[Tater10]

Here is a stupid game i invented when i began reading about game theory a couple years ago. I believe i have found optimal ev for this game, and would like to see if anyone else has the same results.


It's 1st and goal from the 10 yardline. Offense and defense have 2 dice each (a Red die for Run, a Purple die for Pass).

Here is how it works:
Offense and defense secretly select 1 die that he they are going to roll. They each roll at the same time (neither knows the color of the opponents die until the roll.)

This is just like football, you have 4 downs to get into the endzone.

How to gain yards and score:
Offense: Pass die; defense pass die: Incomplete pass, down is over.

Offense: Run die; defense pass die: Offense gains the yards on the die. (offense would gain 1-6 yards)

Offense: Pass die; defense run die: Offense gains 2x yards on the die. (offense would gain 2-12 yards)

Offense: Run die; defense run die: Offense gains 1 yard no matter what he rolls.

Caveat: Just like NFL, the endzones are 10 yards deep. So, if it's 4th and 2 and you throw a 12 yard pass, that pass is incomplete out the back of the endzone and the defense wins.

Obviously, if it's 4th and 1, 3rd and 2, 2nd and 3, offense would just run and there is no way for the defense to stop it, so the game is over when its 4th/1, 3rd/2, 2nd/3.

If the offense scores, he gets 1 unit. If the offense doesnt score, defense wins 1 unit. So, would you rather be offense or defense, and by how much? (you would be playing against someone who knew optimal strategy)

Extra Credit: It's 1st and 10 from the 20, and you can make a 1st down at the 10 yardline. Same rules except offense gets 2:1 from the defense. Would you rather be offense or defense, and by how much?