I think your turn sizing is pretty good and the river seems like a check back given the range you've assigned him (which seems very reasonable to me). It's one of those spots where it's important to remember that betting has to show a higher ev than just checking back rather than betting just showing a profit.

Wait the EV of checking back is 0? So if the bet shows a profit why isn't it automatically better than checking back

James, If we knew for sure the river bet showed a profit, how could it be possibly less EV than checking back? If we make a profit on the money that goes in on the river even just $.01 then I dont see how it could be worse than checking back. You made a similar comment in the comments of your last video as well.

Random example. The pot is $100 and our equity is 90%. Villian has 100 combos, so we beat 90 of them. If we check our EV is $90. There is $100 behind and say say our EV on the money that goes in on the river is 50%, so he calls 10 better hands and 10 worse. 

.8($100) + .2(.5($200) + .5(-$100))

$80 + .2($100 - $50)

$80 + .2($50)

= $90

If we have 50% of the money that goes in on the river our EV is the same as checking. So obviously if we have 51% of the money that goes in on the river, our EV is greater than checking. Doesnt matter how you move around the numbers.

What am I getting wrong?

Ya we need more then 50% when called for this to be a value bet. According to OP s range he stated we only have 46% when called and I would argue that this range is more likely to get worse then better. So its a check.

If we where OOP theres reason to shove when its so close because preventing a bluff that we can t call is worth something.

yeah, we dont need greater than 50% equity for betting to be the highest EV play when we are OOP. In potion if we arent folding out any winners, if we have more than 51% its higher EV than checking back.

He should be far more likely to have hearts than clubs since he called a 2/3rd pot sized cbet on the flop. The Ac river blocks all possible combos of Ac*c, which should be most of his club draws that he plays this way.

Since we can not assume that a riverbet or rivershove will fold out better hands, we should only bet if we have more than 50% equity against his calling range. If we bet less than all-in, this 50% equity should be even higher if we incorporate for bluff check raises.

It also seems reasonable to assume that many of the club combos such as KQcc will 3-bet preflop, that makes his range heavily weighted towards (missed) hearts and AJo/A9o combos.

Since your range is totally uncapped here it is unlikely that you will get check raise bluffed if you bet small you can both opt for a small valuebet or a check behind. With a small bet you should be looking to get value from a 9 or J.

I think the turn should be a larger 3-bet, if you use this sizing all his combodraws can correctly call and realize their equity. You should also expect to induce few bluff rerereraises here. By making it $40 you leave yourself with little over a pot size bet on the river, which implies that if you shove rivers you should be valuebetting:bluffing with a 2:1 ratio. Unless you expected to be perceived to be bluffing here at around this frequency, making it larger on the turn will allow your shove to be called more often.

Hello this is my first post,

If the river is a blank I think this is a good spot for thin value and I agree with the turn 3-bet needing to be a bit larger, say around $48-54, to set us up for river shove that will more reasonably get called by worse. However as the board ran out I just can't find a clear reason to throw another chip in the middle and a x/r here would be horrible for us.

Check it back to funky town :)

I also like a check here. In fact I think even JJ might be a check ffor the reason that we don't have enough bluffs to balance a value range this wide.

I think an interesting and somewhat relevant question is what would our calling range be if he donk shoved the river, what are the implications of this on our value range and where is the equilibrium. If it trns out that in equilibrium he should have a leading range and in reality he's checking 100% then what is the best exploit? (Well I found it interesting at least) :)

Requires more thought I guess.

Great discussion guys! Thanks for your thoughts/input.