bigplayer said:
The other two questions about EV are very interesting ones...97.5% chance of at least 50% of EV and 97.5% chance of at least 100% of EV. You should post these over on BJ21 and see if one of the theoreticians can give an answer.
For 50% of EV or better, the number of hands works required for some specified chance of doing that well or better works out to:
hands = 4 * N0 * Z^2
For a 97.5% chance, the Z statistic is about 1.96, so the number of hands required to have a 97.5% chance of being at or above 50% of your EV is about 15.4*N0, or using N0=18000 hands (as you used previously), it would require 276,600 hands.
For the question on being at or ahead of 100% of your EV, there is no solution. As soon as you have a sufficiently large number of trials for the results to behave normally, you'll always have a 50/50 chance of being above or below your EV. In effect, as you ask the question about numbers closer and closer to 100% of EV, the number of hands required approaches infinity. For illustration, the number of hands required to have a 97.5% chance of being at or above X% of your EV are:
50% 276,600
60% 432,200
70% 768,300
80% 1,729,000
90% 6,915,000
95% 27,660,000
98% 172,900,000
99% 691,500,000