Semi bluff gone wrong

Your mistake starts with the flop stab being too big. On these flops with 3 low cards flatter should generally stab pretty often (55-60 % frequency) but small sizings. Because you mainly want protection from over cards. 1/4 of pot should be good here.
(Opossite situation would be flop like AK5 where you should bet big sizings with low frequency, because its safe to checkback all your second pairs which need very little protection)

And on the turn there is no reason to be 67 anymore, you should be more polarized. Same would be for river, no much of a reason to bet.

(btw I purposely ran it at shallower stacks and put you on CO instead of BTN to adjust for the fact that this was 3bb open which you should of course flat less against than against a more standard smaller open)

Mediumish showdown value with a draw is usually not a great candidate for a bluff. You got your protection on the flop.

One thing I do like is that if we are turning our hand into a bluff on the river, we need to go big. We don't need to target the missed draws.

I am not sure why you exclude Kx from his range. He could have Kxcc or just a stubborn AK. You did manage to find a hand that is better than yours, but they still called, so perhaps this wasn't a good idea vs this Villain.

This flop is fairly standard for solid players to check and not cbet after opening UTG and being HU OOP.

I have no problem with making a flop bet with middle pair. Villain will likely fold non pair hands that aren't straight or flush draws. Sizing wise I have no problem with betting slightly less than 50% pot.

Once Villain calls flop bet it opens up PP (even overpairs which would check to balance) and flush draw possibilities.

Given that our hand doesn't improve, I probably check back turn and call river bet.

On the river I am never betting. I think we are ahead a lot of the time but won't get called by worse hands (except maybe 55). A decent amount of time we have the winning hand and when we don't we are basically not going to get Villain to fold. If Villain was on a flush draw he is never calling unless he has a K. If Villain has 8x hands he is likely never folding. Apparently 77 isn't folding either...

If I was going to bet on the river it would be a blocking size bet (like 20% pot) because Villain can have KXs hands that were flush draws which would beat us and call any sized bet.

We're in position; we can't block.

Not the right spot at all IMO:

1) You have a marginal made hand/showdown value
2) You're targeting a very, very narrow range of marginal hands
3) You don't have the nuts advantage so you shouldn't be polarizing

Its the size I would use. If we get c/r'd we fold. We might get called by Ax flush draw hands. But personally I wouldn't bet the river, I'd just check back.

Not sure about the last part. Yes, we don't have exactly KK, but we have all the sets, and maybe 75/86 suited hands for straights and 2 pairs.

More importantly, Villain has taken nothing but condensing actions postflop, he has check called twice on a dynamic board with many draws.

The problem isn't that we don't have a polarized range, it's that we have a medium strength hand with a bit of showdown, that probably has more ev as a check back than a bluff.

Say we are good 20% of the time. There is ~30K in the pot; we get about 6K of that. Bluffing has to be more valuable than 6K to be better than taking a showdown.

We are putting 20K in the pot, we need to be getting 26K back on average (ignoring ICM for a second). We need to get this through about 37% of the time, or about 17% of the time when we are behind.

The actual results show this was pretty bad. We didn't even get the hand a tiny bit better than ours to fold. I guess Villain could have better 6x, but if we aren't getting this to fold, it wasn't a good bluff.

Of course this is a tournament, and there is some ICM as well, so this makes it even worse to take what is at best a marginal spot, with very high variance.

(If my math is wrong above, please correct...)

See, the difference between this "bluff" and other bluffs is that other bluffs are actually bluffs.

Don’t post outcomes.

Smaller on flop (2k is plenty), smaller on turn (smaller pot so 4k is probably good), check back river and take the showdown value.

Fair enough. Technically we do have the nuts advantage but not by a lot. Villain can have plenty of strong hands himself here, like AA/AK/KK and some sets. Generally speaking if you're going to turn a marginal hand into a bluff with polarized sizing, you want villain's range to be very capped.