Optimal playing strategy for Merlin's game of thirteen

by Russell D. Shaver

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Merlin is an electronic toy offering many games. One game, called blackjack, the author calls "the game of thirteen" since the objective is to come as close to l3 as possible without going over. This paper assumes that the game is played with 10 sequentially numbered cards. The player may request as many cards as he wishes but the dealer takes cards accordingly: if the total is less than 10, he takes a card; if 10 or above, he stands. The author examines the question of when the player should request another card. Out of 90 possible combinations of draws, there are 33 instances in which the player should stand from the start; in 24 instances the player should ask for a single card, standing regardless of the card drawn. In the remaining 33 cases the player should take cards until his total exceeds a given minimum number.

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