaranteed online tourney for $100 and I lucked my way into winning the whole thing for $12.5k.
Not too shabby for a guy who isn't that good of a tourney player who makes his living grinding away at the 3/6 tables.
I didn't have any major suck-outs until it was heads-up (where the river saved me a couple times) and I thought I played pretty well. But I also came back from the short-stack with 16 players left so there obviously had to be some luck involved.
My greatest amount of luck came from the fact that nobody delivered any significant bad-beats on me.
All my AQ's held up against AJ's and so on.


Am i improving as a tournament player? Heck yes. I'm much better now then I ever was before.
Is my win evidence that I am pretty damn good at this stuff?
Nope. Not by a long-shot.
I think I MIGHT be good enough to break-even on these things (or have slight positive expectation) in the long-run but certainly not much more than that.
At least not until Greg and Dan's 2+2 tourney-books come out!!

[mrbaseball]

[ QUOTE ]
most people significantly overestimate the skill difference between winners and losers, in almost every kind of sporting endeavor

[/ QUOTE ]

This is what makes baseball betting so good! The favorites almost always get overbet skewing the lines often toward the underdogs. The talent gap between "good" teams and "bad" teams is minimal and most teams hover in the gray murky middle, Once in a while you have some pathetic outliers like Arizona this season or Detroit last season. Or ocassionally teams like the Mariners or Yankees of a few years back that had +.700 seasons. But these are rare instances. But for the most part the very best teams win less than 60% of the time and the bad teams still win at least 40% of the time. You would never know it though by how the lines can skew. But people want to pick a winner so they are willing to lay more odds than they should on a slight favorite.

[Paul Phillips]

[ QUOTE ]
If we accept your parameter that "we're not being hustled" (ie. its a 50/50 shot on each individual flip of eother heads or tails)

[/ QUOTE ]

A !-&gt; B

You're not being hustled. That means nobody is sitting here influencing outcomes somehow to make you pursue a bad bet, or rigging the coin toss repeatedly in one direction until they can get you to bet in the other, etc, It surely doens't mean the coin is fair! It should be obvious that the coin is not fair.

The whole point is that the coin isn't fair.

[ QUOTE ]
then the second part of your statement makes no sense.

[/ QUOTE ]

It makes sense to me but you're not the first person to suggest that I've got brain-matter issues.

[3rdEye]

Paul,

Even though you're correct in that, given the nature of variance, we can expect extreme results at either end of the tournament "curve," wouldn't you agree that it is perfectly acceptable to think that multiple tournament successes in a relatively short period is more *likely* the result of skill than it is of luck?

In fact, isn't this the whole notion of statistical significance? In a typical hypothesis test, for example, one might employ a t-test to determine whether we can reject "Hypothesis X" with statistical significance of Y%. While it might be true that, in reality, Hypothesis X is correct, statistical practice dictates that we reject it, because of the severe unlikelihood that it is valid.

In other words, while I agree that it is possible and likely that some people are simply more lucky in tournaments than others over the short term, in the absence of qualitative evidence otherwise, it is perfectly acceptable (indeed, it would be incorrect otherwise) to accrue extraordinary short-term tournament success to skill.

[3rdEye]

[ QUOTE ]
[ QUOTE ]
So, Dan can be expected to make every final table from here on in?

Yes, it's not the best use of the concept, but I would be willing to lay odds that, all other things being equal, when you flip heads 50 times in a row, I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]

You have a bad grasp of the concepts involved in statistics and probability theory. I don't want to be mean, but it's true. What you are saying is a fallacy, and a common fallacy at that.

[/ QUOTE ]

Agreed. This is a basic fallacy.

In fact, given that flipping heads 50 times in a row could be construed as a bias in favor of heads, the original poster's assertion is even more off-base.

[lolita16]

Hi Paul,

First, allow me to join with others in saying thank you for sharing your opinions and thoughts on this forum. This article has been of particular interest to me in just getting into some of the smaller buy in tournaments.

Regarding the main event of the world series, many of the top players have expressed how difficult it will be for any top notch pro to win given the huge fields and the huge proportion of internet players changing the style of the game.

