[malisper]

I need to do some Math, but I wonder if there's a better strategy than Kelly betting. An assumption made for Kelly betting is the bets are independent of each other. That's not the case in the problem given.

After making a bet, you gain information about the contents of the rest of the deck of cards. I could see it being possible to do better by pricing in that information into your bet.

[amluto]

But the information gained in this game is independent of your bet. The multi-armed bandit problem is a famous example of the opposite situation.

[necovek]

That seems to be exactly what this strategy is doing: at every step, you account for the probability of the red or black card coming up, and bet accordingly (both the sum and the colour).