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Project Euler Solutions

Project Euler 54 Solution

Project Euler 54 Solution

Project Euler 54: Compare hands in a game of poker and determine a winner


Problem Description

In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:

  • High Card: Highest value card.
  • One Pair: Two cards of the same value.
  • Two Pairs: Two different pairs.
  • Three of a Kind: Three cards of the same value.
  • Straight: All cards are consecutive values.
  • Flush: All cards of the same suit.
  • Full House: Three of a kind and a pair.
  • Four of a Kind: Four cards of the same value.
  • Straight Flush: All cards are consecutive values of same suit.
  • Royal Flush: Ten, Jack, Queen, King, Ace, in same suit.

The cards are valued in the order:
2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.

If two players have the same ranked hands then the rank made up of the highest value wins; for example, a pair of eights beats a pair of fives (see example 1 below). But if two ranks tie, for example, both players have a pair of queens, then highest cards in each hand are compared (see example 4 below); if the highest cards tie then the next highest cards are compared, and so on.

Consider the following five hands dealt to two players:

Hand   Player 1   Player 2   Winner
1   5H 5C 6S 7S KD

Pair of Fives
  2C 3S 8S 8D TD

Pair of Eights
  Player 2
2   5D 8C 9S JS AC

Highest card Ace
  2C 5C 7D 8S QH

Highest card Queen
  Player 1
3   2D 9C AS AH AC

Three Aces
  3D 6D 7D TD QD

Flush with Diamonds
  Player 2
4   4D 6S 9H QH QC

Pair of Queens
Highest card Nine
  3D 6D 7H QD QS

Pair of Queens
Highest card Seven
  Player 1
5   2H 2D 4C 4D 4S

Full House
With Three Fours
  3C 3D 3S 9S 9D

Full House
with Three Threes
  Player 1

The file, poker.txt, contains one-thousand random hands dealt to two players. Each line of the file contains ten cards (separated by a single space): the first five are Player 1’s cards and the last five are Player 2’s cards. You can assume that all hands are valid (no invalid characters or repeated cards), each player’s hand is in no specific order, and in each hand there is a clear winner.

How many hands does Player 1 win?

Analysis

If we can quantify each hand into an array of tuples we can quickly compare each hand and determine a winner or a tie.
The first tuple would consist between 2 and 5 elements representing the frequency of card values sorted in descending order. The second tuple would consist of the same number of elements as the first but describe the value sorted and weighted by frequency in descending order.
Let’s check out how this would look for a few typical hands for both players:
p1 = TH 6H 9H QH JH [(1, 1, 1, 1, 1), (12, 11, 10, 9, 6)], score = 0
p2 = 9H 4D JC KS JS [(2, 1, 1, 1), (11, 13, 9, 4)], score = 1

p1 = 7C 7S KC KS JC [(2, 2, 1), (13, 7, 11)], score = 2
p2 = 7H 7D KH KD 9S [(2, 2, 1), (13, 7, 9)], score = 2

Ties in similar scores are broken by checking the second tuple

By simply comparing hands as p1>p2 we can determine the winner between the two players. The only complication left is to calculate and rank straights and flushes.

Project Euler 54 Solution

Runs < 0.100 seconds in Python 2.7.
from collections import Counter
from urllib2 import urlopen

file_url = 'https://projecteuler.net/project/resources/p054_poker.txt'
hands = (line.split() for line in urlopen(file_url))

values = {r:i for i,r in enumerate('23456789TJQKA', start=2)}
straights = [(v, v-1, v-2, v-3, v-4) for v in range(14, 5, -1)] + [(14, 5, 4, 3, 2)]
ranks = [(1,1,1,1,1),(2,1,1,1),(2,2,1),(3,1,1),(),(),(3,2),(4,1)]

def hand_rank(hand):
	score = zip(*sorted(((v, values[k]) for
		k,v in Counter(x[0] for x in hand).items()), reverse=True))
	score[0] = ranks.index(score[0])
	if len(set(card[1] for card in hand)) == 1: score[0] = 5  # flush
	if score[1] in straights: score[0] = 8 if score[0] == 5 else 4  # str./str. flush
	return score

print "Project Euler 54 Solution =", sum(hand_rank(hand[:5]) > hand_rank(hand[5:]) for hand in hands)
download arrowUse this link to get the Project Euler 54 Solution Python 2.7 source.

Answer

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Afterthoughts

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Project Euler 54 Solution last updated

Discussion

10 Responses to “Project Euler 54 Solution”

  1. The best solution I have ever seen!!!!
    love you

    Posted by Weihong | September 20, 2016, 3:12 PM
  2. Instead of manually coding the rank combinations, you can do it so:

    from itertools import combinations_with_replacement
    ranks = [sorted(i, reverse=True) for j in range(1,6) for i in combinations_with_replacement(range(1,5), j) if sum(i)==5]
    # %timeit: 54 us

    PS. Your idea of scoring Poker is great!

    Posted by Baloo the Bear | November 15, 2014, 8:29 AM
  3. Thank you so much for posting such an elegant solution. I’ve learned tons from this, honestly.

    Just a heads up, I’m pretty sure this doesn’t account for A2345 straights. However, it’s still valid for the Euler problem, as pokers.txt contains no A2345 straights.

    A quick fix I know, just an if statement to check. I was contemplating whether it was worth reviving the dead, but I figured you’d want to know.

    Posted by Nick | March 17, 2014, 3:49 AM
    • To clarify as to why A2345 straights don’t work (and only against other straights), it’s because score[1] will be (14,5,4,3,2) rather than its true score of (5,4,3,2,1)

      Posted by Nick | March 17, 2014, 3:52 AM
      • Good observation! I haven’t really thought about that; I’ll have to look at it when I find some time.

        Glad it helped you out, and thanks for commenting. You should be proud of yourself for figuring it out. There’s a lot going on and it took me some time to get my head around it all again.

        Posted by Mike | March 17, 2014, 3:46 PM
  4. Great solution.
    I think, for flush and straight, if you have sorted the values, you can just compare the first and the last.
    Also, with sorted values for four of a kind you can compare 1 and 4 and also 2 and 5 and one has to be true.

    Posted by MK | September 24, 2009, 10:40 PM
  5. I have seen this problem in the past but I have never seen such a creative solution. Thanks for sharing this with others.

    TJ

    Posted by TJ Mathews | July 3, 2009, 2:39 PM

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