bingopete
Joined: Nov 1, 2019
• Posts: 2
November 1st, 2019 at 8:04:15 AM permalink
How would i figure out odds of Bingo being called if I excluded certain rows from bingo being called? eg. outside 4 corner game with "I' 'N' 'G' not being called (or considered wild) or Vertical 5 "B's" w/o 'I' 'N' 'G' 'O' not being called (or considered wild). These are just examples. I'm trying to figure out a 'standard' rule I can apply for certain rows not being called or excluded during a game before a Bingo would be called..
thanks,
BingoPete
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4460
November 1st, 2019 at 10:53:17 AM permalink
It depends on what you mean by "the odds of Bingo being called." Do you mean, the probability of getting a Bingo within a certain number of balls being drawn?
bingopete
Joined: Nov 1, 2019
• Posts: 2
November 1st, 2019 at 2:26:54 PM permalink
I'm playing 4 outside corners and I won't be calling I, N or G, just B or O. Since I will only be calling B's or O's I wanted to figure out how many B's or O's would be called before the likehood of a Bingo, a 'break even' if you will.

i wanted to do something like 'If you get 4 Corners within 10 #'s you get a bigger reward; After 10 #'s you get a smaller reward. I have some statistics about of how many balls could be called IF all letters would be eligible for calling but I would like to eliminate extra time being spent on calling non-significant balls for a certain column or row that is not necessary to win. There are a number of games they can be played where you would not call a specific row or column . I wanted to find a 'break even' point for a game with only certain columns or rows qualifying for a chance to win. Maybe a formula I can use to determine a chance but not a certainty of a win based on # or rows or columns not being called. This would apply to < 100 non-repeating cards in play
Tks,
bingopete
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4460
November 1st, 2019 at 5:00:13 PM permalink
In the case of four corners, it depends on how many cards you have.

Since you are ignoring the 45 I, N, and G balls, assume you have only 30 balls.
Also assume there is only one card.
In this case, color the four balls needed red, and the other 26 white. It does not matter that two of the balls have to be 1-15 and the other 61-75, since you are looking for four specific balls.
If you draw N balls, there are (30)C(N) combinations, of which (26)C(N-4) have the four balls needed to win, so the probability of winning in N balls or fewer (remember, drawing N balls includes all wins with fewer than N balls) is (26)C(N-4) / (30)C(N), which turns out to be N (N-1) (N-2) (N-3) / (30 x 29 x 28 x 27).

Let P be the probability that one particular card will win after N draws. The probability that none of a set of 100 cards wins is (1 - P)100, so the probability of at least one winner is 1 - (1 - P)100.

The probability of having anybody with all four corners in 10 B and/or O numbers drawn is 0.459569 for 80 cards, 0.499582 for 90 cards, and 0.536632 for 100 cards.