How high do bingo numbers go

Traditional BINGO is played in person in a large hall. Players meet at the hall, pay a fee to get in, then the games begin. A night of BINGO consists of many BINGO games played continuously, one after another.

A single BINGO game proceeds like this: Each player has a number of BINGO cards (players can usually play any number of cards). Each BINGO card has 5 rows and 5 columns thus providing 25 spaces.

The columns are labeled from left to right with the letters: ‘B’, ‘I’, ‘N’, ‘G’, ‘O’. With one exception (the center space is “free”) the spaces in the card are assigned values as follows:

- Each space in the ‘B’ column contains a number from 1 – 15.
- Each space in the ‘I’ column contains a number from 16 – 30.
- Each space in the ‘N’ column contains a number from 31 – 45.
- Each space in the ‘G’ column contains a number from 46 – 60.
- Each space in the ‘O’ column contains a number from 61 – 75.

Here’s a sample BINGO card:

B | I | N | G | O |

10 | 17 | 39 | 49 | 64 |

12 | 21 | 36 | 55 | 62 |

14 | 25 | FREE SPACE |
52 | 70 |

7 | 19 | 32 | 56 | 68 |

5 | 24 | 34 | 54 | 71 |

The number of unique BINGO cards is very large and can be calculated with this equation:

While perhaps interesting to a statistician, the number of possible BINGO cards has nothing to do with player’s chances of winning.

You will note that there are 75 possible BINGO numbers:

When a player has a BINGO (5 marks in a row, column, or diagonal), he or she calls out BINGO. The game pauses while the card is verified. If indeed a winner, the game stops and a new game begins. If the card wasn’t a winner, the game proceeds where it left off. Each BINGO game proceeds until someone wins (there’s always a winner).

The first line of input contains *n*, the number of BINGO games that you will analyze. *n* game descriptions follow. Each game description specifies a card to be played followed by a sequence of BINGO numbers. You are to determine, when the holder of the card will win the game, assuming the player has just this one card and there are no other players.

Each card description consists of five lines, giving the numbers on the card row by row. All but the 3rd row contain 5 numbers; the 3rd contains 4 because of the free space. One or more lines follow that represent some ordering of all 75 bingo numbers. All bingo numbers are simply integers between 1 and 75 – the one-letter prefix is redundant. For each game, ouput the line “BINGO after *n* numbers announced” as appropriate.

##### Chances of Winning

Every BINGO game has a winning card, so a player’s chances of winning depend on the number of cards in the game and how many cards s/he is playing. For example, if a player has 12 cards in a game with 1200 cards, the chances of winning for that player is 1 in 100.

How high do bingo numbers go Traditional BINGO is played in person in a large hall. Players meet at the hall, pay a fee to get in, then the games begin. A night of BINGO consists of many BINGO## Bingo Calculator

### Take control of the outcome of your game

The Bingo Calculator allows you to link together all the parameters that can influence the odds of the players to get a bingo during a game. You can change the number of balls in the bingo caller in order to obtain the game outcome you would want. Per example, you can change those odds depending on how many cards/players you have in the game, how many prizes you give, and how long you want the game to last longer.

File name: 201018-bingomaker-bingo-calculator.xlsx

##### How does it work?

When you create a New Game, in the card settings, you can choose the number of random values in your bingo. By default, the number of values is 75, because the most popular bingo game is with numbers from 1 to 75. You’ll be able to choose from 25 to 150 random values in the settings.

The numbers in the table were found by calculating an average of all the results for each parameter. The number of winners indicated in the graph represents the average number of bingo lines (5 consecutive squares) obtained among all the cards of a game. Keep in mind that this tool is giving you average results and you can end up with slightly higher or lower numbers than the result you will get in the bingo card simulator.

The only parameter you need to set when you use the bingo calculator is the number of cards in the game. The statistics on the table will update themselves automatically. You can start analyzing the results to find which number of values you need to select during your project creation.

#### Parameters that can influence the calculator:

##### Number of total random values of your bingo and number of values drawn during the game

When you create a bingo project, you set how many total values will be in the bingo card squares. The relation between the number of total values and the number of winners can be seen in the bingo calculator for 25 to 100 total values. If the number of values is high, you’ll need to play many values in order to get some winning lines (get a bingo). If this number is low, you’ll need to play fewer values to get winning lines. As you can see in the example below, you can plan to get about 25 winning lines by modifying the number of total values on the cards.

**Example 1:**

If you play a game with 50 total values in your bingo and you have 100 players (100 cards), you will need to play about 24 random values to get an average of 25 winning lines.

If you play a standard bingo game (numbers from 1 to 75) and you have 100 players (100 cards), you will need to play about 35 random values to get an average of 25 winning lines.

If you play a game with 90 total values in your bingo and you have 100 players (100 cards), you will need to play about 40 random values to get an average of 25 winning lines.

##### Number of cards

This relation describes the link between the number of cards and the number of values to be drawn to get a certain number of winners. If you have many cards, you will likely get a lot of winning lines after you draw a small number of values. If you have fewer cards, you will likely need to draw more numbers to get the same number of winning lines as the probabilities are lower for a player to get a bingo.

**Example 2:**

If you play a standard bingo game (numbers from 1 to 75) and you have 25 players (25 cards), and if you play 30 random values, you will get an average of 3 winning lines.

When you have more cards, you will likely get more winners. If you play a standard bingo game (numbers from 1 to 75) and you have 100 players (100 cards), and if you play 30 random values, you will get an average of 13 winning lines.

##### Number of winning lines

Depending on the number of players, the number of total values in the bingo and the number of values drawn during the bingo, you can adjust the number of winners. All you need to do is to set these parameters accordingly.

**Example 3:**

Let’s say that I organize a bingo for 100 players (1 card each, so 100 cards), and I would like to have about 20 winning lines. I have 20 prizes to distribute among the winners. In order to make that scenario possible, I need to adjust the number of total values in the bingo and the number of values drawn during the bingo. Here are some possible scenarios to do so:

- Scenario 1: Draws: 23 / Random values: 50 / Number of winning lines: 20
- Scenario 2: Draws: 34 / Random values: 75 / Number of winning lines: 20
- Scenario 3: Draws: 42 / Random values: 95 / Number of winning lines: 20

I can technically pick any of those three scenarios because they all give me the same approximate number of winners (20 winning lines). Because most of the players are used to playing standard bingo (numbers from 1 to 75), I’m going to use the 2nd scenario. I have to set the number of values during the creation of my bingo project to 75, and draw about 34 random values during the game in order to get about 20 winners among the 100 players.

Bingo Calculator Take control of the outcome of your game The Bingo Calculator allows you to link together all the parameters that can influence the odds of the players to get a bingo during a ]]>