392 Answerswith any square on the board. As second player, Cross, I should take a
comer if Nought led with a center and take the center if he led with anything
else. This would avoid many complexities and should always draw. The fact
remains that it is a capital little game for children, and even for adults who
have never analyzed it, but two experts would be merely wasting their time in
playing it. To them it is not a game, but a mere puzzle that they have
completely solved.
472. THE HORSESHOE GAME
Just as in tic tac toe, every game should be a draw. Neither player can win
except by the bad play of his opponent.
[For a complete analysis of the game, see Edouard Lucas, Recreations
Mathematiques, Vol. III, pp. 128-131.-M. G.]
- TURNING THE DIE
The best call for the first player is either "2" or "3," as in either case only
one particular throw should defeat him. If he called" I," the throw of either
3 or 6 should defeat him. If he called "2," the throw of 5 only should defeat
him. If he called "3," the throw of 4 only should defeat him. If he called "4,"
the throw of either 3 or 4 should defeat him. If he called "5," a throw
of either 2 or 3 should defeat him. And if he called "6," the throw of either
I or 5 should defeat him. It is impossible to give here a complete analysis of
the play, but I will just state that if at any time you score either 5, 6, 9, 10,
14, 15, 18, 19, or 23, with the die any side up, you ought to lose. If you score
7 or 16 with any side up you should win. The chance of winning with the
other scores depends on the lie of the die.474. THE THREE DICE
Mason's chance of winning was one in six. If Jackson had selected the
numbers 8 and 14 his chances would have been exactly the same.
475. THE 37 PUZZLE GAME
The first player (A) can always win, but he must lead with 4. The winning
scores to secure during the play are 4, 11, 17, 24, 30, 37. In the first game