here's a pretty tough one :

[spoohunter]

My opponent raises MP. I put him on A10+. 88+, QJ+, KJ+.

Where exactly should I start to three bet? Any way to figure this out mathemetically?

[OrianasDaad]

Without looking at your own cards first:

~68% of the hands contain at least one ace.
~15% of the hands contain a pocket pair.

Just guessing, I'd say that any PP and AK-AQ are +EV.

[imported_ncray]

I'd like to assume that all players left to act would fold, as that simplifies things a little bit. Knowing that your opponent would automatically call a 3-bet and assuming that he would never cap, would it be correct to 3-bet with his range of hands and them some?

If you raise with any card in his exact range of raising hands, then your hand rates to be neither a favorite nor an underdog, on average, and would be a neutral EV raise without considering other factors.

But, you have several advantages.
1.A positional advantage
2.Your 3-bet shows greater strength, and you have "taken control of the hand"
3.There is dead money in the blinds (assuming that the blinds automatically fold)

I suspect that all these advantages increase your range of 3-betting hands substantially, but I don't know by how much (also defined by how well postflop the both of you play). I'd like to know if this simplied way of looking at things is theoretically correct. You don't have to have the best hand 55% of the time you raise, because you assume he will call the raise everytime it is folded around to him. Also, you don't have to have the best hand 50% of the time, because of the reasons I illustrated. Maybe 40% is a good number.

[DougOzzzz]

all pairs JJ and better, AK (suited or unsuited), AQ (suited or unsuited), and AJ suited all win >50% against the posted range of hands. Everything else wins<50% (according to pokerstove).

[DougOzzzz]

Yes, there's more to it than just picking all hands >50% to win. But it's better to look at what percentage a certain hand will win rather than what percent of opposing hands that hand is better than.

Take a hand like TT. TT is favored to win against AK, AQ, AJ, AT, KQ, KJ, QJ, 99, and 88, and the dog against JJ, QQ, KK, AA (obviously, it is tied with TT). By your reasoning, you're ahead against 75% of your opponents possible hands. Actually, it's more than that. Since there are 16 ways to make an unpaired hand (suited or unsuited) and only 6 ways to make a paired hand, you're actually ahead of 120 hands, and losing to just 24 (83.3%). However, most of the time that you are ahead, you are only a small favorite (53-57%). When you're behind, you're behind 81-19 on average. Thus, TT will actually lose more than half the time against this range of hands (it's very close, though).

[DougOzzzz]

I fudged the poker stove thing and forgot to include some hands I think. Was working through my own explanation of why TT wins <50% and the numbers didn't quite add up right to me, so I checked it again and TT does in fact win >50% (52.4%). The reasoning is still sound, though. I rechecked everything else, and TT is the only hand missing from my original list.