The Kelly criterion (https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion) is one possible way to decide on the amount to

The Kelly criterion (https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion) is one possible way to decide on the amount to bet, in order to "maximiz[e] the expected value of the logarithm of wealth". For a fixed probability of winning a fixed proportion of the bet, the amount turns out to depend on the size of your bankroll. However, as your example fixes the payoff but allows a variable buy-in, I don't see how to directly apply the formula from that article. But, long story short, it is almost sure to depend on the size of your current bankroll, if you accept a Kelly-like criterion.