Bingo Probabilities

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.

each individual game should definitely last longer... you're boss is incorrect in stating "they will win quicker"

Since the games all happen at the same time though, further thought needs to be given to whether or not this will save money. I think it will because assume when 80 people play bingo you expect there to be a winner on average every X days. When we play 4 games with 20 people each individual game should on average take Y days where Y > X. So every Y days the 4 games should end. Hence the 800 is spent over a longer time period (Y and opposed to X)

Those were my thoughts too, the issue is I need to find a way to explain it to him. He feels one way, I feel the other, so is there a way that I can "prove it" to him?

verbally explain using limits as the number of people playing gets huge, someone wins fairly quickly. If everyone in the world played, someone would win in the first 5,6 or 7 numbers. So more people implies games go quicker. Likewise, fewer implies games take longer