Bingo Math

In the below page, The Wizard of Odds calculate the Bingo Probability with different number of balls. Does he calculated based on 13 different patterns( including four corners)?

Also in the calculation of Single Bingo with No free Square the probability a Bingo will be hit at the 45th Ball is 0.0413347161. Lets say he has taken 13 different patterns. Can we conclude that any single line will be hit at the 45th Ball is (0.0413347161/13)? Are the probabilities of hitting any line is equally likely?

Quote: mimoban

In the below page, The Wizard of Odds calculate the Bingo Probability with different number of balls. Does he calculated based on 13 different patterns( including four corners)?

Also in the calculation of Single Bingo with No free Square the probability a Bingo will be hit at the 45th Ball is 0.0413347161. Lets say he has taken 13 different patterns. Can we conclude that any single line will be hit at the 45th Ball is (0.0413347161/13)? Are the probabilities of hitting any line is equally likely?

So, I reviewed several of the many pages WoO has about Bingo. This turns out to be a really good question about the 4 corners included or not, because I can't find a definition of American Bingo, on which the Wizard says these tables are based - not just on his pages, but on googling for the rules.

I believe a "single bingo" would be only 12 ways that include use of the Free Space, and not including the Four Corners win, which wiki refers to as a "special game". But I think the wizard will want to answer for himself, and possibly clarify what basic Bingo rules he's using on the WoO website.

The page I think you're referring to, since as a new poster the link was stripped, is:

https://wizardofodds.com/games/bingo/probabilities/1/

Perhaps you could confirm that's the page you're using?

Edit to add: 12 vs. 13 ways appears to affect both reference tables you're examining. Single hard-way bingo table is separate from both, and appears to indicate free square use is not a winner, but whether 4 corners is included on that seems even more unlikely, since all other winners require 5 numbers to win.

PM'd the Wizard to request he look at this.

You cannot just divide to get the probability for a single line because the 0.04133 includes times when two or three lines were completed at the same time.

4 corners doesn’t count as a bingo. 4/combin(75,4) = about 0.0000032910.

I'm no mathematician but it appears those calculations are wrong based on actual play. I could be interpreting the table incorrectly if it's not. Please explain. I play bingo about three times a week. And it does not take over 40 balls to get a single bingo. Depending on the game (pattern) after a certain number of balls are called, with an average of xxxx many players, I can expect a bingo. For example, the coverall usually bingo's around 57 called balls. The table indicates 71? It's very rare for any coverall to go beyond 60 called numbers. Double Hardway , you can expect to hit in the high teens and around 20 balls called. I think the table indicates over 40. These or my figures are actually based on play.

Quote: Vegasrider

I'm no mathematician but it appears those calculations are wrong based on actual play. I could be interpreting the table incorrectly if it's not. Please explain. I play bingo about three times a week. And it does not take over 40 balls to get a single bingo. Depending on the game (pattern) after a certain number of balls are called, with an average of xxxx many players, I can expect a bingo. For example, the coverall usually bingo's around 57 called balls. The table indicates 71? It's very rare for any coverall to go beyond 60 called numbers. Double Hardway , you can expect to hit in the high teens and around 20 balls called. I think the table indicates over 40. These or my figures are actually based on play.

Those are single card probabilities. See https://wizardofodds.com/games/bingo/probabilities/2/ for multi card probabilities.

Quote: beachbumbabs

So, I reviewed several of the many pages WoO has about Bingo. This turns out to be a really good question about the 4 corners included or not, because I can't find a definition of American Bingo, on which the Wizard says these tables are based - not just on his pages, but on googling for the rules.

I believe a "single bingo" would be only 12 ways that include use of the Free Space, and not including the Four Corners win, which wiki refers to as a "special game". But I think the wizard will want to answer for himself, and possibly clarify what basic Bingo rules he's using on the WoO website.

The page I think you're referring to, since as a new poster the link was stripped, is:

/games/bingo/probabilities/1/

Perhaps you could confirm that's the page you're using?

Edit to add: 12 vs. 13 ways appears to affect both reference tables you're examining. Single hard-way bingo table is separate from both, and appears to indicate free square use is not a winner, but whether 4 corners is included on that seems even more unlikely, since all other winners require 5 numbers to win.

PM'd the Wizard to request he look at this.

Hi Thanks that you PM'd the Wizard. You are correct, i was referring the same link you have given.

Quote: CrystalMath

You cannot just divide to get the probability for a single line because the 0.04133 includes times when two or three lines were completed at the same time.

Thanks very much for this.

Quote: mimoban

In the below page, The Wizard of Odds calculate the Bingo Probability with different number of balls. Does he calculated based on 13 different patterns( including four corners)?

There are different tables for each pattern.

Quote:

Also in the calculation of Single Bingo with No free Square the probability a Bingo will be hit at the 45th Ball is 0.0413347161. Lets say he has taken 13 different patterns. Can we conclude that any single line will be hit at the 45th Ball is (0.0413347161/13)? Are the probabilities of hitting any line is equally likely?

Again, each table is for a specific pattern. What you can assume is if the game ending pattern is a single bingo, the chances of hit hitting on the 45th ball, with a single card, is 4.13%, assuming you're looking at the single card table. There are other tables for multiple cards.

Quote: Wizard

There are different tables for each pattern.

But the table for Single Bingo, is i hope for Single Card with Wild in the middle. But even in a single card there are 12 lines generally possible? There is another special pattern, the four corners, Did you took that into the calculation too?