In WPT events, however, it seems that there is a subgroup of players that make frequent appearances at the final table. While I realize random noise can account for some of this, it does give the impression that at least in average fields some players have a much greater chance of reaching the final table. My inclination is to attribute this to greater skills than average, in addition to luck being on your side at this particular event.

Are there simply a large number of pros that play most of these events, thereby increasing their chances of making final tables in several of them? Do these pros have a higher skill level than most of the field, but remain fairly even amongst each other? When you reach the final say 4 or 5 tables, do you find a large proportion of pros to lesser skilled players, or do the pros still represent a fraction of the entries a bit closer to the first day?

Regards-

[Duke]

Not a comment one way or the other, but here's an interesting read about coin bias. It's definitely tangential to the issue at bar.

Toss Out the Toss-Up: Bias in heads-or-tails (http://www.sciencenews.org/articles/20040228/fob2.asp)

~D

[Jimbo]

[ QUOTE ]
Similarly, consider the effect of just one or two injuries on an NFL football team. With only 16 games in the season, one or two significant injuries will take the "best" team in the league out of playoff contention, because the skill difference between the "best" and "worst" teams just isn't all that great.

[/ QUOTE ]

Unfortunately Chris you cannot have your cake and eat it too. You first state that: [ QUOTE ]
one or two significant injuries will take the "best" team in the league out of playoff contention,

[/ QUOTE ] and then you state:
[ QUOTE ]
the skill difference between the "best" and "worst" teams just isn't all that great.

[/ QUOTE ]

Both statements just cannot be true since all the teams are comprised of players. For the teams to be very close in skill/talent the players themselves must also be close in skill/talent. Contrary to popular belief removing a key player just doesn't have that much effect on a team.

Jimbo

[DonkeyKong]

so Paul, do you agree with Negreanu that the world champ should be decided by pot-limit Hold 'em? Does NL inherently favor luck just too much?? we all know it makes for good TV so it will never happen but just curious your opinion...

[Kurn, son of Mogh]

most people significantly overestimate the skill difference between winners and losers, in almost every kind of sporting endeavor.

e.g., the difference between hitting .320 and .280 is less than 2 hits per week.

[Trainwreck]

Nice post as usual Paul! +EV! 8)

I think we need to consider in tournaments the # of players that don't know GOOD tournament strategy, let alone experts.... this will DOOM much of dead money to fatal errors, while some will luck out on their grievous (to us) decisions and send experts to the rail.

In other words, experts definitely have an advantage (skill set/knowledge/whatever you want to call it...) and the not so expert players do not, and their errors will DOOM a large % of them and randomly send some experts to the rail.

So almost every final table in a large event is likely to have more experts at the final table in my view, but a lucky dolt (in poker skill comparison only) or 2 are likely to squeak through as well.

Not to slam David Wms. but he was looking like the lucky dolt at that final table, but I saw some bad plays through the final 2 tables from many players, IMHO.
Greg R. played great big stack and got more than his fair share of boards, some losses weren't shown, ESPN rushed these final 2 tables big time, so the masses just following via this coverage will likely feel: 'WOW! Greg is the luckiest SOB on the planet!'.

Not sure if that is a disservice to us players or not. 8)

&gt;Trainwreck&lt;

[MicroBob]

[ QUOTE ]
e.g., the difference between hitting .320 and .280 is less than 2 hits per week.


[/ QUOTE ]

Actually, not even that much imo.

Assume 500 ab's (which is higher than average):
.320 = 160 hits
.280 = 140 hits

I believe the baseball season is roughly 24 weeks long and the difference between .320 and .280 is only 20 hits.

So it's actually very close to just 1 hit per week.

[Rick Nebiolo]

Paul,

Glad to see you posting here. About the time you left RGP I spent the greater part of an evening Googling many of your old posts there - the experience made me instantly regret that I had you mixed up with others with the same last name /images/graemlins/wink.gif

I'll take a stab at a few of your propositions and add one of my own:

* dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

I respect Dan about as much as any player but I'd put his chances at about 1/300. There is no one I'd put better than 1/200. I rate Dan's chances a bit worse than the best because the large fields and series of long days work against the older player.

* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

I'm assuming you just mean the final event of 5000 players. I'd say you need to let me chose about 1500 players. Problem is, I couldn't come up with 1500 names e.g., I wouldn't know the names of all those super bright young guys polishing their games online.

* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

About 2X's, maybe a bit less.

[/i]* Two tournament players each play 100 large field tournaments. In the end, player A has averaged a profit of 0.5 buyins/tournament and player B has averaged 1.5 buyins/tournament. With what percentage confidence can you say that player B was actually playing with higher EV than player A?[/i]

The math is beyond my ability but intuitively I'd say about 65% confident.

What if B had averaged 3 buyins per tournament?

Getting that far out over 100 tournaments is substantially better. I'd be 85% confident.

There is a risk-free fortune to be made for the industrious proposition bet seeker by exploiting the gap between perceptions and reality. Go forth and wager!

My Mom would die if I got involved in some legal tangle with running such an operation so there is no fortune for me. On a smaller scale I passed on some of the dubious online sites $50 max bet where you got to pick against a field of 200 or so "big names". Great bet but who wants the hassle of signing up /images/graemlins/smirk.gif

Here is my own proposition:

What are the chances of Phil Hellmuth making the final table in the WSOP final championship event at least once in the next 20 years? (I'd estimate he is a 2 to 1 dog)

BTW, I'd put Phil Hellmuth as a 2 to 1 favorite over you in a WSOP "last longer" bet. Yet I'd rate you as having at least twice the money equity in the tournament (hope this doesn't sound like a suck up).

Regards,

Rick

[Bob Moss]

[ QUOTE ]
Crap. I have no idea what "regression to the mean" even means!

[/ QUOTE ]

Neither does Easy E, unless his post was some kind of sick joke.

Bob

[Leo99]

I bowl competively and often against pro or near pro caliber players. They kick my butt routinely. I try to analyze why. It seems to come down to 1 or 2 frames a game where they strike and I don't. They're not a lot better than me, but they're a little better than me on a consistent basis. I can lucky and beat the better bowler now and then but day in and day out, the more better person is going to win. I think it's the same with poker, baseball, golf, whatever.

1500 names to win the big NLHE turnament in order to break even seems very high to me. I think that if you named everyone you could name heading into the WSOP i.e. everyone that was a respected player capable of winning, you'd only come up with 200 names. One person out of those 200 names should win 5 out of the next 10 years. For DH to make final tables in consecutive years is talent and not luck. My opinion.

Regression to the mean: On average: Taller than average parents have taller than average children. But their children are shorter than the parents. Shorter than average parents have shorter than average children. But their children are tall than the parents.

[Jimbo]

[ QUOTE ]
I think that if you named everyone you could name heading into the WSOP i.e. everyone that was a respected player capable of winning, you'd only come up with 200 names. One person out of those 200 names should win 5 out of the next 10 years.

[/ QUOTE ]

I'll cover that action. You can settle up now if you like for half price. /images/graemlins/smile.gif


Jimbo

[Easy E]

Rick, a gold star awarded to you, for being the only OTHER poster willing to put some numbers to Paul's propositions.

I estimated that very few respondants would, but I expected it to be greater than one other person !

[Easy E]

[ QUOTE ]

I'll take you up on this wager. I know of a site with a simulated online dice roll...we could set the die to only two numbers..and when it came up one of the two numbers comes up many times in a row, we could then make the bet for the next several rolls. What odds exactly are you willing to lay? With this online simulator, we can run thousands of rolls per day. We can transfer all money either through Party, Stars, or through an online service like paypal. Up for it?

[/ QUOTE ]

Sure! You give me a simulator that you can fairly well prove is close enough to random to count (you can generate a large number of trials to show that the numbers are in the range of 50:50), then let me know when you'll know that the very next 50 rolls in a row will result in "1" being generated. I'll sit there with you, watch the 50 "ones" in a row generate.. and then I'll give you 7:5 that the 50 rolls after the streak will have more "twos" than "ones"

We'll even ignore the differences inherent in live poker between people vs. random number generators.

Or, if you'd rather not wait for that, you can read some of my other replies and save yourself the time.

[Easy E]

I would doubt that ANY bet on the WSOP winner would be a +EV bet... the vig must be enormous as a result?

