How long will u need to play to ensure a positive return

[bigfonzy]

Hi guys. My math skills need some serious work. I was wondering if someone might be able to help me out with the formula for determining how many hours would you would need to play to ensure a 97.5% chance of a positive return on a hypothetical example of a player with a win rate of 20 ph and a SD of 100 ph. Any help would be much appreciated.

Cheers!

Fonzy

[Precision1C]

For simplicity I am going to use 3X std deviation for simplicity which will give you a 99.9+% chance of a gain.
F(N) is the lower bound of loss for a given number, N, hands.

F(N)= 20*N - 3*100*(N)^.5

By setting F(N) to zero you will find out at what value of N your EV finally outweighs standard deviation.

0=20N-300(N)^.5

N^.5=15 and N=225. So after 225 you have a 99.9+% chance to be positive assuming that the assumption about your EV is correct.

[BruceZ]

[ QUOTE ]
Hi guys. My math skills need some serious work. I was wondering if someone might be able to help me out with the formula for determining how many hours would you would need to play to ensure a 97.5% chance of a positive return on a hypothetical example of a player with a win rate of 20 ph and a SD of 100 ph. Any help would be much appreciated.

Cheers!

Fonzy

[/ QUOTE ]

97.5% is about 1.96 standard deviations 1-sided, so time to break even is
(1.96*100/20)^2 = 96 hours.