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A348147
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Size of Fair 2-Jack Strip Jack Naked games which the player who goes second is more likely to win compared to the player who goes first.
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1
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1, 6, 8, 10, 12, 19, 20, 22, 23, 24, 26, 27, 30, 31, 32, 34, 35, 39, 40, 41, 42, 43, 44, 46, 48, 50, 53, 55, 56, 59, 62, 64, 69, 70, 71, 72, 75, 76, 77, 81, 85, 86, 90, 92, 96, 99, 101, 102, 103, 106, 107, 109, 114, 117, 118, 119, 122, 123, 125, 126, 127
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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A game of Strip Jack Naked involves a standard 52 deck of cards being shuffled and dealt between two players. Each player then takes it in turn to place a card on top of a central pile from the top of their hand (they do not choose what card they are placing). If a player places a penalty card (Ace, King, Queen or Jack) the other player must pay a number of cards (4, 3, 2, or 1 respectively) into the central pile and then the first player places the central pile at the bottom of their hand. That player then begins a new round. If, while paying a penalty, that player places a penalty card of their own, then they stop paying the penalty and the other player must now pay this new penalty. Play continues until one player has collected all the cards.
A Fair 2-Jack game is a simpler variant of Strip Jack Naked in which a number of cards are dealt to each player but each player has exactly one penalty card each in their hand, which is a Jack. This is the simplest nontrivial variant of Strip Jack Naked because if there were no penalty cards then whoever goes last or has the most cards would win and if there were just one penalty card then whoever is dealt that penalty card would win. With each player having exactly one Jack in their hand, it is not obvious from first glance what the result of the game will be.
The deciding factor in a Fair 2-Jack game is where the Jack is positioned in each player's hand. If each player is dealt n cards then there are n^2 different games that can be played. Simulating these games in software has shown that for all values of n <= 1000 each player is either equally likely to win, or the player who goes last will win in exactly one more scenario than the player who goes first.
This sequence lists those values of n for which dealing n cards to each player with exactly one penalty card each being a Jack, the second player is more likely to win than the first player.
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REFERENCES
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Richard K. Guy, Richard J. Nowakowski (25 November 2002). "Unsolved Problems in Combinatorial Games" (PDF). More Games of No Chance. MSRI Publications. 42. Cambridge University Press. ISBN 0521808324.
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LINKS
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EXAMPLE
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For n = 1, each player is dealt one card each which is a Jack. The first player plays their Jack demanding a penalty of one card, however the second player then plays their Jack, cancelling the original penalty and imposing a new penalty of one card on the first player. With no more cards the first player loses the game. With n = 1 there's only one way this game plays out and the second player wins making n = 1 part of this sequence.
For n = 2, each player is dealt two cards each with exactly one Jack in each player's hand. There are four different ways this game could play out and each player wins exactly 2 of these ways making n = 2 not part of this sequence.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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