[Easy E]

[ QUOTE ]
[ QUOTE ]
I'd wager that you will flip fewer heads than tails over the next 50 tosses.

And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]

You have a bad grasp of the concepts involved in statistics and probability theory. I don't want to be mean, but it's true. What you are saying is a fallacy, and a common fallacy at that.

[/ QUOTE ]

Maybe you'd better reread what I actually wrote, before you assume that I don't know my limitations.

[Easy E]

[ QUOTE ]
[ QUOTE ]
[quote
I may be misreading what Paul wrote, but I belief when he said "winning a bracelet in 2005," he meant from any event, not just the championship event.


[/ QUOTE ]

<font color="blue">dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000 </font>

He is clearly referring to the $10K championship event (unless you expect a different tournament to have a chance of hitting 5,000 entrants)

[/ QUOTE ]

Actually, I did not:

I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

Thats what I was referring to.

[/ QUOTE ]

Okay, I grant you that the "If a single one of those players wins a bracelet at the 2005 WSOP" can be read to mean ANY of the 33 tournaments...

But I still contend that, in the context of his post, Paul meant the $10K championship event.

Paul, care to clear up this trivial point?

[Easy E]

Okay, I was guilty of supposing a freakish run of flips in a "supposed to be" random series of events and nothing more.

Here's a different question- if a coin flip is 50:50, how long of a streak of consecutive heads would you have to see (when you have no direct reason to suspect a rigged coin or toss) before you would ignore the 50:50 probability and bet on the ongoing streak by laying "pretty freaking long odds" on heads on the next toss, or series of tosses?

How long a streak is so long as to be considered almost impossible to occur? And therefore it can be discounted?

Or, in other words- what is the longest "possible" consecutive heads result in a series of 1,000,000 coin flips?

[Easy E]

and some expert programmers before I mention betting against a streak of 50 tosses in a row again.

[MicroBob]

[ QUOTE ]
Regression to the mean: On average: Taller than average parents have taller than average children. But their children are shorter than the parents. Shorter than average parents have shorter than average children. But their children are tall than the parents.

[/ QUOTE ]


ummmmmm....okay.
even if this tall/short childen stuff is true can you see why it has absolutely nothing to do with DH's chances of winning or not winning in future WSOP's??

[Justin A]

Baseball is also great because they play ten times as many games as a football team, so the best team will get to the playoffs more often. Although in any individual game, the better team in football is more likely to be victorious.

Justin A

[Smasharoo]

Or, in other words- what is the longest "possible" consecutive heads result in a series of 1,000,000 coin flips?


1,000,000.

Or was that rehtorical? It's a function of how many flips there are total.

In a set of 1,000,000 flips it's less likely than in a set of 10^100 flips that you'd see 1,000,000 heads in a row. Given a sufficently large number of flips it becomes more and more likely that you will see 1,000,000 heads in a row as you approach infity where, of course, it's gauranteed.

It's still 50/50 that the 1,000,001 flip is heads too, though.

[Easy E]

[ QUOTE ]

Or, in other words- what is the longest "possible" consecutive heads result in a series of 1,000,000 coin flips?


1,000,000.

Or was that rehtorical? It's a function of how many flips there are total.

In a set of 1,000,000 flips it's less likely than in a set of 10^100 flips that you'd see 1,000,000 heads in a row. Given a sufficently large number of flips it becomes more and more likely that you will see 1,000,000 heads in a row as you approach infity where, of course, it's gauranteed.

It's still 50/50 that the 1,000,001 flip is heads too, though.

[/ QUOTE ]


First, you move this all the way down here, then you state the "obvious"

Reread Paul's post, that my reply was originally to, then reinterpret "possible" as something other than the mathematically possible but incredibly tiny mathematical chance of that happening.

[Leo99]

I think that by DH making the final tables the last two years, he is a better than average player. Therefore, he has a better than average chance to make the final table again.

Regression to the mean has everything to do with DH's chances of winning future WSOPs. The point is estimating DH's true mean. /images/graemlins/grin.gif The initial poster's point is that DH's true mean is lower than some of us think. Not to pick on DH, he's just a good example to use.

