GAME Adding Numbers—Lose If Go to 100 or Over (Win at 99)

 
In the second ver- sion, two players again take turns choosing a number be- tween 1 and 10 (inclusive), and a cumulative total of their choices is kept. This time, the player who causes the total to equal or exceed 100 is the loser.

The first pair starts by choosing numbers more or less at random, until the total drifts into the 90s and the player with the next turn clinches a win by taking the total to 99. The second (or maybe third) time you play, when the total gets somewhere in the 80s, one of that pair will realize that she wins if she takes the total to 88. When she does that, the other will (probably) realize that she has lost, and as she concedes, the rest of the class will realize it, too. The next pair will quickly settle into subgame-perfect play as in the first version. Eventually everyone will have figured out that starting at 0 (being the first mover) guarantees not a win but a loss. In this version of the game, it is better to go second: let the first player choose any number and then say 11 minus what the other says. Here, the second player takes the total succes- sively to 11, 22, . . ., 77, 88, 99; the first player must then take the total to 100 (or more) and lose. You can hold a brief discussion comparing the two versions of the game; this helps make the point about order advantages in different games.