Simulate 2 people tossing coin until get first head Python

Question

So I have A and B play a game which begins with A tossing a coin. If it shows head, A wins and game over. Else, B tosses and if B gets a head, B wins and game over. Basically, the game continues until whoever's coin shows a head first.

Theoretically, the probability of A winning is 2/3, and the probability of B winning is 1/3. Referenced here

I'm trying to simulate this in Python, running 4000 simulations. However, I'm not really getting close to 2/3 for A and 1/3 for B. Below is my code:

import random

Atoss = 0
Btoss = 0

Awins = []
Bwins = []

for i in range(4001):
   head = False
   while (not head):
      A = random.randint(0, 2)  # random 0 and 1
      Atoss += 1

      if A == 1:
         head = True
      else:
         B = random.randint(0, 2)  # random 0 and 1
         Btoss += 1
         if B == 1:
            head = True

   totalToss = Atoss + Btoss
   Awin = Atoss / totalToss
   Awins.append(Awin)
   Bwin = Btoss / totalToss
   Bwins.append(Bwin)

probA = sum(Awins) / len(Awins)
probB = sum(Bwins) / len(Bwins)

print("Probability A: ", probA)
print("Probability B: ", probB)

Did I mess up somewhere?

EDIT:

Changing randint(0, 2) to randint(0, 1) solves the problem, as answered by @bart cubrich

Your Awin/Bwin/Awins/Bwins computations don't look anything like how victory in the game is defined. — user2357112
yeah I thought that doing # of tosses / total tosses is not right, but I couldn't figure out how to "code" it like I had it on paper — PTN
The main error is this code is a typo, so maybe deserves a downvote, but it's a cool problem, and generally I liked your solution. Plus you were upfront with that fact that it could just be a mistake. Definitely don't need to keep track of the number of tosses, but it's interesting to see how many more tosses are needed that for loops. — bart cubrich

bart cubrich bart cubrich · Accepted Answer · 2019-03-07T00:59:16

One problem you have is that the random.randomint should be

A = random.randint(0, 1)  # random 0 and 1
B = random.randint(0, 1)  # random 0 and 1

Your version was producing zeros, ones, and twos. That was totally messing up the chances of getting a heads, since you were really rolling a 3 sided die with sides=[0,1,2], where only a "1" wins. Trying the following:

import random
random.seed(123)
Atoss = 0
Btoss = 0

Awins = 0
Bwins = 0

for i in range(4000):
   head = False
   while (not head):
      A = random.randint(0, 1)  # random 0 and 1

      if A == 1:
         Awins+=1
         head = True

      else:
         B = random.randint(0, 1)  # random 0 and 1
         if B == 1:
            Bwins+=1
            head = True



probA = Awins / (Awins+Bwins)
probB = Bwins / (Awins+Bwins)

print("Probability A: ", probA)
print("Probability B: ", probB)

Out:
'Probability A:  0.6653336665833541'
'Probability B:  0.3346663334166458'

I get that the probability is ~A:66% B:33%.

Note, in the documentation from random.py

random.randint(a, b) -Return a random integer N such that a <= N <= b.

which is different than the numpy.random.randomint which gives

-a random integer N such that a <= N < b

Documentation is here

Simulate 2 people tossing coin until get first head Python

2 Answers