My three-year-old son loves BINGO (U.S. version). This morning I took him to observe "senior BINGO" at a local fast food joint, and something interesting (though not surprising) happened:
After a certain amount of numbers had been announced, senior "Paul" exclaimed that he had finally got one (1) to match his board. Fast forward a few more turns of the ball cage, and another player wins. Now, the caller spins the cage until 5-6 balls are out, THEN replaces all of the balls that had been called, and immediately starts the next round with the 5-6 queued balls that were not replaced.
Paul wins the next game, and I start thinking:
How many balls would you have to queue between rounds/games (from those not chosen) to ensure, with a certain confidence C (or a certain probability P?) that there is not a back-to-back winner?
The problem gets complicated quickly, at least the way I look at it. This would surely depend on the number of players, and on the number of spaces on each board that match the winner's board. If the problem is too tricky, I'd certainly be satisfied with a computer output for a few combinations of players, number of balls announced before a win, etc. (or with a description of how/why it is so complicated).
