bingo.ipynb

Kernel: Python 3 (system-wide)

Bingo Simulator

import numpy as np
import random as r

# returns a random bingo board
def newBoard():
    B = np.array(r.sample(range(1,16),5))
    I = np.array(r.sample(range(16,31),5))
    N = np.array(r.sample(range(31,46),5))
    N[2] = 0
    G = np.array(r.sample(range(46,61),5))
    O = np.array(r.sample(range(61,76),5))
    return np.vstack((B,I,N,G,O)).transpose()

# Checks if a bingo board `board` is a winner given called numbers `called`
# returns an numpy truth array of winner of type [R C D]
def isAWinner(board:np.array, called:list):
    blank = np.ones((5,5))
    blank[2][2]=0

    # This will make `blank` have a zero in boxes that `board` has numnbers that were in `called`
    for i in called:
        blank *= (board - i)

    # Check for row of zeros
    R = any([all(blank[i]==0) for i in range(5)])

    # Check for column of zeros
    blank = blank.transpose()
    C = any([all(blank[i]==0) for i in range(5)])

    # check for diagonals of zeros
    D = all([blank[i][i]==0 for i in range(5)]) or all([blank[i][4-i]==0 for i in range(5)])

    return np.array([R,C,D])

# we will collect our data in `winners`
winners = np.array([0,0,0])

# play 100,000 games
for game in range(100_000):

    # in each game call random numbers from 1 to 75
    call = r.sample(range(1,76),75)

    # there are 1000 people playing each game
    boards = [newBoard() for i in range(1_000)]

    # increase the number of called balls for and check for a winner in the 1000 boards
    breakAfterThisBall = False
    for ball in range(1,76):
        called = call[:ball]
        for board in boards:
            test = isAWinner(board, called)
            # if there is a winner, record the types of winners
            if sum(test) >= 1:
                winners += test
                breakAfterThisBall = True
        # Break after the round that found a winner
        if breakAfterThisBall:
            break

# 100_000 games with 1000 boards each
[49125 46586 63840]

# at least 421755 but probably around 700_000 games with 100 boards each
[396054 373104 421755]