Skunk

This is a simplified version of the game "skunk" that is popular in elementary school math classrooms.  This version provides an excellent elementary problem involving probability and strategic thinking. 

Here's how the game is played. To start with you stand. At any point in the game you will have a score.  You begin with score 0.  When the game is over for you, you will get a payoff determined as follows.

Two dice are thrown.

If at least one 1 appears, the game is over for you and your payoff is 0. Otherwise, you add to your current score the sum of the numbers shown on the dice and this becomes your new score.  You now decide whether to sit or stay standing.

·       If you sit, you are leaving the game and your payoff is your score.

·       If you stay standing, you go to the beginning, and the two dice are thrown again.

 The problem is to find the strategy which maximizes your average payoff per game. Of course, a strategy is simply a decision of when to leave the game..

This is a good game to play in class, because students can develop a pretty good intuition for how to play. 

For example, for the sequence of rolls:

(2, 5)

(4, 2)

(6, 1)

Those who sit after the first roll get payoff 7. Those who sit after the second roll get payoff 13. Those who stay standing for the third roll get payoff 0.