Difference between revisions of "Probably not transitive"

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(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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[[File:Probably_not_transitive.png|right|500px]]
 
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 below, 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.
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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.
  
[[File:Probably not transitive|left|150px]]
 
  
 
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

Probably not transitive.png

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.