Are Winrates Normally Distributed?

[Chobohoya]

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i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up

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Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts.

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It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be.

[Derek123]

This would suggest that winrates are not normally distributed, which would mean you are more likely to run good but the bad runs will be worse.


This sentence seems backwards to me. If it is skewed to the left, there are more instances of bad, but the few big wins make up for it.

[felson]

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i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up

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Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts.

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It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be.

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If Josh wins his first hand and quits immediately, then plays again later, then will the hands from his second session be put in the same block as his first hand?

If so, then it doesn't matter if Josh locks up his wins.

If Josh's one hand forms its own block, then that's different -- but I don't think that's what is happening.

[sam h]

This is a cool idea.

I don't know about the conclusions, though, as the distributions look pretty normal to me. The variance is pretty high, so even with a lot of observations its not that surprising to see things look kind of choppy.

Another suggestion to redo the graphs using the same number of "bins" (divisions for bars) in each histogram. You have a lot more bins in the first couple, which makes things look slower to converge on a normal than they probably are.

I think something might be wrong with your BB/100 histogram. It doesn't look like there are 1500 observations there.

[UprightCreature]

For the reason PTjvs states the winrate for one hand should not be normally distributed. There is an interesting fact though, that is the distribution of groups of a samples from a non-normal distribution aproach normal as the size of the group increases (Central Limit Theorem). Eg. winrate/1000 will be more normal than winrate /10.

[disjunction]

http://forumserver.twoplustwo.com/showth...rue#Post3134879

Also there is no reason that I know of to believe that winrates are normally distributed. The normal distribution is a hammer but not every problem is a nail.

Edit: Also I forgot to say in the linked post that a bad table or a bad seat, rather than bad play, can be "Mr. Hyde".

[Chobohoya]

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Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts.

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It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be.

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If Josh wins his first hand and quits immediately, then plays again later, then will the hands from his second session be put in the same block as his first hand?

If so, then it doesn't matter if Josh locks up his wins.

If Josh's one hand forms its own block, then that's different -- but I don't think that's what is happening.

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Ok you're right about that. However, what I think Astro was getting at and I know I was, is that people play longer when they are losing. Over a large sample, this is going to mean that you play more hands when you: have a worse image, a tougher table, less confidence, etc. If you put more hours in with a lesser expectation, you move your curve to the left. If you practice excellent game selection without regard to your immediate results (aka don't tilt - just like you said) then your point stands. Many people do not do this.

[Justin A]

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This would suggest that winrates are not normally distributed, which would mean you are more likely to run good but the bad runs will be worse.


This sentence seems backwards to me. If it is skewed to the left, there are more instances of bad, but the few big wins make up for it.

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Yeah you're right. I think Josh got it mixed up.

In an extreme sense, it's like we're usually treading water with a few really good runs in between that makes our results better.

[MarkD]

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In an extreme sense, it's like we're usually treading water with a few really good runs in between that makes our results better.

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LOL, this is funny because this quote seems to very accurately describe my experience at poker. Nice big bursts between periods of losing or breaking even.

Hi Josh,

I'll take a stab at addressing a few points.

The fundamental Random Variable in poker is the amount of money you win on one hand. This random variable has a distribution, which is certainly not Guassian.
First off, it's a discrete random variable. The mean is your winrate per hand. The max value values it can take are +12BB and -12BB (on Party Poker). The most probable event is 0, since you fold most hands.
Other frequently occurring values are -0.50BB and -0.25BB since these are the values you lose when you fold your blinds, and maybe -1.5BB since this is how much you lose when you raise pre-flop, completely blank the flop, bet the flop, and get raised.

So we get a sense of what the probability mass function of this random variable looks like: It's centered at your winrate (say .02bb) but its peak value is at 0. Then it has smaller peaks at popularly occuring values, such as -0.50BB, -0.25BB, etc. It is, obviously, not a normal distribution.

The Central Limit Theorem tells us that if we ADD together enough of these strange random variables, the sum, regarded as a random variable, must start looking more and more Guassian.

In your charts, when you group together a string of hands, you are adding all the random variable in each group, and this sum should starting looking Guassian the larger the group is (BB/1000 should look more Guassian than BB/10). With a 150k hand sample, I don't think you have enough hands to get a graph that shows this, since if you went to, say, BB/1000, you would only have 150 sample points. But I'm pretty sure that at some point, it would look like a nice bell-shaped curve.

Edit: You can start to see at BB/50 how the graph is looking more Guassian. Below BB/50 you have the nice feature that you have many smaple points. BUT each sample point is not yet being taken from a very Guassian distribution. Above BB/50 (BB/100 and up), you have the nice feature that the samples are being taken from a pretty Guassian distribution, BUT you don't have enough samples to draw the curve. If your DB was much larger, I think you would see the BB/100 look much closer to Guassian than the BB/50.

-v