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.
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).
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.