Kelly Can't Fail

A very similar card game played by deciding when to stop flipping cards from a deck where red is $1 and black is −$1 as described in Timothy Falcon’s quantitative-finance interview book (problem #14). Gwern describes it and also writes code to prove out an optimal stopping strategy: https://gwern.net/problem-14

That is a nice game and writeup.

Nice!

Only quibble i have is that black should be +$1 and red -$1 to follow standard finance conventions, i.e. be in the "black" or "red".