import random
def play():
	def roll():
		return random.choice([True,False])
	first=roll()
        if(first):
            return True
	else: #start best of 3?
		middle=roll()
		if(not middle):	#lost both
			return False
		else:
			return roll() #need to win the last one

def simulate(n):
	total=[play() for _ in range(n)].count(True)
	return float(total)/float(n)

print(simulate(200000))

0.62416