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?