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bingo odds and probality

Bingo Odds

The long term odds of winning at bingo will vary from bingo room to bingo room dependent upon the proportion of money the bingo room pays back to the players. For example, if the bingo room at which you are playing pays back 95% of the money it takes as prize money, then over the long term you are likely to win back 95% of your money.

Of course, bingo players don't usually concern themselves with longterm odds - you would prefer to know the probability of winning each game. The answer to that question is higher than one divided by the total number of players. So if you are in a room of ten people playing for a full house, your odds of winning that particular game are higher than one in ten, or 10%. Why higher than 10%? Well, there is always the possibility that two or more of you might win on the same number.

You might say, well, if I play 10 games and the odds of winning each game are higher than 10%, won't I be guaranteed a win? Sadly, probabilities do not work like that - they have no memory. So if you lose one game, you will be no more likely to win a subsequent game than the person who won the previous game. If you play ten games, and the odds of winning each one are 10%, here is the way to calculate the probability that you will win one or more games:

Prob(winning one or more games)=1-(9/10)10= 0.65 or 65%

In reality, it can be difficult to know what the odds of winning any particular game are, as generally you are not made aware of the number of players.

The House Edge

The house edge is defined as the the percentage difference between the gross amount taken and returned. So if the bingo room takes £100 and pays back £90, the house edge is £10.

Interesting Fact

If you were playing a 90 ball game of bingo, with ten players in total, on average 77 numbers would need to be called before one player got a full house. If you multiplied the number of players by 10, the average number of calls would decrease to 67. In order to get a full house in 40 numbers or less, on average you would need over one million players!

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