Average Win Time of Bolt Deck with Fetch Lands and Mulligans

import random
from random import shuffle

LIFE_TOTAL = 20
LAND_COUNT = 18
FETCH_LAND = 0
def playAGame():

    deck = ["land"] * LAND_COUNT + ["bolt"] * (60 - LAND_COUNT-FETCH_LAND)+ ["fetch land"]*FETCH_LAND

    hand = []

    landCounter = 0

    damageDealt = 0

    turnCounter = 0

    draw = 7

    mulligan(draw,hand,deck)
# Opening hand 7 cards

    while damageDealt < LIFE_TOTAL:

        turnCounter += 1
       #print "Turn", turnCounter
       #print "My hand", hand
        drawPhase(deck, hand)
        landCounter = landPhase(hand, landCounter, deck)
        damageDealt = boltPhase(hand, landCounter, damageDealt)

    # print "I win on turn", turnCounter
    return turnCounter

def drawPhase(deck, hand):
    myDraw = random.choice(deck)
    #print "I drew", myDraw
    deck.remove(myDraw)
    hand.append(myDraw)

def mulligan(draw,hand,deck):
    if draw != 0:
        for a in range(draw):
            drawPhase(deck, hand)
        if (hand.count("land") + hand.count("fetch land")) < 1 or (hand.count("land") + hand.count("fetch land")) > 5:
            #print hand
            #print "I mulligan"
            hand = []
            mulligan(draw-1,hand,deck)
    else:
        pass


def landPhase(hand, landCounter, deck):
    if "fetch land" in hand:
        #print "I play a fetch land"
        hand.remove("fetch land")
        #print "I crack my fetch land"
        try:
            deck.remove("land")
        except ValueError:
            #print "No more lands in library"
            pass
        #print "I shuffle my library"
        shuffle(deck)
        return landCounter + 1

    if "land" in hand:
        #print "I play a land"

        hand.remove("land")
        return landCounter + 1

    else:
        return landCounter

def boltPhase(hand, landCounter, damageDealt):
    damageDealtThisPhase = 0
    for a in range(landCounter):
        if "bolt" in hand:
         #   print "I play a bolt"
            hand.remove("bolt")
            damageDealtThisPhase += 3

    return damageDealt + damageDealtThisPhase

totalTurns = 0;
#playAGame()
for a in range(100000):
    totalTurns += playAGame();
print totalTurns / 100000.