#!/usr/bin/python
# -*- coding: utf-8 -*-

# Some fundamental constants
N = 52 #total cards
C = 13 #cards in color
M = 4 #colors
K_max = 13 #desired number of cards in a hand

class Hand (list):
    def __repr__(self):
        res = [('%1d' % r) for r in self]
        return '-'.join(res)
    def __hash__ (self):
        h = 0
        for k in self:
            h = h * C + k
        return h
from copy import copy
old_hands = {Hand([1]+[0]*(M-1)):1.0} #K = 1 => (1,0,0,0) & P=1
for K in xrange(2, K_max+1): #cards in set
    new_hands = {}
    for h0, p0 in old_hands.iteritems():
        for c in range(0,M): #adding colors
            h = copy(h0); h[c] += 1;
            h.sort (reverse=True)
            dp = p0 * (C - h0[c])/(N - K + 1.0)
            if not (h in new_hands):
                new_hands[h] = 0.0
            new_hands[h] += dp
    old_hands = new_hands
res = [{'hand':h, 'p': p} for h,p in new_hands.iteritems ()]
def by_probability (v1,v2):
    if v1['p'] > v2['p']:
        return 1
    if v1['p'] < v2['p']:
        return -1
    return 0

res.sort (cmp=by_probability, reverse=True)
p_total = 0.0
for obj in res:
    p_total += obj['p']
    print 'P = %e' % obj['p'], 'H =', obj['hand']

print 'Total:', p_total

groups = (
    ('Равномер',(Hand((4,3,3,3)), Hand((4,4,3,2)), Hand((5,3,3,2)))),
    ('Боевая 5ка',(Hand((5,4,2,2)), Hand((5,4,3,1)))),
    ('Трёхцвет',(Hand((4,4,4,1)), Hand((5,4,4,0)))),
    ('Стандартный двуцвет',(Hand((5,5,2,1)), Hand((5,5,3,0)))),
    ('Двуцвет Конюховского',(Hand((6,4,2,1)), Hand((6,4,3,0)))),
    ('Плоские шестёрки',(Hand((6,3,2,2)), Hand((6,3,3,1)))),
    ('Резкий двуцвет',(Hand((6,5,1,1)), Hand((6,5,2,0)))),
    ('Блок',(Hand((7,2,2,2)), Hand((7,3,2,1)), Hand((7,3,3,0)))),
    ('Юло-фиты',(Hand((7,4,1,1)), Hand((7,4,2,0)))),
)
p_standard = 0.0
for g, l in groups:
    p = 0.0
    for i in l:
        p += new_hands[i]
    p_standard += p
    print '%s %s: %e' % (g, l, p)
print 'Все остальные нестандартные расклады: %e' % (1.0-p_standard)