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 I 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
Graphs of how many times it takes a certain number of balls to get a “line”, for a given number of players, in 3D
The scale on the players/depth/z axis on the above 4 graphs is 2, 3, 4, 5, 7, 10, 15, 20, 30, 40, 50, 70, 80, 90, 100, equally spaced
There is a CSV file with the data for the above 4 Excel graphs formatted for the Excel spreadsheet
There is a CSV file with the data for the above 4 Excel graphs formatted for the Excel spreadsheet
Graphs of how many times it takes a certain number of balls to get a “house”, for a given number of players, in 3D
The scale on the players/depth/z axis on the above 4 graphs is 2, 3, 4, 5, 7, 10, 15, 20, 30, 40, 50, 70, 80, 90, 100, equally spaced
There is a CSV file with the data for the above 4 Excel graphs formatted for the Excel spreadsheet
There is a CSV file with the data for the above 4 Excel graphs formatted for the Excel spreadsheet
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
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
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
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 7 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
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
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
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 25 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 30 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 40 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
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 60 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 70 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 80 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 90 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
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
| Constant | Value |
|---|---|
| a | 92.11309 |
| b | 0.4841813 |
| c | 2.526737 |
| d | 18.16825 |
Graph of the average number of balls to get a “house” for 2 to 50 players
| Constant | Value |
|---|---|
| a | 92.8501 |
| b | 0.4983197 |
| c | 12.43463 |
| d | 57.50341 |
Graph of the average number of balls to get a “line” for 2 to 200 players
| Constant | Value |
|---|---|
| a | 145.1422 |
| b | 0.3053657 |
| c | 0.2895424 |
| d | 8.711613 |
Graph of the average number of balls to get a “house” for 2 to 200 players
| Constant | Value |
|---|---|
| a | 103.4377 |
| b | 0.3104399 |
| c | 10.74819 |
| d | 48.12477 |
Graph of the average number of balls to get a “line” for 2 to 300,000 players
| Constant | Value |
|---|---|
| a | 274.5214 |
| b | 0.2369405 |
| c | 0.005209487 |
| d | 4.610405 |
Graph of the average number of balls to get a “house” for 2 to 300,000 players
| Constant | Value |
|---|---|
| a | 179.4388 |
| b | 0.1217371 |
| c | 0.04500176 |
| d | 22.43121 |
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 200 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