A certain slot machine is rigged to pay out, on average, once every 10 games. It costs 1 dollar to play, and the machine pays out 11 dollars if you win. On average, then, you will be up one dollar every ten games. On average, mind you.
However, there is a catch. The slot machine is an up-and-coming machine and takes a credit card. If you win, it locks out your card. So you can only play once.
Now, a certain person has particularly bad credit and bad health. They have missed some payments on their debt and have multiple unpayed hospital bills. They have only one credit card. Suppose they've played the slot machine four times already. If they win they cannot play again - the bank will not issue them another card. They are four dollars down. Is it profitable to keep playing until they win?
Edit: Suppose they lose their fourth and fifth game. What then?