Variance of a poker tournament
This is just an indepedent project I'm working on because I think it's fun.
Suppose we have a 9-man poker tournament. Buy in is 6.50, payouts go to 1st, 2nd and 3rd place like such
1st - 27
2nd - 16.20
3rd - 10.80
We have a player who plays n of these tournaments, and has some distribution of finishes
1st - x%
2nd - y%
3rd - z%
out of the money = 1-x-y-z = oom
To calculate profit per tournament (PPT), we would just take 27x +16.2y+10.8z-6.5
Return on Investment (ROI) is another statistic of importance, and is equal to PPT/(Buy-in), so in this case PPT/6.5
How can we find the variance of PPT and ROI? This step I feel like I know how to do, but just want to double check. Once we do find the variance of PPT and ROI, can we build confidence intervals for them?