When I was younger, me and my neighbor would routinely create systems using dice or cards to decide football game, baseball, hockey, tennis, boxing basketball and auto racing. And usually we revised our system every few months.
In the cases of football and baseball, we would do it play-by-play (or pitch-by-pitch). Hockey was in 10 second "turns" as was boxing. Tennis, shot-for-shot. Basketball was possesion-for-possesion. With auto-racing, I had a Daytona 500 board game that we used combined with our system of dice and cards. I usually only got 1 or 2 seasons into it (with hockey, basketball and baseball, I used short seasons) before I would either move to something else or feel the need to revise it and start over.
No, my family didn't have much money when I was growing up.
