The 22 Game
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Apart from the exhaustion of cards, the winning series is 7, 12, 17,
22. If you can score 17 and leave at least one 5-pair of
both kinds (4-1, 3-2), you must win. If you can score 12
and leave two 5-pairs of both kinds, you must win. If you
can score 7 and leave three 5-pairs of both kinds, you
must win. Thus, if the first player plays a 3 or 4, you
play a 4 or 3, as the case may be, and score 7. Nothing
can now prevent the second player from scoring 12, 17,
and 22. The lead of 2 can also always be defeated if you
reply with a 3 or a 2. Thus 2-3, 2-3, 2-3, 2-3 (20), and,
as there is no remaining 2, second player wins. Again,
2-3, 1-3, 3-2, 3-2 (19), and second player wins. Again,
2-3, 3-4 (12), or 2-3, 4-3 (12), also win for second
player. The intricacies of the defence 2-2 I leave to the
reader. The best second play of a first player is always 1.
The first player can always win if he plays 1, and in no other way. Here are specimen games: 1-1, 4-1, 4-1, 4 (16) wins. 1-3, 1-2, 4-1, 4-1, 4 (21) wins. 1-4, 2 (7) wins. 1-2, 4 (7) wins. |
