The Kelly criterion doesn't quite apply in this problem, since you are asked to optimize a more conservative strategy, namely to guarantee (with high probability) a certain amount of winnings rather than maximize log(winnings). In fact the Kelly value for f (in the problem's notation) is 0.25.

I used something else - don't want to give too much away but the general idea is to try it on a smaller problem (4 flips, $5, etc) and seeing if any patterns develop.