Let me try to explain regression to the mean as I see it applying to WSOP. Assume you had Godly powers and could rank all the players from best to worst. Or alternatively, you could get all 5000 players to play the tournament an infinite number of times using their fixed initial skill level. Several things could happen. 1. You would have a random normal distribution of finishes among all the contestants. Everyone would average 2500th place. That would mean it's just random luck. 2. Each contestant would have a mean finish with a normal distribution around it.

If you assume option 1, then regression to the mean for DH would mean his average finish should be 2500. Since he's finished way higher than that, his SD must be very large. If you assume option 2, we find (or God tells us) DH is the 20th best player in the field. Assume his SD is 10 places, he should finish between 40th and first, 99% of the time. Maybe DH would average 150th place with a SD of 50 meaning he'd finish between 300th and first place 99% of the time.

[Homer]

[ QUOTE ]

* dan harrington - What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

1/600, based on regression to the mean. Based on pure skill (meaning, talent, experience, intangibles) I'd put Dan H at 1/250. I would put him higher, but I think his somewhat less aggressive style will make it less likely that he'll catch the lucky hands in big pots to give him the chips to survive.

[/ QUOTE ]

This is a common misunderstanding. It's like saying that a player with an expectation of 2 BB/100 who has won 3 BB/100 over his last 1000 hands should expect to win at a rate of 1 BB/100 over his next 1000. The player's expectation is still 2 BB/100. Note that if the player wins 2 BB/100 over his next 1000 hands, then he has won 2.5 BB/100 over his last 2000 hands and thus is regressing to the mean.

-- Homer

[David Sklansky]

These points have, of course, been made by others. But I don't recall them ever being voiced by one of the recipients of the better than average luck. And of course Paul is right.

[Paul Phillips]

[ QUOTE ]
These points have, of course, been made by others. But I don't recall them ever being voiced by one of the recipients of the better than average luck.

[/ QUOTE ]

It's my clever way of making it easier for me to shrug when I have a year as bad as my last year was good.

[vulturesrow]

[ QUOTE ]
And of course Paul is right

[/ QUOTE ]

I didnt know paul went to MIT. /images/graemlins/grin.gif

[MicroBob]

To continue on Homer's thought....
I guess DH shouldn't even bother to enter the next WSOP. This is because his success in the past two WSOP's means that he has 'used-up' his good luck and now HAS to finish below average in order to 'balance-out' his results.

Since some cosmic force was looking out for DH in the past two he needs to get out while he can because the evil-karma is now out to get him.

[billb]

Paul how did you hone your poker skill? I know you were born with the luck portion.

[Ed Miller]

I didnt know paul went to MIT.

His sister did. That's close enough. /images/graemlins/tongue.gif

[vegasone]

[ QUOTE ]

* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?


[/ QUOTE ]

i'll take a sniff at this one, as i don't recall much on it from the original thread on RGP, back when Tom Weideman first posted this line of thinking.

my best guess is about 25.

after reviewing the results of the fantasy pools that daniel n. ran in rgp, it seems that with 20 selections, many people didn't have a bracelet winner on their team. (checking which players were chosen, and how often)
add increasing entries, and my best guess is that 20 wouldn't be sufficient.
for the upper limit, with 30+ selections a higher than 50/50 shot seems likely.

[FeliciaLee]

Hi, Paul. Glad to see you here! I love your journal (long time reader).

Just out of curiosity, are you speaking of all tournament games, or solely NLHE?

Felicia /images/graemlins/smile.gif
www.felicialee.net (http://www.felicialee.net)

[Smasharoo]

First, you move this all the way down here, then you state the "obvious"


Yet you still seemed to find it! A tribute to either your dilligence or megalomania.


Reread Paul's post, that my reply was originally to, then reinterpret "possible" as something other than the mathematically possible but incredibly tiny mathematical chance of that happening.


I understood it the first time, thanks. I stated the obvious because it seemed you weren't grasping it completely. If you were asking what the likelyhood of seeing 1,000,000 heads in 1,000,000 flips is, I imagine you could do that math yourself fairly easily.

If you were asking what a "reasonable" number of consecutive heads would be, you'd have to define reasonable first. If you said a 1 in 100 likelyhood was reasonable enough, then it's around 7 in a row.

