#poker.py

def fact(n):
    prod = n
    for i in range(n-1,1,-1):
        prod *= i
    return prod


def combos(n,k):
    return int(fact(n) / (fact(k) * fact(n-k)))


poker = {}

five_card_hands = combos(52,5)
print("Number of 5-card hands:",five_card_hands)

poker['straight_flushes'] = 4*10

poker['four_of_a_kinds'] = 13*48

poker['full_houses'] = 13*combos(4,3) * 12*combos(4,2)

poker['flushes'] = 4*combos(13,5)-(4*10)

poker['straights'] = 10*4**5 -(4*10)

poker['three_of_a_kinds'] = 13*combos(4,3) * combos(12,2)*4*4

poker['two_pairs'] = combos(13,2)*combos(4,2)**2 * 44

poker['one_pairs'] = 13*combos(4,2) * combos(12,3)*4*4*4


#print(poker)

for hand in poker:
    print('#%-16s  %9d  %6.5f%%'%(hand,poker[hand],poker[hand]/five_card_hands*100))


print()
print("outside straight:",8/47*100,"%")
print("2-pair to full house:",4/47*100,"%")
print("3-of-a-kind to full house:",12*combos(4,2)/combos(47,2)*100,"%")
print("3-of-a-kind to 4-of-a-kind:",1/47*100,"%")  #?
print("4 same suit to flush:",9/47*100,"%")