At my work, we are currently playing a game of bingo, #'s 1-75 (B: 1-15, I: 16-30, N: 31-45, G: 46-60, O: 61-75, with randomly selected numbers in each letter, and 24 numbers per board), and there are 80 people playing, pulling a # a day, with a pot total of $800. We want to split the game into 4 separate games with 20 people playing, pulling 1 # a day with a pot total of $200/game. We are doing this so that more people can win. Now, I believe that each game SHOULD take longer to win, because there are fewer people playing/game, meaning that in the long run, this should save money. My boss feels that we will spend more money, because there are more games being played so more winners, and they will win quicker.
How could I possibly figure this out? Basic statistics and probabilities I get, but this seems so much more complicated to me. Thanks.