The 22 Game
A Classic Puzzle by Henry Ernest Dudeney
Lay out sixteen cards as shown.
Two players alternately turn down a card and add it to the common score, and the player who makes the score of 22, or forces his opponent to go beyond that number, wins. For example, A turns down a 4, B turns down a 3 (counting 7), A turns down a 4 (counting 11), B plays a 2 (counting 13), A plays 1 (14), B plays 3 (17), and whatever A does, B scores the winning 22 next play. Again, supposing the play was 3-1, 1-2, 3-3, 1-2, 1-4, scoring 21, the second player would win again, because there is no 1 left and his opponent must go beyond 22.
Which player should always win, and how?