[elindauer]

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To do this, I think we would start by determining the game theoretical strategy for our opponent to three bet.

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You're on the right track. To figure out what our opponent 3-bets, we need to know our raising range, from which we need to know opponent's betting range...

The tricky part is that we can't know opponent's betting range until we see the EV from the counter-strategies it produces! So to really know the answer, you have to solve the entire system mathematically, all at once.

This is really hard, but fortunately you can make some arguments about what it's likely to look like. I agree with your general premise that it should contain lots of good draws, and won't contain 77 / AKo.

You can also help find these optimal strategies by noting the definition... an optimal strategy can't be exploited. It has the right mix of bluffs / value bets no matter what cards hit. etc. Any strategy that is exploitable is wrong, so you adjust it to elliminate that and you are moving toward the optimal strategy.

One of these days I'm going to have to put together a tool for calculating the true optimal strategy...

-Eric