Quote Originally Posted by kfaess
The way I see it:
The fundamental reason to bet is to induce your opponents to make mistakes. If you think that he absolutely has AK
He flipped his hand up, so he definitely has AK and he knows you know that.

and will continue on the turn when you make a bet, then make the bet that will maximize your expectation for the bet. He has 10 outs (3 aces, 3 kings, 4 tens) assuming that he does in fact have AK. So you bet enough to make drawing to those outs a bad play but a play that he would still make.
Right, his optimal strategy is to call just enough to have pot odds to hit his pair on the next card. But he's not playing that strategy, he's playing check/fold. Against which your optimal strategy is to bet.

If you bet the turn and he calls then you do not necessarily have 70% of the larger pot because he may hit his card/bluff you off your hand. I feel like in order to make a calculation like that you have to consider every possible scenario.
On average you have 70% of the larger pot. He can't bluff you off your hand if you know his cards.

That point about widening people's ranges postflop is interesting, I'm pretty sure I do that when trying to talk myself into a call with a marginal hand.