chabibi
02-10-2005, 11:13 PM
I constantly read posts about win rates, standard deviations and confidence intervals. Most seem to agree that a big sample size is important, but some of the more experienced players seem to think that the mathematical evidence for true win rates in smaller sample sizes is inaccurate. I may be in way over my head here but this is what I was thinking,
The sd of bets is affected by the betting style of the player. When calculating a CI for a relatively small sample size only the sd of the betting style is taken in to account, but the distribution of the hands is ignored. The true win rate is a function of both the betting style and the quality of cards that a player receives. Theoretically couldn’t you set up a model with two explanatory variables, one with the sd involved with the playing style of a given player and the other with the sd of the hands he has received. The second variable would account for the type of hands that player has seen over his sample size. This way you could attribute how much of the win rate is due to the person’s skill and how much is due to running hot or cold.
You could also use several variables for the specific hands (i.e. pairs, two pairs, flushes etc…) to be even more accurate. By including the deviation for the expected mean times that you should receive certain hands for that sample you can know exactly how hot or cold your running and adjust your expected win rate accordingly now as the sample size increases, the overall quality of cards dealt evens off and plays less of a role in determining the true win rate so when the sample size is large this variable can be ignored. Hence the error in smaller sample sizes
The sd of bets is affected by the betting style of the player. When calculating a CI for a relatively small sample size only the sd of the betting style is taken in to account, but the distribution of the hands is ignored. The true win rate is a function of both the betting style and the quality of cards that a player receives. Theoretically couldn’t you set up a model with two explanatory variables, one with the sd involved with the playing style of a given player and the other with the sd of the hands he has received. The second variable would account for the type of hands that player has seen over his sample size. This way you could attribute how much of the win rate is due to the person’s skill and how much is due to running hot or cold.
You could also use several variables for the specific hands (i.e. pairs, two pairs, flushes etc…) to be even more accurate. By including the deviation for the expected mean times that you should receive certain hands for that sample you can know exactly how hot or cold your running and adjust your expected win rate accordingly now as the sample size increases, the overall quality of cards dealt evens off and plays less of a role in determining the true win rate so when the sample size is large this variable can be ignored. Hence the error in smaller sample sizes