Are Winrates Normally Distributed?

[Justin A]

Nice work Max, thanks a lot.

[ QUOTE ]
So if I play 20,000 hands and my BB/100 is 1.5, I know that the sampling distribution for samples of that size is normally distributed.

[/ QUOTE ]

Don't the numbers you posted indicate that this is not the case? Sampling distributions are going to approximate normal with n sufficiently large. What your numbers seem to show is that n=100 is not large enough.

Correct me if I'm wrong, but you've shown that the sampling distribution for bb/100 is decidedly not normal. What I want to know is how does this affect confidence intervals?

[MaxPower]

[ QUOTE ]
Nice work Max, thanks a lot.

[ QUOTE ]
So if I play 20,000 hands and my BB/100 is 1.5, I know that the sampling distribution for samples of that size is normally distributed.

[/ QUOTE ]

Don't the numbers you posted indicate that this is not the case? Sampling distributions are going to approximate normal with n sufficiently large. What your numbers seem to show is that n=100 is not large enough.

Correct me if I'm wrong, but you've shown that the sampling distribution for bb/100 is decidedly not normal. What I want to know is how does this affect confidence intervals?

[/ QUOTE ]

If your BB/100 is based on exactly 100 hands, then the sampling distribution is not normal. If it based on thousands of hands, then it will be.

The BB/100 is just a measure, don't get hung up on it. We can measure height in feet, inches, centimeters, etc. Regardless of the units we use your height stays the same and the distribution stays the same.

[MaxPower]

[ QUOTE ]
Nice work Max, thanks a lot.

[ QUOTE ]
So if I play 20,000 hands and my BB/100 is 1.5, I know that the sampling distribution for samples of that size is normally distributed.

[/ QUOTE ]

Don't the numbers you posted indicate that this is not the case? Sampling distributions are going to approximate normal with n sufficiently large. What your numbers seem to show is that n=100 is not large enough.

Correct me if I'm wrong, but you've shown that the sampling distribution for bb/100 is decidedly not normal. What I want to know is how does this affect confidence intervals?

[/ QUOTE ]

There is no such thing as sampling distribution for BB/100 (the measure), only a sampling distribution for samples of size X (in this case, 100). If I did the same analysis using BB/hand or BB/1000 or bb/21, I would find the exact same results.

[MaxPower]

[ QUOTE ]
from looking at the q-q plot, it seems that the upper tail of the poker data is fatter than the gaussian, and the lower is thinner. shouldn't this result in large downswings happening less often than a normal assumption would predict?

i need to spend some more time thinking about this, the repetition of trials inherent in poker makes this more complicated than a standard VaR calculation.

[/ QUOTE ]

These are based on 100 hand samples, so in order win a lot or lose a lot you probably need to play some big pots. Typically , you win more bets when you take down a big pot than you lose bets when you lose a big pot (I am talking about multiway pots here). So the big wins should be bigger than the big losses.

This has got me curious. I will run another one using a very large sample size and see what it looks like.

[stinkypete]

[ QUOTE ]
from looking at the q-q plot, it seems that the upper tail of the poker data is fatter than the gaussian, and the lower is thinner. shouldn't this result in large downswings happening less often than a normal assumption would predict?

[/ QUOTE ]

yes, but not really. what it really suggests is that really bad 100-hand stretches would happen less often than a normal distribution would predict. big downswings occur over 10,000 or more hands, and the sample size should reflect that if you want to know how likely big downswings are. over that many hands though, it should be very very close to a normal distribution, considering that this is quite close as well (even though everyone's saying it's not for some reason... just look at the damn graph, it's pretty close).

anyway, i say "yes, but not really" because the chart with 10,000 samples should be shaped somewhere between this and a normal distribution. it should differ from a normal distribution in the same way, though not by nearly as much. (someone correct me if i've misunderstood on this)

on the other hand, while the shape suggests that really terrible downswings should happen less than in a normal distribution, it also suggests that pain-in-the-ass break-even streaks should be longer on average than a normal distribution suggests, since that's what will happen when you don't get any of those rare, winrate boosting surges that are illustrated on the far right of the graph. you can see this by noting that the graph is "fatter" on the left side of the mean than the right side (the bars near the mean are above the normal on the left side, and below the normal on the right side).

edited some errors. i dont know why i can't type what i'm thinking the first time.

[BillC]

I think the way this excellent line research will show is that BB/100 is both:

-approximately normal, but
-signifigantly different than normal.