PTO QUESTION

[poet]

Just got PTO and was wondering how many hands you need to get a realistic view on how you are doing. 50000? thanks

[beset7]

Millions.

150k might give you a nice peak at something close to your true win rate.

A good book to read to help understand win rates, standard deviations, confidence levels, etc is Gambling Theory and Other Topics by Malmuth.

The best way to think about this question is to consider confidence intervals. You construct these intervals around your sample winrate (read: the winrate you have after X number of hands), and they tell you what the chance is that the constructed interval actually contains your *true* winrate. For example, a 95% confidence interval (most commonly used) tells you that there is a 95% chance that this interval contains your true winrate, and is calculated by the formula:

sample win rate +/- 2*SD/sqrt(X/100)

where 2 comes from the normal distribution (95% density contains ~2 std dev's either direction from the mean), X/100 comes from the fact that your winrate is reported in BB/100 hands, and SD is the standard deviation in win rate (sessions tab, details sub-tab, listed there).

For example, my SD is about 65 BB/100 for PLO8. This means that after 50k hands, a confidence interval around my winrate has a range of:

4*65/sqrt(500) = 10.75 BB/100

More explicitly, if my winrate over those 50k hands is 10 BB/100, then the 95% CI is [4.625 BB/100, 15.375 BB/100]; there is a 95% chance that my true win rate falls in this interval.

As you can see, 50k hands doesn't give you that firm of an idea of your true win rate, assuming you have a comparable SD. At other hand samples, the ranges are:

100k: 8.2 BB/100
150k: 6.2 BB/100
200k: 5.4 BB/100
250k: 4.8 BB/100

So even after a quarter million hands, I only "know" my winrate to within a few BB/100.

What does this mean? A couple things:

1) there are diminishing returns to increasing sample size when it comes to pinpointing your true winrate
2) people love to toss around figures like 150k, or 200k; in fact, it's a matter of opinion (or what degree of certainty you personally want to have), and really people should just be talking about these things in raw statistics like CI's...
3) the short term is much, much longer than most people realize; in fact, a reasonable "long term" is *so* long that it's pretty difficult to believe the assumption that your playing style remains constant over that length of time, which is implicit in this analysis

--> most discussion of winrate, and self-evaluation based therein, needs to be taken w/ a grain of salt



As an aside, statisticians generally use CI's and the like to judge statistical significance. If they are testing the hypothesis that a given player's winrate is zero (that is, that the player is a breakeven player), then in order to *reject* this hypothesis--that is, to declare the player to be a statistically significant winning (or losing) player--then the 95% CI cannot contain the value zero. If someone tells you they win at 3 BB/100 after 50k hands, and you ask them for their SD and calculate a 95% CI that is something like [-1, 7], then no statistician would be willing to admit that this player is statistically different from a break-even player.