TITLE: Why does this not seem to be random?
QUESTION [40 upvotes]: I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are.
from random import randint

def averager(times):
    tests = list()
    for _ in range(times):
        l = [randint(0,100) for _ in range(100)]
        tests.append(len(set(l)))
    return sum(tests)/len(tests)

print(averager(100))

For some reason, the number of different guesses averages out to 63.6
Why is this?Is it due to a flaw in the python random library?
In a scenario where people were guessing a number between 1 and 10
The first person has a 100% chance to guess a previously unguessed number
The second person has a 90% chance to guess a previously unguessed number
The third person has a 80% chance to guess a previously unguessed number
and so on...
The average chance of guessing a new number(by my reasoning) is 55%.
 But the data doesn't reflect this.

REPLY [7 votes]: This is an example of the Birthday Paradox / Birthday Problem.
Birthday problem - Wikipedia, the free encyclopedia
I was just looking at my Online Cryptography class video lecture today on this very problem.
Coursera.org: crypto-009
There is an apparent paradox that there is more duplication of numbers than expected when the random numbers are supposedly independent. 
But the Birthday Paradox is just one example of when our intuitive statistical sense is dead wrong.