ShipItUPS

I have never done this intensive of math analysis before so I could be totally wrong, but I think i got it

Going to try to figure this out with math. Lets say he has X% continuing range if we jam consisting of all 2 pair+, all sets, 7s6s, As9s+ and Y% folding range. Y=(1-x) If we jam we have 45% equity vs his continuing range. So we then get that

EV(bluff)= X(W%($won)-L%($loss)+Y(current pot)
=X(.45(2268)-.55(1732))+((1-X)908).

For the jam to correct we need Y to be => some number such that EV(bluff)>EV(call) If we call its a little tougher to figure out because of implied odds, redraws etc. Feel like someone should CRev it (I would but don't have the program). By saying we GII on all turns we hit, Fold all board pairs, and continue on non paired turn if he bets less than pot. Then get the rest in on all rivers we hit. (seem reasonable?) Here is my rudimentary attempt saying we have 80% equity when we hit turn and 90% on rivers (he can have higher flushes) and we call 800 on all non paired turns (Just about 2/3 pot seemed reasonable) priced in folding all missed rivers. Using 2x rule to get 30% chance of hitting

EV(call on flop)= %(hit turn)(W%$won-L%$lost)-$call%(board pairs)+ %(all other turns)((turn equity)$won-(1-equity)$(call flop+call turn))
= .3(.8(2268)-.2(1732))-372.2+.5((.32268)-(.7*1172))
=296

So then solve for Break even X

296=X(.45(2268)-.55(1732))+((1-X)*908)
296=68X+908-908X
-612=-840X
.72=X
Y= (1-X)=.28

So we need him to fold 28% of the time for a jam to be as profitable with these assumptions. If he bets more or less on turn will change that number, but i think it shows given reads seems like this is a call and he isn't folding enough for a bluff to be maxEV.

well played, feels really hard to get called by worse if we 3b on flop

I hate turn sizing, missing so much value long run. That said we only need 29% equity to call off here and are like 23% vs a range of all flushes and straights. If he ever has semi bluffs or two pait here its a snap call

Bet turn check call non heart river make money

I don't agree with Mykal's analysis. The 4bet click back is very indicative of a monster, usually AA exactly. Why? They have little to fear when you call. The 1 combo of KK is more likely to ship/4bet larger or call the 3bet and get it in on non A flops. I would also heavily discount the 6 combos of QQ. Most people will call pre and decide on the flop.

In my experience the majority of opponents are not clicking back with AK considering you will rarely if ever fold and they will miss the flop 2/3 of the time and be out of position. They will either peel or 4bet large/ship to maximize fold equity. I think this is a spot where most players call it off on the river and call it a cooler. But assuming his value range consists of 6 combinations of AA, 3 combos of QQ, and 1 combo of KK, you are crushed. If we stretch to include JJ and TT in his range, which IMO is unlikely, he will most likely look to showdown hoping you have AK or a lower pair that called pre with great odds.

Obviously the decision comes down to his air combinations and bluff fffrequency of his click back range. Again, I'm having a hard time putting my UTG opponent on many air combos with his PF play. Misclicks may account for the majority of air combos. Also, the bet check shove line is generally indicative of a strong hand. QQ could easily check back turn since it has the board crushed, allowing you to bluff and ship,the river for value after you attempt to pot control. AA can easily play the same. Spazz AK, turned draws, and airball bluffs are generally more likely to jam turn.