I've been thinking about these types of situations for a while. Basically, you get to the river and it's most likely the case that the best you can do is chop.

If we're in position and get bet into, should we almost always fold?

If we're out of position, should we just check/fold?


REASONING:

Let's say we get to the river in a totally different case where we might have the best hand but might not, but villain bets 1/2 PSB. We only have to be good here 25% of the time to breakeven (getting fairly good odds of 3:1), so I think we have to consider a call here depending on the situation.

Ok, so now consider the hand that most likely the best we can do is chop. I'll give a couple of examples below (that might differ), but let's say we want to more-or-less give ourselves the same chance at breaking even as the above normal case. In a pot where most likely the best we can do is chop, the villain would have to bet <= 1/6 of a PSB. Anything larger makes the times we have to be good in order to breakeven bigger than 25%. On top of that, villain should expect a 1/6 PSB to almost always be called, so it's unlikely to be a bluff. Does this mean we should just fold and move on?


EXAMPLE 1:

Villain is sticky and bluffy and can take shots at pot when shown weakness. Hero raises preflop in position with KQo and gets called by Villain. A63r flop, Villain checks, Hero checks (Hero's plan is to calldown reasonable bets, which may or may not be a good plan, but whatever). 6 turn, Villain bets 1/2 PSB, Hero calls. River 3 for a final board of A6633, so the absolute best Hero can do is chop (Hero is playing board, any A, 6, 3 or pair != 22 is ahead). Villain, who can still very well be "bluffing" bets 1/2 PSB on the river. On a blank like a 8r or whatever, Hero might have a hero call on his hand since K high will beat some hands here. But here, Hero has to fold, right? (perhaps ignoring FPS raise play)


EXAMPLE 2:

Slightly different from Example 1 in that I guess there are some worse hands that could call turn and bluff river (such as two pair), so I'm not really sure this applies, but, anyhoo. Villain has position on Hero who is in BB with J5o, limped pot. AKTr flop, checked around. Q turn bringing 2 to a flush. Hero bets pot with nut one-card straight, Villain calls. Non-pairing flush card comes on river. Now, I *guess* it's possible Villain might call a bet with worse hands (such as two pair or even a set), but other than that, I'm chopping with another J or losing to a flush. I'm assuming we fold if we bet and are raised. If we check and villain bets 1/2+ PSB, again, do we have to fold? [Meh, the more I think about it, this isnt' the greatest example cuz there are hands that we can beat here that could turn a showdownable hand into a bluff, so maybe this example isn't very good]


BOTTOM LINE: In cases where the best we can do is most likely a chop (such as Example 1) should we be folding to pretty much any bet?

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I had a discussion with one of my friends about a similar spot. Consider having a hand like A8 on a A44K5 board. Most of the time by the time you get to the river you are either chopping with anyone else with an A playing two pair and K kicker. There are going to be some times where you're losing to higher two pair or trips. One thing my friend likes doing is making a blocker bet on the river when OOP. This way most opponents will fear that you may have better than just an A and you are setting your own price at the pot. The problem you might run into though is that this is very exploitable. If you do this too much than people will start raising your river blocker bets so you need to make some blocker bets with the nuts to keep them guessing. When in position, I think you need to consider more factors, like how tricky the opponent is, what range of hands he is representing, does he think you are capable of bluffraising him on a chop board. Most of the time against straight forward opponents I fold when facing a PSB on the river and I know the best I can do is chop. There's no shame in folding when you're calling 100 to win 50.

Mindfull, what would you do in your example if you faced even a smallish bet of 1/2 PSB? Keep in mind that we have to be chopping 50% of the time just to breakeven! I'm not factoring in times villain is bluffing with a worse hand (such as Kx), but still, on this drawless board and non-scary river, I'm not so sure how often Kx bets a quite callable 1/2 PSB into us...

Unless I know villain will only bet this river with a hand better than an Ace I say call. If they show up with better than an Ace I take note and don't call them as light next time.

These kind of examples like all of poker are just depend on villain/math of situation. Depending on villain, I might raise or call or fold. If villain is capable of bet/calling (instead of bet folding or c/c) hands like Ax or something, I'm almost always folding. If villain is not capable of betting Ax here, I'm either calling or raising, depending on how bluffy I perceive villain. If villain can bluff (with what he perceives as a bluff) hands like 55 here, I'm usually just folding. If villain is only value betting a 6 here but can bluff a decent amount I'd probably call. If villain is bluffy enough to take his whole preflop range and take this line on the flop/turn/river, but can fold an Ax, I'm always raising. It also depends on what I think his 1/2 pot, 1/2 pot line means. Does this mean he really loves his hand? Is this how he's bluffed in the past? I mean there's a lot to guess about how a villain thinks, but there's never an easier answer in close spots. Against a random 1/2 player, I probably just fold the turn. If I think this guy bluffs too much when weakness is shown, I'll just wait until I flop a little better hand vs them like middle pair and slowplay with plans on calling down, as I think betting the flop is a little better vs most villains as they usually just c/f a lot of their hands like 88, 6x, KT, JT right on the flop and make things easy.


These kind of situations I like to try and figure out what their bet-sizing means. Is this the guy that always raises a J on the turn or almost always just calls? Will this guy call with one pair on the turn? How many suited cards does this villain play preflop for a limp (is he the "any 2 sutied" kind of player?) in whatever position he is in? Does this guy usually raise his good cards pf (AJ, KQ,QQ, TT etc). Does this guy ever check really good hands last to act fearing the flush when he shouldn't? Against a random opponent I would assume they often just call with the J on the turn, and would bet the flush a little bigger on the river once they hit, so I would often call here expecting a chop.