Birthday paradox python - incorrect probability output

I am having issues with the programming the birthday paradox in Python. The birthday paradox basically says that if there are 23 people in a class, the probability that two of them will have the same birthday is 50%.

I have attempted to code this paradox in Python, however it keeps coming back with a probability of closer to 25%. I am very new to Python and so no doubt there is a simple solution to this problem. Here is my code:

import random


def random_birthdays():
    bdays = []
    bdays = [random.randint(1, 365) for i in range(23)]
    bdays.sort()
    for x in bdays:
        while x < len(bdays)-1:
            if bdays[x] == bdays[x+1]:
                print(bdays[x])
                return True
            x+=1
        return False

count = 0
for i in range (1000):
if random_birthdays() == True:
    count = count + 1


print('In a sample of 1000 classes each with 23 pupils, there were', count, 'classes with individuals with the same birthday')

Solution

Error in this line:

for x in bdays:

should be

for x in range(len(bdays)):

Because you need to iterate over indices of birthdays but not birthdays itself.

And one more optimization:

count = 0
for i in range (1000):
    if random_birthdays() == True:
       count = count + 1

can be replaced by

count  = sum(random_birthdays() for _ in range(1000))