Once again our disagreement is based on what we think of our opponents. There's little I can do to convince you otherwise and vice versa.I will make one last ditch attempt however. :-)
You have to keep in mind that you 3-bet PF and then c/r the turn, signalling you just made a BIG hand on the turn.
I did make a BIG hand on the turn!You have to account for what my opponent thinks of me. He's seen me play very aggressively. My range of hands to c/r that turn is fairly wide. I'm sure he's thinking something along the lines of AA-QQ,AQ, and KQs.Also, I'm sure he discounts the likelyhood of AA-QQ after I just call his flop 3-bet. Most of the time, I have a pair of queens. Therefore, being a solid player, he knows he should 3-bet with AA, KK, and QQ. But he will be a bit more inclined to 3-bet AA/QQ than KK, but not by much.
When he 3-bets the turn, he's telling you he can beat your big hand, and that tells me QQ. KK is an outside chance, but I don't give it anywhere near 50%. Let's face it, this hand is so noteworthy because noone plays KK like this!
I think this is where the disagreement comes into play. I think he's a bit less likely to play KK this way on the turn than QQ and AA.To break it down % wise, I think he plays [AA,KK,QQ] on the turn[35,25,40]PF might look something like [30,30,40]Then for the whole hand up to the turn [31,22,47]Multiplying these numbers by the card frequencies and we get:AA ~ 15%KK ~ 63%QQ ~ 22%So our bet given these estimates still has value.To find the break even point, KK = 50% (from earlier EV river calculations).Now (p x 6/8)/[(1 - p) x 1/8 + p x 6/8] = 50%Solving for p we get, p = 14.3%.
The only important number is that if you think he plays KK this way 14.3% of the time, and AA/QQ 85.7%, then betting or check/calling this river have the same value. So now the numbers are here for you to make your decision. I'm not going to try and sway anyone one way or the other, because everyone has different opinions on how their opponents play. All you have to do is assign a probability to how often he plays KK vs AA/QQ. If it's below 10%, then you think the river is a check/call. If it's above 10%, than you think the river is a bet/call.
Check/call: You don't take into consideration the times where he value bets his KK on the river (even with the Ace) and you win that bet, too. I posit that this occurs approximately 1/3 of the time, making the expectation 0.
I don't think he ever value bets KK. This was a good player who should put me on a range. If he bets KK here, he may also raise the river with a hand I beat, destroying the whole risk 2 to win 1 thing.Another point worth mentioning is I don't have to call his river raise. The only reason I would is because I think there's a better than 1/20 chance that I have the best hand. If we factor this small chance into when I call, it pretty much cancels out the small fraction of the time he value bets his king on the river.