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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# This programme tests the "HHT and HTT" probability problem
# by Xilin SUN

# Problem: A fair coin is tossed consecutively. Once the sequence
# "HHT" appears, person A wins and the game is terminated. Once the
# sequence "HTT" appears, person B wins and the game is also terminated.
# Find the probability that person A wins.

# The solution to this problem is not very straightforward, but by
# no means difficult to find. I am not going to paste the solution
# here. The answer should be 2/3. Below is a program to verify such
# answer.

from random import randint

CaseHHT = 0
CaseHTT = 0
NumberofCases = 500000
print "Doing a test with " + str(NumberofCases) +" cases."

for i in range (1,NumberofCases):
	digit1=randint(0,1)
	digit2=randint(0,1)
	digit3=randint(0,1)
	while True:
		if digit1 == 0 and digit2 == 0 and digit3 == 1:
			CaseHHT +=1
#			print "Number of cases when 'HHT' wins = " + str(CaseHHT)
			break
		elif digit1 == 0 and digit2 == 1 and digit3 == 1:
			CaseHTT +=1
#			print "Number of cases when 'HTT' wins = " + str(CaseHTT)
			break
		else:
			digit1=digit2
			digit2=digit3
			digit3=randint(0,1)
else:
	print "Number of cases when 'HHT' wins = " + str(CaseHHT)
	print "Number of cases when 'HTT' wins = " + str(CaseHTT)
	print "Probability of 'HHT' winning = " + str(100*CaseHHT/float(NumberofCases)) + "%"