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Stacking the Deck

By Dennis Shasha
Communications of the ACM, April 2017, Vol. 60 No. 4, Page 96
10.1145/3040969
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Stacking the Deck, illustration — Credit: WildNight

Consider 16 cards consisting of the ace through 8 of hearts and the ace through 8 of spades. You are allowed to arrange the cards as you wish. Your opponent chooses a number between 1 and 8. You deal that many cards from the top of the deck and put the last card face up, with a value of, say, k. You next deal k cards (ace is considered 1) and put the last card face up, with a value of, say, k'. You then deal k' cards and so on. You continue until the number revealed is more than the remaining cards, in which case your opponent wins or the last deal ends with the final card of the 16 and is an ace, in which case you win.

Warm-Up. Find an arrangement in which you can win this game.

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