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)