I'm sure a flop donk or c/c, donk hand post would go over just swell here...the first two checks mean nothing.
I'd think he has a 9 a lot, w/ some 4s & decent Aces. That's if he's not capable of c/r'ing a good hand, which he definitely should since everyone just expects vill to vbet J high for value.

Some Heroes can also have Qs and 8s, not to mention, if OP subscribes to this philosophy, KK and AA.

I can most certainly have any of these hands. FWIW though, I'd be more apt to b/c these hands on that River vs x/r them (though it's not impossible for me to go for a check raise with KK, QJ, etc)

Isn't this pretty much always a check call here given the info? It most likely goes c/c on river a majority of the time and you take it down. If you are perceiving the 55 as a bluff catcher now, no reason to bet it out or c/f to a bet. That would be the opposite of what you want your hand to accomplish at this point.

If he played a pretty big hand like a flush, an 8, etc. like this, then kudos to him, he most likely got the minimum value out of the hand and gave you a free card to catch up. The only thing I could see beating you would be hands like 66, 77, J10 and maybe 99, 1010, JJ. Even then, I don't see him checking anything but possibly the 66 or 77 behind on the turn and I do not think he even checks that. Good limit players playing a hand HU are usually not worried about getting checked raised by made flushes on the turn.

If you bet out, what are you getting value from? A4, 33, 22 or AK? Maybe, but you are certainly not moving a better hand than yours, so no need to bet out. Too thin of a possibility for you to bet, to get him to bluff raise, then you read that correctly and call as well IMO.

Check/call all day and make adjustments from there based on the show downs in these hands with villain since you play together so much.

it should be impossible for the above to play out. If rechecks back it would go down as the worst played hand ever.

On second thought, you're right, I probably wouldn't even bother construct a x/r range on this board/action.

Hero's approximate range
9 combos of 56/57/67; 4 combos of AcTx, 32 combos of AJ/AK. If we never donk turn, I count ~90 combos of pairs/trips/flushes

Villain's approximate range:
Discounted 9 combos of K-hi; Discounted 32 combos of AJ/AK. Based on description, villain will barrel most of his value. I give ~25 combos of pairs, ~5 combos of trips+.

Our range dominates villains. Even if we check river, I still think our range is stronger due to villain's turn check. Villain vbetting AJ/AK is insane. Since our range is so strong, this should reduce his bluffing%. I agree that villain will rarely be betting river here. I disagree that our check x3 makes us look weak. The board is just so favorable for us. My read is that he will rarely be bluffing here, which is why I liked folding 55. That might be too nitty though -- calling with it is standard. x/r is also a possibility since we have so many more trips+ in our range.

Don't forget that 3 of those 9 76/75/65 combos, and two of the AK/AJ are now flushes. And a few pair combos (22/33) are also behind.

So that 40 combos of not awesomeness (AK/AJ not flush = 30, AcTx = 4, busted gutter = 6) that you count. I think that sounds pretty close. Plus, if I defend A4s, that leaves 15 made hands weaker than my current holding (55). So 55 worse combos.

I probably also check 66/77 on this river. MAYBE T9s? Let's pretend I do.

So say I bluff my whiffed gutters, and check my A-hi / T9s-. I really don't have a lot of "better" hands when I check this river, leaving 55 as a pretty slam dunk call / massively exploitative fold. Of course if I learned people were value betting J9s+ and folding 55 once they check, I'd be betting very liberally when checked to OTR.

After bb takes the check call flop line, check turn, check river line I count 0 combos of trips+flushes, curious how you arrived at a number >0. Also probably way less combos of pair but don't care enough to count them.

check folding is just terrible, I don't think its close

I was speaking at the start of the river.

FWIW, the 40 player pool is pretty much a subset of the 20 pool at foxwoods, as 40 doesn't go often enough for a group of players to be dedicated to it. So when I say one of the strongest players in the pool, I mean one of the best limit players in the house.

Anyway, results:

I don't think you're getting much value from betting, as A-his and worse are folding. You may bluff out hands like 77/66 some of the time.

If you think villain can value-bet thinly too much here, seems like a candidate for c/raise?

Why would villain bet/call AK if he's not even planning on calling this river with it?

Just asking.