52 poker cards (half red and half black). Every time you draw a card, if you draw a red card, then you win one dollar. If you draw black card, then you lose one dollar.
Say you start with $n$ dollars, if you can stop/quit this game anytime you want, how much are you willing to pay this game?
What would be your optimal play strategy?
I think this is very similar to the gambler's ruin problem; We can let each state denote the amount of money that the gambler has. However, the transistion probability would be dependent/varied from state to state.