Single Line Bingo Probability Formula
February 20th, 2014 at 8:26:04 PM
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I'm creating a bingo style game where the host (a non-participant) needs to control the average length of a match. Based on this chart, it will take one player an average 41.36 rounds to claim a single line bingo.
There are two inputs in effect here, 1) the number of players and 2) the range of numbers available (1-75). In my case, assume the number of players is a fixed amount (say 100), and the desired rounds is 50.
1) What is the formula that was used to calculate the chart?
2) How could this formula be refactored so that round is an input and the numbers available (e.g. 85 instead of 75) is output?
With this information I plan to generate bingo cards for the 100 individuals with the expectation that the average game will take 50 rounds.
Any pointers or references would be greatly appreciated.
There are two inputs in effect here, 1) the number of players and 2) the range of numbers available (1-75). In my case, assume the number of players is a fixed amount (say 100), and the desired rounds is 50.
1) What is the formula that was used to calculate the chart?
2) How could this formula be refactored so that round is an input and the numbers available (e.g. 85 instead of 75) is output?
With this information I plan to generate bingo cards for the 100 individuals with the expectation that the average game will take 50 rounds.
Any pointers or references would be greatly appreciated.
February 20th, 2014 at 11:32:16 PM
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Loosely, I can build a simulation for you which would give those answers. However, I would wager the language I would build it in is not one you have access to (Matlab).
In terms f an actual formula to calculate these things I would guess that it would be so complicated and intractable that you would be just as well to build a simulation.
Let me suggest the following references (lifted from the bottom of the page you were on):
https://wizardofodds.com/games/bingo/probabilities/2/
http://www.durangobill.com/Bingo.html
If those don't do it post again and I will see if I can help you (I'm a bit drunk right now and can't really be of use at the moment)
In terms f an actual formula to calculate these things I would guess that it would be so complicated and intractable that you would be just as well to build a simulation.
Let me suggest the following references (lifted from the bottom of the page you were on):
https://wizardofodds.com/games/bingo/probabilities/2/
http://www.durangobill.com/Bingo.html
If those don't do it post again and I will see if I can help you (I'm a bit drunk right now and can't really be of use at the moment)
February 21st, 2014 at 5:17:59 AM
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You're right, I don't have access to MatLab, and likely wouldn't understand the mathematics enough to be able to convert it (to C, C#, Java, javascript, etc).
I think a simulation is going to be the most appropriate anyway. Ultimately, I plan to have a function where I can just pass the number of players and desired game length and return the total numbers required. The user will drag sliders for the desired game length and players, confirm, then the cards will be generated based on the derived total number range.
I also found this as a great resource:
http://www.claysturner.com/dsp/probability.pdf
I've actually went though those pages extensively, and mostly understand each individual concept (probability that a card with X matches has bingo and probability that after 10 calls with 4 matches, that a player calls bingo, etc), but I'm not sure how to relate them to my requirements. I've even been studying hypergeometric distribution, the concept of PMF and CDF, but I'm not fully understanding them yet (it's beyond my studies in school). Compound this with mathematical syntax like the ( ) combination syntax, and I'm struggling a bit to convert it to a programming language.
I think a simulation is going to be the most appropriate anyway. Ultimately, I plan to have a function where I can just pass the number of players and desired game length and return the total numbers required. The user will drag sliders for the desired game length and players, confirm, then the cards will be generated based on the derived total number range.
I also found this as a great resource:
http://www.claysturner.com/dsp/probability.pdf
I've actually went though those pages extensively, and mostly understand each individual concept (probability that a card with X matches has bingo and probability that after 10 calls with 4 matches, that a player calls bingo, etc), but I'm not sure how to relate them to my requirements. I've even been studying hypergeometric distribution, the concept of PMF and CDF, but I'm not fully understanding them yet (it's beyond my studies in school). Compound this with mathematical syntax like the ( ) combination syntax, and I'm struggling a bit to convert it to a programming language.