[Easy E]

[ QUOTE ]

First, you move this all the way down here, then you state the "obvious"


Yet you still seemed to find it! A tribute to either your dilligence or megalomania.

[/ QUOTE ]

well, I had to go hunting to find where you'd moved this from... so I'm claiming diligence.

[ QUOTE ]


Reread Paul's post, that my reply was originally to, then reinterpret "possible" as something other than the mathematically possible but incredibly tiny mathematical chance of that happening.


I understood it the first time, thanks. I stated the obvious because it seemed you weren't grasping it completely. If you were asking what the likelyhood of seeing 1,000,000 heads in 1,000,000 flips is, I imagine you could do that math yourself fairly easily.

If you were asking what a "reasonable" number of consecutive heads would be, you'd have to define reasonable first. If you said a 1 in 100 likelyhood was reasonable enough, then it's around 7 in a row.

[/ QUOTE ]

That was the original point of my QUESTION (well, one point anyway)


Okay, let's be specific about what was actually intended before you have me pictured, drooling in the corner, playing with my toes (I save that for Friday nights)

<font color="red">If you knew you weren't being set up or hustled somehow and saw a coin flipped the same way fifty times in a row, wouldn't you be willing to give some pretty freaking long odds that it's going the same way next time too? I should hope so! </font>

Which led to this "rebuttal" by Mr Megalomania

<font color="blue"> if a coin flip is 50:50, how long of a streak of consecutive heads would you have to see (when you have no direct reason to suspect a rigged coin or toss) before you would ignore the 50:50 probability and bet on the ongoing streak by laying "pretty freaking long odds" on heads on the next toss, or series of tosses?

How long a streak is so long as to be considered almost impossible to occur? And therefore it can be discounted?

Or, in other words- what is the longest "possible" consecutive heads result in a series of 1,000,000 coin flips? </font>

See, possible was in quotes for a reason...

[Easy E]

I'm glad SOMEONE truly gets it! I was worried about myself there for a while.

However, your reasoning is a bit off:
[ QUOTE ]

I guess DH shouldn't even bother to enter the next WSOP. This is because his success in the past two WSOP's means that he has 'used-up' his good luck and now HAS to finish below average in order to 'balance-out' his results.

[/ QUOTE ]

No, if Dan wants to win one, or get to the final table again, he's forced to get some of his losses out of the way. Besides, I may be wrong and he's actually only 50:1 to get to the final table again- so it could happen much sooner than expected!
I'm still not sure if burning up some losses in WPT events actually works or not- more research is needed.

[ QUOTE ]
Since some cosmic force was looking out for DH in the past two he needs to get out while he can because the evil-karma is now out to get him.

[/ QUOTE ]

See, now you're confusing me! This absolutely brilliant deduction doesn't gibe with your confused logic in the first part. Maybe you're bipolar... tell the other half to stop screwing up in the "3+1" picks!

[Smasharoo]

I see. You more asking Paul what his definition of "reasonable" would be. Poor reading comprehention skills on my part, likely. What I get for four tabling and reading forums.

[Easy E]

And yet, that's what I am arguing to a certain extent.

<font color="blue"> It's like saying that a player with an expectation of 2 BB/100 who has won 3 BB/100 over his last 1000 hands should expect to win at a rate of 1 BB/100 over his next 1000. The player's expectation is still 2 BB/100. Note that if the player wins 2 BB/100 over his next 1000 hands, then he has won 2.5 BB/100 over his last 2000 hands </font>

Okay, how did we get to the certainty that this player's "expectation is still 2 BB/100"? Unless s/he is the world's most freakishly consistant player, winning exactly 0.02 bets in cash on every single hand, expectation is based on an average of their results . Therefore, this 2BB expectation is based on 1 BB/100 streaks and 3 BB/100 streaks and -5BB/100 streaks and so on, combining in their results over time. THIS is what allows us to declare them a "2 BB/100 expectation player."

If we are saying that "The player's expectation is still 2 BB/100" as a central truth to this- this player isn't really a 2.5 BB/100 or 1.75 BB /100 player, with skewed short-term results now- then that 2 BB/100 value is essentially a <font color="green">
"mean (mn)
n.

