Some Python code to tinker with the ideas presented in the Numberphile episode "How to Win a Guessing Game".

guessing_game.py

"""
Some Python code to tinker with the ideas presented
in the Numberphile episode "How to Win a Guessing Game".
See: https://www.youtube.com/watch?v=ud_frfkt1t0
"""

import random
import time


a = None
b = None
k = None
loss = 0
wins = 0
ties = 0
fmt_intro = "    a |     b |     k "
fmt = """{a} | {b} | {k}"""
print fmt_intro
for i in range(1000):  # Number of "tries".
    a = random.randint(1, 100)  # Pick an integer between 1 and 100, inclusive.
    b = random.randint(1, 100)
    k = 50  # In this trial, I am setting `k` to a constant value.
    if a > k:
        # Guess that `A` will be the larger number...
        if a > b:
            wins += 1
        else:
            loss += 1
    elif a < k:
        # Guess that `B` will be the larger number...
        if a < b:
            wins += 1
        else:
            loss += 1
    elif a == k:
        # Unclear how to count these, so we specifically
        # keep track of ties.
        ties += 1

    print fmt.format(
        a=str(a).rjust(5),
        b=str(b).rjust(5),
        k=str(k).rjust(5)
    )
    # Does sleeping mess with the PRNG? Try it.
    # time.sleep(float("0.001"))
print "Wins:", wins
print "Loss:", loss
print "Ties:", ties
print "-" * 70
# Percentage of Wins, out of Tries. "i+1" because `i` is zero-based.
p1 = (float(wins) / float(i + 1)) * 100
print "Percent wins:", p1
print "-" * 70

Example output:

$ python guessing_game.py
    a |     b |     k
   81 |    68 |    50
   57 |    89 |    50
    7 |    36 |    50
    7 |    98 |    50
   28 |    58 |    50
   39 |    88 |    50
   83 |    68 |    50
   21 |    78 |    50
   81 |     3 |    50
   92 |    24 |    50
   98 |    57 |    50
[... snip! ...]
   59 |    71 |    50
    4 |    14 |    50
   64 |    53 |    50
    6 |    54 |    50
   90 |    21 |    50
   33 |    37 |    50
   15 |    30 |    50
   50 |    21 |    50
   24 |    24 |    50
   84 |    39 |    50
   28 |    88 |    50
   92 |    79 |    50
   81 |    93 |    50
   33 |    45 |    50
   53 |    65 |    50
   85 |    63 |    50
   97 |    42 |    50
    3 |    27 |    50
   59 |    34 |    50
   96 |    68 |    50
   45 |    21 |    50
Wins: 727
Loss: 261
Ties: 12
----------------------------------------------------------------------
Percent wins: 72.7
----------------------------------------------------------------------