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The Possibility to Calculate Bingo Odds and Probabilities

For gamblers who believe that calculating the odds and probabilities is only applicable to casino games and not with bingo, they may have to think twice. This is because it is also possible for a bingo player to determine their bingo odds and probabilities.

Often time bingo player will shrug off the idea of the possibility of calculating the odds and probabilities of their bingo game. They would assume that this context is impossible since bingo is a game of chance and involves a complex game that has incalculable odds and probabilities.

However there is the big chance of being able to assume the possible odds of playing bingo and to determine the probability of winning from a bingo game.

In order to determine the bingo odds and probabilities, two vital factors are needed to help calculate these possibilities. The first is to determine the number of cards the player is planning to play for a particular bingo game session.

The second information needed is the total numbers of card being at play during a bingo session. The first factor may seem easy to determine as this can be a personal choice of a bingo player. The second piece of information needed on the other hand is more difficult to determine.

But granting that a bingo player is able to establish a more reliable estimate as to the total numbers of bingo cards being at play on a particular bingo session, the odds and probabilities of the a player to win is calculated by dividing the number of cards being played by a bingo player from the total numbers of bingo cards at play and then multiply by 100. The answer is the player’s chances of winning which is presented in the form of a percentage.

Although it is not a common practice to calculate the bingo odds, it can somehow provide a bingo player significant figure on what are their odds to win from a bingo game. However the main problem that arises from using the above mentioned formula is the inability to access reliable figures on the total numbers of cards being at play since a single bingo player can play multiple bingo cards at once.

However some wise bingo players found a means that allow them to possibly determine their odds and probabilities from playing bingo by playing in a bingo game with less number of players.

With fewer competitions one can find less difficulty on tracking down the total number of bingo cards at play. This is vital information that is hard to obtain but once one is able to determine this figure, one can reliably calculate the odds of winning of a player from bingo.

Free bingo games online The Possibility to Calculate Bingo Odds and Probabilities For gamblers who believe that calculating the odds and probabilities is only applicable to casino games and

Bingo probability calculator

Durango Bill’s
Bingo Probabilities

(Math notation is generally the same as that used in Microsoft’s Excel. The MathNotation link will also give examples of the notnotation as used here.)

For 90 number Bingo ( 3 rows, 9 columns) please see Bingo 90.

The Bingo Statistics link gives tables and graphs showing the probability for getting “Bingo” after the announcer has called “N” numbers. Tables and graphs cover both a single board and a 50 board game.

The Bingo 4 Corners and Letter “X” (both diagonals) link shows the single board probability of getting these patterns after “N” numbers have been called.

The Bingo Picture Frame (all 4 edges) and Letter “Y” link shows the single board probability of getting these patterns after “N” numbers have been called.

The Bingo Probabilties for a Complete Cover link shows the probabilities for covering all squares on a Bingo board.

The “How to calculate” link shows how to calculate these numbers including how to calculate the probabilities when any arbitrary number of boards are being played in a game.

Probabilities for Swedish Bingo. A Swedish Bingo card has the familiar 5 rows and 5 columns, but the middle cell is not free. It has to be filled by having its number called.

Rules of the game: A typical Bingo card has 24 semi-random numbers and a central star arranged in a square of 5 rows and 5 columns. A Bingo card might look like:

We used the phrase “semi-random” to describe the numbers because the numbers in each column are confined within ranges. Column 1 will contain 5 random numbers in random order, but they are within a range of 1-15. Similar ranges exist for the other 4 columns (16-30, 31-45, 46-60, and 61-75). The central location is a “Free” spot. There are (15!/10!)^4 * (15!/11!) = 5.52+ E26 (more than 552 million billion billion) possible combinations that could exist – any one of which would be a legal Bingo card. (The “!” symbol is the mathematical notation for Factorial. e.g. Factorial(5) = 5 * 4 * 3 * 2 * 1 = 120.)

Note: The above number of combinations assumes the numbers in any column can be in random order. If the numbers in any column are always in sorted order with the lowest number on row 1 and the highest number on row 5, then the number of combinations in each of 4 columns is reduced by 5! = 120 and the number of combinations in the center column is reduced by 4! = 24.

Initially, the central “*” is counted as a “free” or “called” cell. Then, an announcer will call out numbers selected randomly within the total 1-75 range. (Usually this is done by randomly removing numbered balls from a revolving drum.) Whenever one of these called numbers matches a number on a player’s Bingo card, the player marks that number as “called”. Eventually, there will be a straight line of 5 called numbers that fill a row, fill a column, or form a corner-to-corner diagonal line. (Note: the “Free” center space can be part of the straight line). At this point the player yells “Bingo” and the game is over.

Probabilities: Of interest, in a single board game – What is the probability the player will have a “Bingo” after the announcer has called “N” numbers? Also, in a multiboard game, what is the probability that the first “Bingo” will show up after “N” numbers have been called? (Check the Bingo Statistics link.)

Variations on Bingo: Other patterns can be used for the game of Bingo. For example, a winning Bingo could be defined as filling a 2×2 block anywhere on a Bingo card. There are 16 possible locations where a 2×2 block could be located. Other Bingo variations could include filling any of the 9 possible 3×3 blocks, or filling a 2×3 block. A 2×3 block could also be rotated for 24 possible winning “Bingos”.

Other Bingo websites: The “Wizard of Odds” also has bingo statistics information – especially the gambling aspects of Bingo as well as a lot of good stuff on gambling in general. The probabilities given here match those in the “Wizard’s” tables. (It’s reassuring to have two independent calculations come up with the same results.)

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Probability Analysis that you will have a "Bingo" after "N" numbers have been called.