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AKICIF: A mathematical query
Jul. 8th, 2009 12:34 pmLast Wednesday, I stopped on impulse at the Tailgate bar to play Buzztime Trivia. Which I did, but there was also a bingo-type game going on. (I say "bingo-type" because it's called GATES rather than BINGO, for whatever reason. And you yell "Gates!" when you have the requisite combination.)
So anyway, the final game was the big $600 prize game, where you had to fill in the entire board to win -- a 5x5 grid of 24 numbers, because of the free space in the center. They called out (IIRC) 62 numbers, and there were no winners -- I was two numbers shy.
What I'd like to know is: At what point (how many numbers being drawn) does any one board have a 50% shot of winning, where winning is defined as filling in the entire board? And do multiple players increase those odds? How?
This is based on the standard bingo setup of 75 numbers in 5 columns, with each column containing 15 numbers, sequentially. (I assume the third column, with the free space, nudges the odds for that column somewhat.)
I have no idea how to work the math for this, other than assuming that factorials are involved somewhere.
So anyway, the final game was the big $600 prize game, where you had to fill in the entire board to win -- a 5x5 grid of 24 numbers, because of the free space in the center. They called out (IIRC) 62 numbers, and there were no winners -- I was two numbers shy.
What I'd like to know is: At what point (how many numbers being drawn) does any one board have a 50% shot of winning, where winning is defined as filling in the entire board? And do multiple players increase those odds? How?
This is based on the standard bingo setup of 75 numbers in 5 columns, with each column containing 15 numbers, sequentially. (I assume the third column, with the free space, nudges the odds for that column somewhat.)
I have no idea how to work the math for this, other than assuming that factorials are involved somewhere.
