N% Unfair Coin

There is an unfair coin. It tends to land on one side more than on the other.

Make a fair (unbiased) coin from an unfair (biased) coin.

Write a program which provides a solution for above problem statement.

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Solution:

John von Neumann described the procedure like this:

1. Toss the coin twice.

2. If the outcome of both coins is the same (HH or TT), start over and disregard the current toss.

3. If the outcome of both coins is different (HT or TH), take the first coin as the result and forget the second.

Coding Solution:

from random import randint

# Biased function that returns Heads with head_prob% probability and
# Tails with (100-head_prob)% probability
def toss_biased(head_prob):

 # generate random number between 1-100, both inclusive
 r = randint(1, 100) 
 # return Head if we got number between [1 to Head probability], else return tail
 return H if (r <= head_prob) else T

def toss_unbiased(head_prob):
 # difference = 0 in case of HH or TT toss again
 # difference > 0 in case of HT return H
 # difference < 0 in case of TH return T
 difference = toss_biased(head_prob) - toss_biased(head_prob)
 if difference > 0:
    return H
 if difference < 0:
    return T
 return toss_unbiased(head_prob) 

# Generate Fair Results from a Biased Coin
if __name__ == '__main__':

 # Head
 H = 1
 # Tail
 T = 0

 head_prob = int(input("Enter the probability of getting Head:"))
 if(head_prob <1 or head_prob >99):
     print("Enter probability between 1 & 99")
     exit()
 if(head_prob == 50):
     print("No need to apply a solution")
     exit()
     
 print("the probability of getting Head:", head_prob,"%")
 print("the probability of getting Tail:", 100-head_prob,"%")
 head_count = tail_count = 0
 for i in range(10000):
    val = toss_unbiased(head_prob)

    if val == 1:
        head_count += 1
    else:
        tail_count += 1 

 print("the probabilities after applying a solution:")
# Heads with ~50% probability
 print("HEADS% ~", head_count / 100, "%")
#Tails with ~50% probability
 print("TAILS% ~", tail_count / 100, "%")

Note : (Keeping non-coder readers in mind, code optimization may not be fully utilized.)

Test Output 1:
Enter the probability of getting Head:59
the probability of getting Head: 59 %
the probability of getting Tail: 41 %
the probabilities after applying a solution:
HEADS% ~ 50.19 %
TAILS% ~ 49.81 %


Test Output 2:
Enter the probability of getting Head:77
the probability of getting Head: 77 %
the probability of getting Tail: 23 %
the probabilities after applying a solution:
HEADS% ~ 49.8 %
TAILS% ~ 50.2 %