Consider a single player card game with a standard 52 card deck.
You shuffle the cards and turn over the top card.
If you turn over a black card, you win £1. If you turn over a red card, you lose £1.
You can keep turning over cards as long as you want to.
It is impossible to lose money in this game; if you have turned over more red cards than black cards, you can just keep turning over cards until the end of the deck to end up at net £0. If you stop turning over cards before reaching the end of the deck, you keep the money that you have won up until that point.
Is there an optimal strategy for this game?
We played several games of this in maths club just with 10 cards (5 red and 5 black), keeping track of our winnings to start to guess at the best strategy.