[cartman]

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Not a bad idea. A few things that make me question it though. If I raise, button cold calls, and SB 3-bets, then I think I have to call one more for my 2outer and fold the turn UI

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I agree.

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On the flip side, if I raise, button folds, and SB 3bets, can I really fold HU like this for one more? When I'm playing well the answer could be yes, but this guy was tricky enough that when I fold to the 3-bet I still don't feel good about it.

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I can easily fold for one more. Here is my assessment of the communication between us so far this hand:

SB 3-bets preflop: "I have a some showdown value"
You call two in the BB: "I have a hand too"
(SB's flop bet says nothing)
You raise the flop: "Look, I know damn well you may have a K and I don't care"
SB 3-bets: "I know you know damn well I may have a K and that you like your hand well enough to raise anyway and I don't give a rat's ass because I do have at least a K and I probably have you outkicked if we both have one!"

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One last question with this, suppose I raise button cold calls and SB calls. Turn rag I bet, both call. What's my river line here? I'd assume I'm looking to check and hope button checks through as well. If he bets though and SB calls as well, I think it's a fold for me.

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Under normal circumstances I think this is the only river plan. But given button's state of mind, I can certainly see him betting with a worse hand and when we check the river I can see SB calling with something as weak as a good Ace. I'm sure your judgment of the situation would be better than mine because you were the one playing with them, but by my estimate the pot would be about 12.5 BB when it came back to me on the river. I would think your hand would be good the required 7.4% of the time required to make the crying call.