You have $x$ red cards and $y$ black cards. I flip them over one at a time. The probability of flipping a particular colour is proportional to the amount of those coloured cards left. You start with $1$ and for every flip you can bet some proportion of your money on red or blue. If you win the bet, you gain twice your bet, but if you lose the bet, you gain nothing. What is the strategy that maximizes expectancy and minimizes variance?
I think the correct strategy to use is the Kelly Criterion, but I honestly do not know how to set the formula and how to find the expected value and variance of the game. The fact that the probability is dynamic really confuses me.