from random import *
def we(dr=111):
    # USCF formula for winning expectation
    # dr = rating difference
    return 1./(1.+10.**(dr/400.))

class player:
    def __init__(self, name, rating):
        self.name = name
        self.rating = rating
        self.score = 0.0

def match(drawprob=.25, maxrounds=4):
    sloan = player('Sloan', 1936)
    brock = player('Brock', 1936+111)
    white_advantage = 50.
    sloan_white_first_round = False
    
    if sloan_white_first_round:
        white, black = sloan, brock
    else:
        white, black = brock, sloan
    assert maxrounds % 2 == 0
    result = []

    for round in xrange(1,maxrounds+1):
        expectation = we(white.rating + white_advantage - black.rating)
        winprob = expectation - drawprob/2.
        lossprob = 1. - (winprob + drawprob)
        assert abs(winprob+lossprob+drawprob-1.0) < .0001
#        print '%d PW=%.3f PL=%.3f PD=%.3f'% \
#              (round, winprob, lossprob, drawprob)
        r = random()
        if r < drawprob:
            white.score += .5
            black.score += .5
            result.append('draw')
        else:
            winner = (black, white)[r < (drawprob + lossprob)]
            winner.score += 1
            result.append(winner.name + ' wins')
        if sloan.score >= maxrounds//2 or brock.score > maxrounds//2:
            break
        white, black = black, white
    rr = brock.score > maxrounds//2
    return rr

def sim(n=10):
    a = [0,0]
    for i in xrange(n):
        a[match(drawprob=.25)] += 1
    print a  # a = (sloan score, brock score)

trials = 100000
sim(trials)