## ## 1 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

## ### 1.1 Introduction

## ### 1.2 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

## #### 1.3 Graphs of how many times it takes a certain number of balls to get a “line”, for a given number of players, in 3D, as charts in Excel

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

## #### 1.4 Graphs of how many times it takes a certain number of balls to get a “house”, for a given number of players, in 3D, as charts in Excel

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

## ### 1.5 Graphs 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 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

## ## 2 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

## #### Approximation for 2 to 50 players for line

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

## #### Approximation for 2 to 50 players for house

Constant | Value |
---|---|

a | 92.8501 |

b | 0.4983197 |

c | 12.43463 |

d | 57.50341 |

## ### 2.1 Graphs of the average number of balls to get a “line” or “house” for 2 to 200 and 300,000 players

#### Graph of the average number of balls to get a “line” for 2 to 200 players

## ##### Approximation for 2 to 200 players for line

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

## ##### Approximation for 2 to 200 players for house

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

## ##### Approximation for 2 to 300,000 players for line

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

## ##### Approximation for 2 to 300,000 players for house

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

## ### 2.2 Graphs of the average number of balls to get a “line” or “house” (together) for 2 to 200 and 300,000 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