Finds the best strategy for a simplistic decentralised POMDP game

deckgame.py

from random import shuffle
from itertools import chain, combinations

def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))


players = 15
runs = 1000

bestWins = 0
bestRule = ()
deck = range(1,11)*3

for rule in powerset(range(1,11)):
    
    wins = 0
    for i in range(runs):
                
        shuffle(deck)
        draw = deck[0:players+1]
        
        showing = filter(lambda x: x in rule, draw)
        if not showing:
            continue
        res = sum(showing)
        if res > 10 and 1 <= res % 10 <= 5:
            wins += 1
    
    print rule, 100 * wins / runs, "%"
    
    if wins > bestWins:
        bestWins = wins
        bestRule = rule
        
print "Best:", bestRule, 100 * bestWins / runs, "%"

rules.txt

We have a deck of cards consisting of the numbers 1 through 10, four times (40 cards in total). 
Each of you will be given one card from that deck, face down. Do not show your card to anyone! 
Everyone simultaneously takes a decision: you either choose to turn over your card or leave it face down. 

To win: The sum of the face up cards must be greater than 10 and the last digit must be 1 through 5; e.g.:
	11, 12, 13, 14, 15
	21, 22, 23, 24, 25
	31, 32, 33, 34, 35 and so on... 
The catch: You will have some time to collaboratively think and plan your strategy in advance.