The math behind the Bingo game

Bingo is really old and fun game to play. It doesn’t require special knowledge to start playing. Millions of people enjoy it either live or in the internet. Of course live is much more fun to play where real people are involved. The internet bingo in other hand gives you freedom to choose when to play and where to play.


Let see how this game is played and what can be your odds to win. The game is simple – player gets a bingo card with 24 of 75 semi-randomly selected numbers. The card has five rows and five columns of numbers. The center cell is called free. The numbers in Bingo card is distributed as follows:

B column have numbers from 1 to 15;

I column have numbers from 16 to 30;

N column have numbers from 31 to 45;

G column have numbers from 46 to 60;

O column have numbers from 61 to 75;

The moderator draws the balls with numbers and there are usually 12 ways of winning that involve getting row, column or diagonal to be marked. Four winnings involve “free” cell (row, column and two diagonals). Of course there are more versions of Bingo that involve things like four corners, X, all edges, “T” and more. The calls are continued until someone achieve Bingo – at least one of 12 ways are filled.

The winning probabilities in Bingo is calculated according to number of calls N. In other words what is probability of Bingo after N numbers? Here is an interesting calculations of statistics and probabilities that involve single and cumulative turns.


Nothing new here – the more numbers are caller, the better odds to win. Calculations show that to get 50$% chance of winning, there must be at least 41 call. And to have 90% chance – 54 calls.

The table below represents probabilities of winning according to number of calls:


And lastly here is a number of total possible combinations that could exist on Bingo card:

\left ( \frac{15!}{10!} \right )^{4}\cdot \left ( \frac{15!}{11!} \right )=5.25\cdot 10^{26}

So just relax enjoy the game that is always a bit different every time. There are many ways to play bingo online that involve different rules, cards, styles. You can install an app to play your favorite game on smart phone where ever you are. And be careful, as any game – Bingo also is addictive.

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