Re: Game theory football
That looks doable, I'll take a look when I have a few mintues.
Here's one (with answer) from real football that's always bothered me.
Team A is down by 14 points and scores a touchdown with one minute to go. Obviously, any scenario in which Team B scores at all, or Team A fails to get another touchdown, means team B wins. So Team A should assume it will get another touchdown.
We all know that Team A always goes for one point in this situation. That has about a 98% chance of success in NFL football, versus 45% for two points. If it makes the one point, when it gets the next touchdown it will have a choice between going for 1, with 98% chance of overtime so a 49% chance of winning, or 2 with a 45% chance of winning. So going for 1 point on the first touchdown gives a 98%*49% = 48% chance of winning, assuming Team A gets another touchdown.
If Team A goes for two instead, it will make it 45% of the time. Then it will go for one at the next touchdown, for a 98% chance of victory. 55% of the time it will miss, then go for two on the second touchdown, for a 45% chance of overtime and a 22.5% chance of victory. 45%*98% + 55%*22.5% = 56% chance of winning.
Now I know specific game situations could change this, maybe the kicker has been erratic or the short-yardage running back is hurt. But these could work either way, so a lot more than half the time, two points is the right answer. But no one ever tries it. Why not?
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