Quote:
Originally Posted by statmanhal
Assume you have sample data that indicates you have a positive win rate of W/100 with a standard deviation of S/100. To determine what sample size you need to assure with a specified confidence that you are a winning player, you can use the following formula:
N =100*( Zc*S / W)^2
where Zc is the normal distribution factor corresponding to a one-sided C% confidence interval: Z80 = 0.84, Z90 = 1.28, Z95 = 1.645. Note that N increases with C and S, and decreases with W.
Example: You have an estimated win rate of 5 per 100 hands with a corresponding standard deviation of 75/100. To be 80% confident you are a winning player,
N = 100*(0.84*75 / 5)^2 = 15,876.
For C=90%, N = 37,000 (approx.) and N = 61,000 for 95% confidence.
The above assumes your win rate is distributed normally (valid by the Central Limit Theorem) and that your win rate and standard deviation are relatively constant over the sample period. If your win rate is not constant but is increasing, then the sample size result can be considered to be conservative.- i.e., it is more than you need.
Ok so 5BBs/100 with sd of 75, that's 15,876 hands to be 80% sure I'm a winning player. That's over 500 hours if I play live at 30/hands per hour, which would be over 3 months of play playing 40 hours/week every week. (Note - I have a normal full time job, not planning on changing to poker, just trying to put this into perspective.).
Am I correct in assuming that this also means that for those values, I would be down 20% of the time for any given 3 month stretch?
Fwiw, my winrate *seems* to be much much higher than this (playing live 2/5), and my SD is probably a lot higher too (I'm very often up or down 100BBs from one hour to the next - so if my SD is like 100BBs/hour or 100BBs/30 hands, then that should be like 100*sqrt(3.33)/100 hands right? Or ~180/100 hands. Maybe that's an overestimate though). But I've only recently started logging my sessions - and it's only 12 sessions for 102 total hours, so probably much too soon to try to start calculating these stats.
How many sessions would it take to have a good idea of my SD/hour? (I saw another post here, i think by BruceZ where he showed how to calculate SD per hour given only session totals - but I don't know what the standard error in this SD calculation would be).