you know he has the nuts here given his nut peddling image, should you still call since your getting 6 to 1?

If you "know" he has the nuts, like you can see his cards, then no, of course you don't call.

Look, it's a very very simple EV equations. Given P, the percentage of the time that he has the nuts, what is your EV when you call? Therefore, what is the value of P where folding is the same EV as folding (zero)? For any value of P over that, you fold.

EV = (1-P)*(6) - P*1
see? You win 6 whenever he doesn't have it, and lose 1 when he does. Set EV=0 to find the breakeven point

0 = (1-P)*(6) - P*1
0 = 6 - 6P - P
-6 = -7P
P = 6/7
(this result should be fairly obvious but I show the work here so you can see why)

So, if he has it more than 6/7 times, you fold. If he has it less, you call. You're going to have to make your estimate of whether he has it using your information on him, AKA play poker.

No, you shouldn't care about odds when you know what your opponent has OTR.

So are you asking if you should ever call when you know that you can't win the hand? Surely you meant to ask something else so please clarify it.

While I agree that it's +EV to fold vs a player who's that transparent, you should be aware that this will change the way future hands should be handled. Humans are going to adapt based on what they witness from you.

More importantly, other players who witness this may make adjustments in their game for future sessions which is much more difficult to keep track of.

For this reason, I tend to pay players off on small value bets even though I think they have it often enough to fold.

You can think of it in terms of they are making a larger mistake by not betting larger or bluffing more often than you are making by paying them off a small amount. By paying them off, you encourage this behavior to continue but adjusting to save a small bet now will encourage more optimal play against you in the future that will end up costing more in the long run.

Excellent point here. There are factors other than immediate EV and pot odds that can influence calling decisions. Maybe that was the intent of the question.

I don't think taking an immediately -EV line to encourage continued bad play is a good enough reason here. I mean people can decide to improve their play even if you pay off these bets or they can decide they'll never improve their play even if you don't.

I do think the incomplete information in the game may be a good reason to pay off small value bets. Especially as the size of your potential error becomes larger relative to the equity required to make a breakeven or profitable call.

It is known plus ev to make small minus ev plays from preflop to river when not doing so would cost more for one reason or and the other. Called the metagame i guess, and gto. It just is minus ev if one makes this a blind rule.

Making "small minus ev plays" is certainly not GTO.

Not if u think about the whole range.

Wrong. If a move is -EV, then pretty much by definition it cannot be part of a GTO strategy.

You may well make a -EV call in the hope of sucking out if you believe you have big "implied tilt odds" later on and such ... stuff like that may or may not work for you, but it is not "GTO".

If im getting 6 to 1 on the river and the only hand that beats me is the nuts Im never folding ever , unless im in a tournament where the last bet my mean im out of tournament then other considerations could be made.

Now if its like a AKQ10 board and a single jack in his hand makes the nuts and ive got so much history with a player that i know for example he would never bluff on that board out of position then i may fold as well.