Decision Support Puzzles for Applied Mathematicians
December 2008 - 5x5 Poker
Five by five poker is a solitaire poker variant in which a player arranges 25 cards in a five by five grid. Each column and each row in the grid represents a poker hand, making 10 hands in total. The object of the puzzle is to rearrange the cards to maximize the summed points from each hand. Hands are awarded points based on the accompanying table:
Straight flush 8
Four of a kind 7
Full house 6
Three of a kind 3
Two pair 2
One pair 1
For example, in Figure 1, the first row contains one pair of Kings (worth 1 point), the second row contains three Jacks (worth 3 points), the fourth row contains a straight (worth 4 points), and the fourth column contains a flush (worth 5 points). The remaining rows and columns contain no hands of value and are worth 0 points. This yields a total score of 13.
Only the following 25 cards may be used: Hearts Q J 9 4, Diamonds A K Q J 9 8 7 6 5 4 2, Spades K J 10 9 4 2, Clubs K Q 9 4.
Question: What arrangement of cards maximizes the total point value from all 10 hands?