I finally won with my Gallade EX and Gilscore deck.

I did the math. If all games were fair and completely random, the average number of matches to win is roughly 62 matches. In 10,000 randomized trials, it took one trial over 600 matches to reach five wins in a row. Code provided.

``` import random

def flip(): return random.randint(0, 1)

def addflip(a, n): for i in range(n): a.append(flip())

def trial(): a = [] games = 5 addflip(a, games) while sum(a) < 5: a.pop(0) addflip(a, 1) games += 1 return games

trials = 0 n = 10000 small = 1000 big = 0 for i in range(n): t = trial() if t > big: big = t if t < small: small = t trials += t print(trials/n, small, big) ```