Bingo Probabilities for 90 balls

Updated:

These statistics come from the British Bingo game which can simulate the players

Index

How many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players

Introduction

The number of balls to get a 'line' may vary more than for houses because you need to get five balls in a row.

The shapes of these graphs are not quite the bell-shaped normal distributions you might expect for random events.

A similar skew was found by a simple simulation of American-style bingo.

It might be that the random-number generator is biased but the same pattern is seen on both Linux and Windows systems which probably use different ways of generating random numbers. Linux may partly use the noise from mouse movements and key-presses whereas Windows may just use a mathematical series.

The numbers on a board in the British Bingo game are chosen so that:

  • the numbers are in a given range for each column. For example, the first column has numbers in the range 1 to 9,
  • each column probably has at least one number.

Therefore not all random selections of numbers from 1 to 90 can be represented on a board in British Bingo. For example: 1, 2, ... 15 cannot. Therefore it may take longer to get a 'line' or 'house'. This layout of numbers comes from the set of bingo cards the developer played with at on old folk's home.

The normal distributions below are based on the average and variance of the collected data. There is a discussion of the mathematics elsewhere

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players, showing approximate normal distributions

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players, showing approximate normal distributions
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for a given number of players, showing approximate normal distributions

Graph of how many times it takes a certain number of balls to get a 'line', for a given number of players, in 3D

Graph of how many times it takes a certain number of balls to get a 'line', for a given number of players, in 3D
Graph of how many times it takes a certain number of balls to get a 'line', for a given number of players, in 3D

Graph of how many times it takes a certain number of balls to get a 'house', for a given number of players, in 3D

Graph of how many times it takes a certain number of balls to get a 'house', for a given number of players, in 3D
Graph of how many times it takes a certain number of balls to get a 'house', for a given number of players, in 3D

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 2 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 2 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 2 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 3 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 3 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 3 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 4 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 4 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 4 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 5 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 5 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 5 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 10 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 10 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 10 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 15 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 15 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 15 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 20 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 20 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 20 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 50 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 50 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 50 players

There are CSV files with the data for the 'lines' and 'houses'

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 100 players

Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 100 players
Graph of how many times it takes a certain number of balls to get a 'line' or a 'house', for 100 players

There are CSV files with the data for the 'lines' and 'houses'

There is a file with the raw data for the above graphs together with the scripts used to total that data

Average number of balls to get a 'line' and 'house' for a range of number of players

Graph of the average number of balls to get a 'line' for 2 to 50 players

Graph of the average number of balls to get a 'line' for 2 to 50 players
Graph of the average number of balls to get a 'line' for 2 to 50 players
Approximation for the average number of balls to get a 'line' where there are 2 to 50 players

Approximation for 2 to 50 players for line

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a92.11309
b0.4841813
c2.526737
d18.16825

Graph of the average number of balls to get a 'house' for 2 to 50 players

Graph of the average number of balls to get a 'house' for 2 to 50 players
Graph of the average number of balls to get a 'house' for 2 to 50 players
Approximation for the average number of balls to get a 'house' where there are 2 to 50 players

Approximation for 2 to 50 players for house

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a92.8501
b0.4983197
c12.43463
d57.50341

Graph of the average number of balls to get a 'line' for 2 to 200 players

Graph of the average number of balls to get a 'line' for 2 to 200 players
Graph of the average number of balls to get a 'line' for 2 to 200 players
Approximation for the average number of balls to get a 'line' where there are 2 to 200 players

Approximation for 2 to 200 players for line

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a145.1422
b0.3053657
c0.2895424
d8.711613

Graph of the average number of balls to get a 'house' for 2 to 200 players

Graph of the average number of balls to get a 'house' for 2 to 200 players
Graph of the average number of balls to get a 'house' for 2 to 200 players
Approximation for the average number of balls to get a 'house' where there are 2 to 200 players

Approximation for 2 to 200 players for house

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a103.4377
b0.3104399
c10.74819
d48.12477

Graph of the average number of balls to get a 'line' for 2 to 300,000 players

Graph of the average number of balls to get a 'line' for 2 to 300,000 players
Graph of the average number of balls to get a 'line' for 2 to 300,000 players
Approximation for the average number of balls to get a 'line' where there are 2 to 300,000 players

Approximation for 2 to 300,000 players for line

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a274.5214
b0.2369405
c0.005209487
d4.610405

Graph of the average number of balls to get a 'house' for 2 to 300,000 players

Graph of the average number of balls to get a 'house' for 2 to 300,000 players
Graph of the average number of balls to get a 'house' for 2 to 300,000 players
Approximation for the average number of balls to get a 'house' where there are 2 to 300,000 players

Approximation for 2 to 300,000 players for house

y=d+(a-d)/(1+(x/c)**b)

sigmoidal

Constant Value
a179.4388
b0.1217371
c0.04500176
d22.43121

Graph of the average number of balls to get a 'line' or 'house' for 2 to 50 players

Graph of the average number of balls to get a 'line' or 'house' for 2 to 50 players
Graph of the average number of balls to get a 'line' or 'house' for 2 to 50 players

Graph of the average number of balls to get a 'line' or 'house' for 2 to 200 players

Graph of the average number of balls to get a 'line' or 'house' for 2 to 200 players
Graph of the average number of balls to get a 'line' or 'house' for 2 to 200 players

Graph of the average number of balls to get a 'line' or 'house' for 2 to 300,000 players

Graph of the average number of balls to get a 'line' or 'house' for 2 to 300,000 players
Graph of the average number of balls to get a 'line' or 'house' for 2 to 300,000 players

There is a CSV file with the data for the above graphs. We are collecting new data

Index