Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e.g. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Who is most likely to win?

flips_coins.py

# -*- coding: utf-8 -*-
"""
Flip a fair coin 100 times—it gives a sequence of heads (H)
and tails (T). For each HH in the sequence of flips, Alice
gets a point; for each HT, Bob does, so e.g. for the
sequence THHHT Alice gets 2 points and Bob gets 1 point.
Who is most likely to win?


https://x.com/littmath/status/1769044719034647001

@author: Nicolás Guarín-Zapata
@date: June 2024
"""
import numpy as np


np.random.seed(45)


nrounds = 100000
nflips = 100
bob_wins = 0
alice_wins = 0
ties = 0
for rounds in range(nrounds):
    
    bob = 0
    alice = 0
    flips = np.random.randint(0, 2, nflips)
    for cont in range(nflips - 1):
        consecutive_flips = list(flips[cont:cont + 2])
        if consecutive_flips == [0, 1]:
            bob += 1
        if consecutive_flips == [0, 0]:
            alice += 1
        
    if bob > alice:
        bob_wins += 1
    elif bob < alice:
        alice_wins += 1
    else:
        ties += 1