Skunk
This game is a modelling and probability problem that involved some algebra. The goal of this game is to find the strategy that maximizes your payoff per game.
Here is how to play:
To start with you stand. Two dice are thrown. If neither of them show a 1, you get the sum of the dice as your score. But if a 1 comes up the game is over and your payoff is zero. If the game can continue you decide whether to leave the game (sit down). If you do, you get your current score as a payoff. If you stay in the game the process repeats. The dice are thrown again and If neither of them show a 1, you add the sum of the dice to your current score and again you decide whether or not to stay in the game. And everything continues as before.
For example, for the sequence of rolls:
(2,5)
(4,2)
6,1)
Those who sit after the first roll get payoff 7. Those sit after the second roll get payoff 13. Those who stay standing for the third roll get payoff 0.