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Thirty One Game

Answer :

By leading with a 5 the first player can always win. 
If your opponent plays another 5, you play a 2 and score 12. 
Then as often as he plays a 5 you play a 2, and if at any stage he drops out of the series, 3, 10, 17, 24, 31, you step in and win. 
If after your lead of 5 he plays anything but another 5, you make 10 or 17 and win. 
The first player may also win by leading a 1 or a 2, but the play is complicated. 
It is, however, well worth the reader's study.

Medieval Brain Teasers