Bingo Odds

I was playing Bingo and managed to catch 3 of the first 4 called numbers on the same diagonal, leaving just one number for BINGO. Unfortunately, just like the Eagles receivers today, I didn’t catch it. However, it got me thinking...

Since the winning numbers have to be in certain positions relative to each other, does it affect the probability calculation that you will catch 4 of the first 5 numbers drawn for a diagonal BINGO?

I think the answer is No.

However, it does affect the probability that any of N bingo cards will get the 4 numbers that are needed for Bingo when the you are drawing for a diagonal bingo. That is because, even if there are a million bingo cards in the game there will always be a zero chance of a diagonal Bingo after say 5 numbers are drawn whenever two or more of the drawn numbers are N31-N45.

I haven't played bingo for many years but in the UK they sometimes had fun games (most use the 90-number version). On one occasion they were playing a little book of US-style bingo and I had a winning N line. Amazingly someone else had exactly the same N-line, so I had to share the prize. In regular UK bingo (3-lines of 5 numbers across, assuming there are less than 12000 pages sold for a in-house game), no two lines or houses should be identical. If it does happen, I heard it did once, the house has to pay out the full prize to both winners.