Quote Originally Posted by a500lbgorilla
If either person has a 3:1 chiplead, I push every sb reguardless of which one I am when stacks are 10bets. +EV?
Not unless your opponent is way too tight.*
Restricting the possible actions to pushing or folding preflop makes the game simple enough that you can actually solve it by direct computation. There is a "minmax strategy", a range of hands you play that guarantees that no matter what your opponent does you have at least 50% chance of winning (starting with equal stacks and button is allocated randomly). If both players play the minmax strategy the outcome just depends on who gets the best cards. If you play the minmax strategy and your opponent does not you get an edge.
What you give up if you play the minmax strategy is the ability to exploit weaknesses in your opponents play.
Paper, scissors, rock is an example of a game with a very simple solution. The minmax strategy is to pick one of the three with equal probabilites each time. No matter what your opponent does he can't get an edge over you. But if you get a "read" on your opponent's strategy you could be better off picking a strategy that exploits that (like in The Simpsons where Bart and Lisa play, Bart thinks "Good ole rock, nothing beats rock!" and Lisa picks paper).
In summary it is possible to make a bot that is essentially unbeatable HU (in the sense that you can't get an edge over it) as long as you stick to push-folding PF. And such a bot would push about 58% of hands when stacks are 10BB.*

* minor caveat: so far I've only done the computations for chip EV, not match equity EV. My hunch is that under optimal (minmax) play there is not much difference heads up.