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Problem of the Week 825

Poker Hands

Rank the following poker hands from best to worst. The game is being played with an ordinary 52-card deck, and there are no wild cards.

  1. AS AH AD KS KH
  2. AS AH AD QS QC
  3. AS AH AD QS QH
  4. AS AH AD 6S 6C
  5. AS AH AD 3S 3C
(For people with non-graphical browers: S=spades, H= hearts, D=diamonds, C=clubs, A=ace, K=king, Q=queen)

Source: A.J. Friedland, Puzzles in Math & Logic, Dover (1970).


Here is a summary of poker hand rankings from high to low. For an explanation of each, visit http://www.contrib.andrew.cmu.edu/org/gc00/reviews/pokerrules
  1. Straight Flush
  2. Four of a Kind
  3. Full House
  4. Flush
  5. Straight
  6. Three of a Kind
  7. Two Pair
  8. Pair
  9. High Card
Ties are broken by high cards. To answer all those questions: yes, the problem is more subtle than simply saying that the first hand beats all of the others.
Playing card images taken (with permission) from oxymoron's Egyptian Ratscrew page.
See Jeff Erickson's solution.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998