import os, math
from decimal import Decimal
# functions and code to calculate binomial coeffecients and probabilities of winning ping pong games
# used to calculate the liklihood of me beating Dan Hostetler in ping pong
# arnie larson									
# www.arnie.frisbolero.com

# calculate the liklihood of winning a ping pong game..  winning n out of m points with a probability p.
def liklihood(n,m,p):
	if not (n<=m):
		print('n must be greater than m')
	else:
		q = Decimal(str(1-p))
		a = choose(n,m)*Decimal(str(math.pow(p,n)))*Decimal(str(math.pow(q,m-n)))
		#print(' probability of winning %s out of m points %s with p = %s is %s'%(n,m,p,a))
		return a

		
# calculate m choose n. (m is bigger)
def choose(n,m):
	num = Decimal(str(math.factorial(m)))
	den = Decimal(str(math.factorial(n))) * Decimal(str(math.factorial(m-n)))
	try:
		choose = num/den
	except:
		print('Overflow error in %s / %s calculation'%(num,den))
	return num/den

# probability of winning a ping pong game given the probability of winning a given point p
def gameProb(p):
	prob = 0
	for points in range(21,41):
		prob += liklihood(21,points,p)
	return prob

# probability of winning at ping pong, winning n games out of m, given the probability of winning a given point p
def gameProbFromEven(p,n,m):
	prob = 0
	for points in range(n,m):  # n = 16, then it's a game to 5.  so 5, 2*5 - 2
		prob += liklihood(n,m,p)
	return prob
	
# probability of winning a game with two distinct point probabilities.  After player gets to n, winning percentage goes down to p2 from p1
# the assumption here is that after a critical point in the game, the second player will play much better.
def gameProb2(p1,p2,n):
	if n > 20 or p2>p1:
		print('choose n around 15 and p2 less than p1')
	else:
		prob = 0
		for firstgames in range(n,n+21):
			temp = liklihood(n,firstgames,p1)*liklihood(21-n,41-firstgames,p2)
			#print('checking for n = %s, subprobability is: %5f'%(firstgames,temp))
			prob += temp
		return prob
		
		
# quits when the probability of having one a game after n games > .5
def winOnceMedian(g):
	# todo:  Loop through starting with n = 1;
	begin = 1
	start = 2
	prob = 0
	while(True):		
		for games in range(begin,start+1):
			prob+=liklihood(games,start,g)
		print('after %s games, the liklihood of winning is: %5f when p: %5f'%(start,prob,g))
		if prob>Decimal('.5'):
			print('mean number of games: %s where liklihood of winning is greater than one half' % start)
			break
		begin = start
		start = math.floor(start*1.7)
		
# probability of winning a game out of 'num' games for probability of winning a given game is p
def winOnceMedian(p,num):
	prob = 0
	for games in range(1,num+1):
		prob+=liklihood(games,num,p)	
	#print('probability of winning a game is %8f after %4d games with a p_game of %5f' % (prob, num, p))
	return prob	

# Calculates the probability of winning a game out of 'num' games, approximates this by only calculating the first 'n' dominant terms
# This approximation is valid if the p is very low, (less than a few percent or so)
def winOnceMedian2(p,num,n):
	prob = 0
	for games in range(1,n):
		t = liklihood(games,num,p)	
		prob+=t
		#print('probability of winning (%s) games out of %s with a p_game of %5f' % (t, num, p))
	return prob	
	
		

p = []
p.append(gameProb(.33))
p.append(gameProb(.25))

print('probability of winning match if p = .33 : %5f'%p[0])
print('probability of winning match if p = .25 : %5f'%p[1])

# this is the closes I can really get to calculating the true liklihood of winning a given game..
p.append(gameProb2(.33,.20,16))
print('probability of winning match if p at start = .33  and p at end = .20 is: %5f'%p[2])

#winOnceMedian(.5,2)
for pgame in p:
	num = 11
	while(True):
		prob = winOnceMedian2(pgame,num,8)
		#print('probability of winning a game is %8f after %4d games with a p_game of %5f' % (prob, num, pgame))
		if prob > Decimal('.5'):
			print('probability of winning a game is %8f after %4d games with a p_game of %5f' % (prob, num, pgame))
			break
		num+=4
	
#prob1 = winOnceMedian2(p2,2100,8)
#print('probability of winning a game is %8f after %4d games with a p_game of %5f' % (prob1, 2100, p1))
#prob2 = winOnceMedian2(p2,2300,8)
#print('probability of winning a game is %8f after %4d games with a p_game of %5f' % (prob2, 2300, p2))

#winOnceMedian(p2)