# Difference between revisions of "Probably not transitive"

Oscarlevin (talk | contribs) (Created page with "I first heard a similar version of this puzzle on the {{Math factor}}. ==Puzzle== Consider the following card game: the 2 through 10 of spades are placed in three piles of t...") |
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I first heard a similar version of this puzzle on the {{Math factor}}. | I first heard a similar version of this puzzle on the {{Math factor}}. | ||

==Puzzle== | ==Puzzle== | ||

− | Consider the following card game: the 2 through 10 of spades are placed in three piles of three cards each. Player 1 picks any pile, then player 2 picks one of the remaining piles. Each player picks one of their three cards at random - high card wins. Now in the piles pictured | + | Consider the following card game: the 2 through 10 of spades are placed in three piles of three cards each. Player 1 picks any pile, then player 2 picks one of the remaining piles. Each player picks one of their three cards at random - high card wins. Now in the piles pictured, player 1 has a winning strategy: pick pile A, as any card in that pile would be a winner. But if the cards were arranged differently, things might not be so simple. |

− | |||

Find an arrangement of the cards into three piles so that player 2 has a winning strategy. That is, player 2 can always pick a pile that has a greater than 50% chance of beating the pile picked by player 1. Or prove that this is impossible. | Find an arrangement of the cards into three piles so that player 2 has a winning strategy. That is, player 2 can always pick a pile that has a greater than 50% chance of beating the pile picked by player 1. Or prove that this is impossible. |

## Revision as of 18:59, 13 July 2013

I first heard a similar version of this puzzle on the Template:Math factor.

## Puzzle

Consider the following card game: the 2 through 10 of spades are placed in three piles of three cards each. Player 1 picks any pile, then player 2 picks one of the remaining piles. Each player picks one of their three cards at random - high card wins. Now in the piles pictured, player 1 has a winning strategy: pick pile A, as any card in that pile would be a winner. But if the cards were arranged differently, things might not be so simple.

Find an arrangement of the cards into three piles so that player 2 has a winning strategy. That is, player 2 can always pick a pile that has a greater than 50% chance of beating the pile picked by player 1. Or prove that this is impossible.