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The first thing you want to ask yourself is how strong or weak your opponents threebet calling range is. The 2nd thing you want to ask yourself is how strong or weak your range is. Now without making a bajillion page post, I'll say this: If heroes range is much weaker than our opponents, then we want to keep the pot small and see as many streets as possible. If our range is stronger than our opponents range, cbetting and bulding pots is a great strategy. Regarding the different flops.
K97, (There are soooooo many factors to talk about so dont go thinking its as cut and dry as this), if my range is weaker than my opponents, or vice versa, i'm checking this flop everytime, unless there's some overwhelming factor to sway us otherwise. You just dont want to build a pot for your whole stack when if that happens your losing.
T42 is a little trickier. If your opponent has a relatively weakish threebet call range (maybe say 22+, KJ+, sc's), I'd cbet this for a few reasons. One, its a range that misses our opponent a lot and therefore we are going to cbet it a lot as a bluff. Secondly, there are a lot of hands that we can easily take a two street bet check bet value line against (AK/AQ, 55,33,54,66,77,88,99).
Now if our opponents range is stronger than ours and relatively strongish (88, AJ+) I'd be much more inclined to check this since we cant easily get two streets and may get bluffed off easily by a raised cbet. I think were less likely to get bluffed off from a two barrel after we check this flop. Let me make this clear: Versus a tight 3bet call range, WE ARE NOT wanting to stack off with T9 here.
Lastly, AK7, I have learned to love checking these flops since we have no equity and its such a good cbet board. Some people tend to assume you have a hand when you check this board, and you get to take the turn away with a bet more easily.
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