Re: Game theory football
Yeah, your numbers match up with mine if the offense were to win with a 12 yd pass on 4th and 2. I found the game to be better with a loss for the offense. (actually, i got +.00003 EV for the Offense if you were to split on a 12 yard pass on 4th and 2, but thats no fun)
4th down numbers (the D_run% is the same as the O_pass%):
Yds / O_run / O_pass /O_EV
6 / .80 / .20 / (.73333)
5 / .667 / .333 / (.55556)
4 / .625 / .375 / (.37500)
3 / .556 / .444 / (.25926)
2 / .500 / .500 / (.16667)
My 3rd down numbers:
Yds / O_run / O_pass / D_Run / D_Pass /O_EV
10 .8108 / .1892 / .1892 / .8108 / (.81945)
9 .7780 / .2220 / .2220 / .7780 / (.73071)
8 .7264 / .2736 / .2736 / .7264 / (.64769)
7 .7351 / .2649 / .3930 / .6070 / (.39843)
6 .6640 / .3360 / .4261 / .5739 / (.17520)
5 .6447 / .3553 / .4418 / .5582 / +.03893
4 .5800 / .4200 / .4769 / .5231 / +.18798
3 .5643 / .4357 / .4772 / .5228 / +.34163
and 'yes' to the earlier post by AB that if 1 player plays according to the percentages above, the other "plays" optimal as well.
Typed this fast, so sorry about grammar & wording.
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