The Law of Averages and Poker

[Aver-aging]

I've got a question, relating not to odds while playing poker, but how variance can effect people on the individual level.

In the Boston Museum of Science they've got this display (well I don't know if its still there or not), but it shows how the law of averages predict that full systems of probability shape themselves to a bell curve. It has balls that fall randomly on the middle of a pegged board, and each ball has a 50/50 chance of either going left or right on the peg, and naturally over the course of time, the balls are mainly congregated near the center, and spread thinly more and more so the farther from the middle they get.

Anyways, I was comparing this experiment to a field of poker players over the course of their playing career. Each poker player would be like a ball dropped on the pegged board. The pegged board representing a scale of variance (the left would be people with consistent negative results due to misfortunes of fate, the center being those people who have 'average' rates of forture and misfortune, and the right being those people who have great positive results due consistent fortunate occurences.

Now, my concern is that I always hear people say "Don't worry, your luck will change, it all balances out". But my question is, does it really for everyone? Naturally wouldn't someone - even someone who may be a great player - be subject to a fate of constant failures, even for as long as their career? Isn't it possible that some people are just luckier than other people? Most of us would fall into the average, but that still leaves alot of people who could just be overall luckier in the long run than others. So, doesn't luck actually exist? Someone has to fall on the negative end of the bell curve, and some people have to fall on the positive end. So does some unlucky bastard out there actually have fate working against him at every turn? Or am I over-looking something?

[drbst]

I think you are totally right.

In statistics however, we cannot predict the fate of an individual, we can only make predictions about the attributes of groups of individuals. Therefore, as long as there is no other information we assume that the "luck" is equally distributed. We know that some individuals will be more lucky than others but we cannot say which one the lucky guy is.

It is well known that smoking causes statistics and other things, so let me give you an example. Although we know that the EV of life time for smokers is like 15 years shorter than for non-smokers, you will find in a group of 10,000 smokers one or the other which may get 90 years old or even older. I hope you agree that it would be not reasonable to start smoking just because you know one smoker who got 90 years old if you want to maximize your EV for life time. Even if we don't know if smoking would kill you 15 years before your time, we still say that it will kill you 15 years earlier and we leave out the words "on average".

[Aver-aging]

Oh yes, I by no means meant to say that we can predict who will be more lucky, it was more or less just an observation that some people are indeed luckier than others, and that occasionally a few small number of people will be doomed to fall on the negative end of the bell curve, making all their gambling pursuits virtually useless.

It was just meant as a comment against the typical notion that we 'all have the same luck', when in reality, we don't. Most of us have similar luck, but it definitely is not the same, and some few are subject to be drastically luckier or unluckier than the rest of us. I just find it interesting that the 'myth' of luck is actually provable thanks to the laws of probability. All my gambling education has drilled into my head that everyone is equally lucky over the course of time, and you'll read that and hear that from every professional gambler, often even from ones who are experts in probability. I just find it odd that people are over-looking this fact so much.

[MathEconomist]

You're thinking about this the wrong way. No player is "doomed" to have below average luck. Some people have had below average luck, in some cases way below average. However, their expectation for future luck is the same as everyone else's. There are no lucky or unlucky people, only people who HAVE BEEN lucky or unlucky.

Thus, it is correct to tell people not to worry about the luck because they should expect average luck in the future whatever has happened in the past. Some of those who have been unlucky will continue to be unlucky, but it will be the exact same proportion getting unlucky as the proportion of people who have been very lucky getting unlucky (as the sample sizes get large).

Beyond that though, over a reasonable number of hands, it is exceedingly likely your luck has been reasonably close to average. If all you know is that over the past, say, million hands you're losing 2BB/100, the probability that you're actually a losing player is huge, and the probability that you're a winning player who has gotten unlucky is miniscule. For practical purposes, you should generally make inferences about your play and decisions as though luck doesn't exist provided you have a reasonable sample.