1)Something having a position, quality, or condition midway between extremes; a medium.
2) A number that typifies a set of numbers, such as a geometric mean or an arithmetic mean. "

"arithmetic mean
n.
The value obtained by dividing the sum of a set of quantities by the number of quantities in the set. Also called average." </font>

If I expect to win 1 out of a thousand times and I can somehow treat this as a hard valid number , then shouldn't I expect a large number of losses pretty soon?

Call it gambler's fallacy if you'd like (the "Easy E effect" has a nice ring to it) but:

a) given that streaks have no proven predictability power if we assume our initial BB mean is fairly accurate and not in flux
b) I'd be willing to gamble and give slightly greater odds on short-term future results with a stop-loss (before y'all start salivating again!) based on my knowledge of recent events.

Specifically, I'd bet at 10% worse odds than normal that Dan Harrington wouldn't make the final table in the 2005 $10K, based partially on the fact that he's been to the last two (along with a whole host of other factors). And, if you'd read my other posts in this thread in a similar vein, you will remember this:
<font color="red"> "And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it. " </font> because I'm willing to gamble in a limited manner on this fallacy of regression to the (estimated) mean.

[b]<font color="orange">[i] This, of course, opens the resulting corollary- If Action Dan DOES get to the final table in 2005.... then forget all about "Jesus"- Dan H is the god of tournament poker!

[daryn]

easy e, didn't you have a "craps system" before? was that you or another guy? that was a pretty funny thread, but then i realized you were serious /images/graemlins/frown.gif

[maurile]

[ QUOTE ]
And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.

[/ QUOTE ]
This is a tangent, but . . . if you know you'd be taking the worst of it, why would you gamble on it?

Lots of people knowingly take the worst of it all the time. Walk into any casino and look at how many people are playing slots, craps, or roulette. They know it's a bad bet, but they do it anyway. And thank god -- because if nobody was willing to take the worst of it in poker, the rest of us would be unable to make any money at it.

It just strikes me as odd that a 2+2er would knowingly take the worst of a bet.

On the other hand, TJ Cloutier is well known for enjoying craps. I believe Phil Ivey also plays craps. Stu Unger and Doyle Brunson both apparently took the worst of it on golf bets quite often. All of these people understand the odds inside and out, so they knew they were making -EV bets.

Is it just a psychological urge to gamble? Would you bet on tails in your example just for fun? Wouldn't it be more fun to find a +EV wager instead of taking a -EV wager?

[Easy E]

"craps system" is not a term that lives up to the glory that is "Easy E: All Crap(s), All the time"

One of these days I'll enlighten you all...

[Easy E]

regression toward the mean

n : the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x)

[MaxPower]

Regression toward the mean is really a group phenomenon, you can't really apply it to a particular person.

[Easy E]

Maybe I'm Gus Hansen's long-lost blood relative or something..

[ QUOTE ]
And yes, I know I'd be taking the worst of this bet... and I'd still gamble on it.
This is a tangent, but . . . if you know you'd be taking the worst of it, why would you gamble on it?

[/ QUOTE ]

dictionary.com is getting a workout today!
<font color="green">gam·ble v. gam·bled, gam·bling, gam·bles
v. intr.

To bet on an uncertain outcome, as of a contest.
To play a game of chance for stakes.
<font color="red">To take a risk in the hope of gaining an advantage or a benefit. </font>
To engage in reckless or hazardous behavior </font>

[ QUOTE ]
It just strikes me as odd that a 2+2er would knowingly take the worst of a bet.

[/ QUOTE ]

Who wants to be a robot? Besides, I'm gambling on gambler's fallacy- always a +EV move!

[ QUOTE ]
All of these people understand the odds inside and out, so they knew they were making -EV bets.

Is it just a psychological urge to gamble? Would you bet on tails in your example just for fun? Wouldn't it be more fun to find a +EV wager instead of taking a -EV wager?

[/ QUOTE ]

That explains why I don't do much but play poker these days.

But the basic premise behind my willingness to make these less-than-optimal bets (Dan H, 50 consecutive heads) is that I'm gambling that I'm more "likely" to win than I should be, given recent history that's extremely unusual.

