Another way people could use this idea, but still run plays if they have time, is to use cards to determine where the game is entering the final quarter. If it's a blowout, you might just leave it. But if it's close, then you could play the 4th quarter on the field to see how it comes out based on the situation depicted from a set of cards.
I think the old Pennant Race baseball game was kinda like this, where you picked up a season 120 games in and took it from there to the end to determine the winners.
Ed
