Twenty one

Let's count together to twenty one, starting from one, with each person adding one, two, or three numbers. Whoever says “twenty-one” wins. Would you like to go first or second?

Consider next the game of Twenty-One, in which two players cooperate to count together to twenty-one, with each player saying either the next one, two, or three numbers, starting from one.

Whoever says “twenty-one” is the winner. Perhaps our game proceeds like this:

You: One, two.

Me: Three, four, five.

You: Six, seven, eight.

Me: Nine.

You: Ten, eleven.

Me: Twelve, thirteen.

You: Fourteen.

And so on. How shall I reply next? Who will be able to win by saying “twenty-one”? Kindly find a partner and play the game a few times. Get a good feel for the game. Can you find a winning strategy? This is a game that you can likely figure out.

Interlude

Please enjoy this selection from Infinite Games: Frivolities of the Gods, my new book-in-progress serialized here on Infinitely More, with fresh material on games and the logic of games each week. Follow along with my new class at Notre Dame on the philosophy and logic of games.

We begin with some fun finite games, which also happen to illustrate several subtle game-theoretic concepts.

Did you find a winning strategy? Let’s discuss it.