On the website Wizard of Odds I entered the pay table for a video poker game and it gave me the expected return and variance, which were 1.07 and 13.8 respectively. As it's been a while since I took stats, I was wondering how I would figure out the expected value and variance if I played, say, 100 games bidding 10 each time.
Thanks
The return is payout divided by 10. Write the returns $R_1,R_2,\ldots, R_{100}.$ The realized average return is $$\bar R = \frac{R_1+R_2+\ldots +R_n}{100}$$ and the realized variance is $$ \frac{(R_1-\bar R)^2+(R_2-\bar R)^2+\ldots +(R_{100}-\bar R)^2}{100-1}.$$
A spreadsheet is probably your best bet, in which case you can probably use built in functions to compute these.
Note that the variance is very noisy, and presumably mostly comes from hitting the jackpot, so don't expect it to be even close from playing 100 hands. Depending on where your edge is coming from, the return may be very noisy as well. In any event, I would expect a lot of it to come from fairly rare hands and for 100 hands not to be enough.
(This is purely an explanation of the math and is contingent on the odds you see being 'right' and all the niceties of optimal play... not an endorsement of sinking a lot of money into this.)