[AaronBrown]

Of course people are not equally lucky. Some are born wealthy, powerful, smart, good-looking, loved and free. Others die painful and horrible deaths before they learn to talk.

But while people tend to underestimate the amount of luck in life, attributing success to skill and criticizing miserable people for causing their own problems, they also tend to overestimate it in gambling. Over 10,000 fair independent coin flips, you'll amost certainly be within a few percent of 5,000 heads. Over 10,000 poker hands, you'll get your fair share of good and bad cards.

[drbst]

If we consider for example Hold'em players drawing for a flush at the river then there will be some who make the flush much more often than average and others who make the flush much less than average (me for example).

Knowing that, should I adjust the required pot odds when I am drawing for a flush? No, of course not. But that does not mean that the gap between the luckies flush drawer in the world and the unluckiest one is not getting larger and larger.

[Aver-aging]

You guys are completely missing the point of my post.

I'm not saying that this should affect anyone's game, and I'm not saying that you can adapt to this.

What I am saying though, is that through taking a large sample of equally skilled players, and let's say, running an experiment with fixed time (like 35 years - a full career), the whole group of players will eventually succumb to the law of averages, where the majority of players will have balanced luck, but a small proportion of the players will have experienced much more favorable, and likewise a proportion equal to that would have experienced very unfavorable conditions.

Now, what I'm saying is that at the begginning of the people's career who inevitably succumb to being on the negative end of the bell curve after the 35 years were doomed practically from the start from being a losing player. Did they have any way of predicting that? No. Did they have any way of adapting to that? No. Should that in anyway effect the way they play? No. Should that allow them to predict the future? No. Regardless though, they ended up being a loser solely due to the fact that someone has to end up on that side of the bell curve, and it was unfortunate for them that they had to be the person to be there.

However, what I am saying is this - that even making a choice (and this is what I'm talking about - the choice of beginning to gamble) to play poker, you are entering the ultimate crapshoot. You don't know where you're going to end up on the bell curve of players after the long run. For all you know you could be in the small 0.1% group of all players who will lose a larger majority of the time than 99.9% of every other player - putting you at a drastic disadvantage. Even being someone who is in the bottom 30% of the bell curve will suffer a drastic disadvantage. So there's one variable that you have absolutely no control of - regardless of how well you play, regardless of how much you're ahead in every hand you're in, regardless of every factor associating the actual game. You just might end up on the wrong part of the bell curve when its all over and done.

I don't know. My main concern is that most people who educate themselves on poker don't even know about this phenomenon, and it does affect a large number of people who play - albeit a drastic minority of players.

[MathEconomist]

[ QUOTE ]
and it does affect a large number of people who play

[/ QUOTE ]

No. Use the CLT and think about the probability of being even .25BB/100 (not enough to turn all but the most marginal winners into losers) away from your average after 10 million hands given a reasonable variance. Now think that even 10 million hands isn't THAT many hands with internet poker. The kind of bad luck over a career that you're talking about is not really a problem.

It is true that as the number of people playing poker goes to infinity, some are guaranteed to be much much worse than average in luck over even large finite samples of hands for each player. But over a lifetime of hands, the distribution of your BB/100 is centered very very very very tightly around the true value, which means that the number of players you'd need before you start expecting some people to experience really meaningful deviations from their average over their entire lifetime is huge, particularly given that in the age of internet poker people can play really HUGE numbers of hands.

[Aver-aging]

I think I sort of understand. It would be interesting to see the bell curve for an entire website, and see some actual results. I wonder if any internet websites are even capable of tracking statistics like that, though. Probably not.

[Nottom]

FWIW, you have a very valid point, but the main problem is that no one is forcing someone to keep playing when they lose.

If the best poker player of all time (obviously he doesn't know this) sat down and got crushed the first 10 times he played poker despite playing flawlessly, its unlikely hes going to keep trying. On the other hand there are probably quite a few players running a couple SDs above their skill level over some significant lengths of time, particularly in live tourney play. Who knows which ones they are, but its very possible some of the big names fall into this category.