# Bingo Mathematics

Bingo is one of the most sociable and enjoyable gambling games that exist. An announcer calls out numbers between 1 and either 75 or 90, and players mark off the numbers on their Bingo cards until they form a full row of marked-off numbers in any direction. There are 12 ways to form a win; eight of these do not use the “free” block in the centre of the card, while the remaining four do. Bingo is largely a game of luck, but there are still various principles of mathematics at play in the game.

## Probability in Bingo

Since each player has an equal chance of winning a game of bingo, the probability of any one player winning is simply one divided by the number of players that are playing. For example, if there are 50 players participating in a game, they all have a one in 50 chance of winning. This is a very simple example of how probability theory can be applied in Bingo.

Another more complicated example involves the probability of a Bingo being called after a certain number of calls. The following table shows the probability of a single player (with no other players playing) getting a Bingo after a certain number of calls. After just five calls, the probability is very low, but on the other hand, if the player still has not got a Bingo after 65 calls, he can consider himself extremely unlucky, as the probability of getting Bingo by the 65th call is 99.9%.

 Number of Calls 5 10 15 20 30 40 50 60 65 Probability of getting a Bingo 2e-05 0.0008 0.0059 0.0229 0.1435 0.4456 0.8144 0.9859 0.999

These probabilities will increase with an increase in the number of players playing the game. For example, if 100 players are playing a game of Bingo, the probability that someone will win by the 20th hand is 87.5%, which is much, much higher than the 2.29% chance that would be the case if there was only one player playing.

These probabilities only relate to how quickly a game will be won, and have nothing to do with the chances each player has of winning a game. As mentioned above, theoretically, each player has an equal chance of winning a game, since the numbers on their cards are random, and the numbers called out are also random, and each new call and game are an independent events, i.e. they have no bearing on future calls/games and are not influenced by previous calls/games.

Learn about how mathematics applies to other casino games, or refer to our Gambling Mathematics Glossaryto brush up on the main mathematical concepts that are at play in many popular casino games.