[CardCuda]

* dan harrington made the final table of the two largest fields in big buyin tournament history, on top of having won the wsop a decade prior. What are his chances of making the final table in 2005, assuming a field of 5000? Say final 10 to simplify the math. The exactly average player's chances are 1/500. What are dan's?

Dan has the same chances 1/500 to make the final table (final 10 assuming 5000 players).

* I'll let you pick some number of players. If a single one of those players wins a bracelet at the 2005 WSOP, you win the bet. How many players do you need to list before you are a favorite in this bet?

Say 5000 players, I’d have to list 2501 to have an advantage…. or 100 players, I’d have to list 51.

* How much positive equity does the very best player have in whichever currently existing $5K+ tournament you believe has the weakest field? Ignore juice. The exactly average player gets paid back his $X buyin on average. How good is the best? 3X? 5X? 10X? 20X? More?

$X buyin on average is your “mean” expectation. You have 0 positive equity. (I confess I have no idea…but that’s my answer.


* Two tournament players each play 100 large field tournaments. In the end, player A has averaged a profit of 0.5 buyins/tournament and player B has averaged 1.5 buyins/tournament. With what percentage confidence can you say that player B was actually playing with higher EV than player A? Alternately: what line would you place on player B winning more than A over the next 100 tournaments as well? What if B had averaged 3 buyins per tournament?

Percentage of confidence = 0%

MY line = 50/50

With 3 buy-ins per tournament for player B, what did player A average for buy in’s? assuming Player B = 3 and Player A = 1 – I’d venture to say that would be a 3/1 advantage for each tournament. Again I have no idea…but there’s my answer.

Disclaimer: I am the furthest away you can get from a math wiz....I suck at math. These are "common sense" driven... or applied with the simplest thought answers. Flame away.

[eamato]

the math to this question is quit sound but the problem i have is the diminishing value to ability or skill.

lets take it out of the poker world. if 5000 random people have a chance to hit 1 pitch for a home run who do you bet on? The experience of that person factors in to their ability to not only make contact but to do so when the pitch is bad or not in their favor.

the cards and or pitch will never be the same for all and therefore, how you handle each pitch or cards will effect your outcome.

i have read many interesting posts and this is my first reply

[srblan]

That's the logic that casinos were hoping people will use when they put up the board that keeps track of the last N roulette numbers to come up. If 9 hasn't come up in 20 spins, it must be "due". It is still an independent trial.

[MicroBob]

I was being sarcastic.
I honestly can't tell whether you are bein serious or not though. Perhaps that's my own fault.

[Moozh]

[ QUOTE ]
Okay, how did we get to the certainty that this player's "expectation is still 2 BB/100"? Unless s/he is the world's most freakishly consistant player, winning exactly 0.02 bets in cash on every single hand, expectation is based on an average of their results . Therefore, this 2BB expectation is based on 1 BB/100 streaks and 3 BB/100 streaks and -5BB/100 streaks and so on, combining in their results over time. THIS is what allows us to declare them a "2 BB/100 expectation player."

[/ QUOTE ]

If a solid 2BB/100 player is running at 3BB/100 for 1000 hands, he does not need to experience an 'expected' 1BB/100 1k hand streak to stay on his mean.

The reason you need to look at the long term in the statistics of random numbers is not because over time there will be high and low swings that even each other out. Rather, the longer the player plays, the smaller the swings will be in relation to the number of hands played.

For example, if a 2BB/10 player has a 30BB/1000 spike and then continues to play solid 2BB/100 poker for another 10k hands (without any major swings), he will improve only a 2.1BB/100 rate. The longer he plays, the close his real world rate will asymptotically approach to his true rate.

Thus, a single spike is not balanced by a spike of exactly the same magnitude in the opposite direction. Instead, it is balanced by a larger sample size at the true mean.

Looking for a downswing immediately after an upswing is plain wrong. In fact, since an upswing is more likely when the observed average is below the true rate, it is more likely that the player's true average is higher than previously expected.

[Easy E]

According to Paul, you read it correctly and I didn't.

Bobbo 1-0!
<font color=" blue"> I thought this obviously meant win a bracelet in any event. That's why it says "win a bracelet", not "win the main event." Read for context; I do try to choose my words carefully.