import random

colors = ['R', 'U', 'W', 'G']

# 35 avg turns
crystalPicks = ['G']*5
cardPicks = ['W']*5

# 32 avg turns
#crystalPicks = ['R']*5
#cardPicks = ['R']*5

turns = 0
roundTurns = [0]*6
trials = 10000
for test in range(0, trials):
    cards = []
    for l in colors:
        cards.extend([l]*4)
    random.shuffle(cards)
    crystals = ['R', 'R', 'U']

    newCrystals = []
    newCards = []

    newCrystals.extend(crystalPicks)
    newCards.extend(cardPicks)
    # fill in rest randomly
    for i in range(len(newCrystals),5):
        newCrystals.append(random.choice(colors))
    for i in range(len(newCards),5):
        newCards.append(random.choice(colors))

    discard = []

    for round in range(0, 6):

        while len(cards):
            roundTurns[round] += 1
            turns += 1
            c = None

            # draw 3
            for i in range(0,3):
                if not len(cards):
                    break
                c = cards.pop()
                discard.append(c)

            # draw more if color matches
            for cry in crystals:
                if c and c == cry and len(cards):
                    discard.append(cards.pop())
        turns += 1 # player's last turn
        roundTurns[round] += 1

        if round == 5: # last round
            break

        # give dummy a card&crystal and shuffle
        crystals.append(newCrystals.pop(0))
        discard.append(newCards.pop(0))
        cards = discard
        random.shuffle(cards)
        discard = []

print turns/float(trials), 'avg turns per game'
for r in range(0,6):
    print r, roundTurns[r]/float(trials)