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Originally Posted by SammyG-SD
what you do is draw two EV lines, one for the pitcher and one for the batter,
where the intersect (.260) is the EV on the balance strategy.
OK, woot for guessing close. I almost typed in .260, but I hedged and put .260-.265, lol.
But I still don't understand. You can't draw an EV line for the pitcher... there are too many variables. Its an EV plane. The EV plane for the pitcher and the EV plane for the batter intersect in a line between .250 and .300. But I still don't understand how you get it down to a point.
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Now whats interesting is that the Nash Equilibrium is actually the same for each player, guess fastball 4/5 of the time, and then it moves back to the EV cross section (un exploitable), but if either player is not doing the 4/5 strategy, the other player can exploit it.
I know the Nash equilibrium mostly by name, not in practice. Which probably explains why I couldn't solve this one.