[PokrLikeItsProse]

[ QUOTE ]
thanks for the feedback eric.

also, thanks for correcting some points that i left unclear or stated in error. my plan for this post was to come up with a range from a game theory POV. after that i wanted to come up with adjustments to the range based on certain player tendencies(in other words how to exploit certain mistakes made by opponents and how to adjust our range in relation to this).


[/ QUOTE ]

I think we would go about this by determining our raising range and dividing that into hands we would raise with and fold to a three-bet, raise with and call a three-bet, or raise with and cap vs a three-bet. (More cases with a five bet cap.)

To do this, I think we would start by determining the game theoretical strategy for our opponent to three bet. This can be complicated because you must consider the competing strategies of capping and putting your opponent into check-call mode where you may check behind on the turn vs just calling and planning on raising on the turn where your opponent may not bet the turn or bet-fold. In fact, an answer to the questions in the original post is incomplete unless you take into account your tentative plans on future streets. If you cap with a flush draw, are you checking behind if you miss on the turn and are you checking behind with any other hands as well?

One could think of adjusting optimal strategies to player tendencies, but it may just be easier to solve for specific profiles. We could imagine an opponent who a) will only three-bet the flop with a made hand that is two pair or better or b) likes to jam draws on the flop regardless of his opponent's raising range c) plays top pair hands aggressively on the flop regardless of kicker, but may like to slowplay sets. In all of these, we would be defining out opponent's three-betting range, but it's more like solving for different strategies rather than figuring out adjustments. It amounts to the same thing, but viewing the problem thusly might make things easier to understand.

My guess is that the game theoretical capping range is going to be close to capping with all strong draws plus enough made hands to make it difficult for our opponent to bluff you on later streets. I don't think the range is going to be containing hands like AKo or 77.