If it's actually a fair game, then martingale is 0 expected value, with variance being a function of the number of interactions you plan on going too.
Discussion
yes, but only if u have infinite funds. ......
It's the same whether it's limited or infinite funds, the EV is zero (assuming a fair game).
For example, I have 3 sats, first round is 50% chance of winning 1 sat, on second round 25% chance of winning 1 sat (-1 from 1st round + 2 from 2nd round), and 25% chance of losing 3 sats total (-1 + -2), therefore EV = 50% x 1 + 25% x 1 - 25% x 3 = 0
The infinite sum also works out to EV=0.