We are playing ACR $11 $10k guarantee. Fairly early. We have 105 bbs and am in really great shape. SB in this hand has 60 bbs and we have some history. He 4 bet all in on me on flop earlier in tourney with flush draw. I called with set and he caught. BU has 50 bbs and BB has 20 bbs. Anyhow OTTH:

I am UTG with TT and raise to 2 bbs. BU, SB and BB all flat.

Flop (9 bbs): K47 Checks around

Turn (9 bbs): 4 Checked to me. I bet 4.5 bbs Only sb calls.

River (18 bbs): K SB donk piles for 53 bbs.

Would play this line with K? Looks like a busted straight or flush draw, but I don't know.

It's certainly possible he'd do it with a K-- I think check/calling makes sense there from the SB in a 4-way pot. It could be a bluff, but he could also think you're going to check back all your non-K hands here. And maybe he chose the max size because he wants max value and he thinks based on your history that you think he's going to bluff a lot. But, he could assume you'd bet a king or better on the flop as well, and so maybe he can push you off with a missed draw.

At 3x pot it's so polarized that it's really just a factor of how often you think he's bluffing. I'm not sure how to come up with the best answer for that.

You're calling 53bb into 53bb+17bb = 53:70. 53/123*100 = 43.09%, meaning to break even on a call here, villain needs to show up with worse than TT at least 43.09% of the time.

MDF can also be applied here, allowing you to call at an unexploitable frequency. MDF is (potsize/(potsize+betsize))*100 = (17/(17+53))*100 = 24.28%, meaning you should continue with the 24.28% of hands in your range that best block value and unblock bluffs while still beating the bluffs.

You can construct your and your opponent's ranges and see whether TT makes it there. TsTd looks promising since you block KsTs, a reasonable value holding, and unblock clubs, which may take this line as a bluff.

Thanks Nath and Asjbaaf. In game this is a lot of math and/or guesswork. Is this just something where we need to put in the time to study and do a lot of approximations from hueristics?

But my intuition did tell me this was a good hand to bluff catch with. My intuition also told me that the 3x pile was quite bluffy as my range had very few Ks given the flop check on such a dry board when I had all the best Ks in my range compared to everyone else.

Although the $11 population bluff more these days there is no way that 43% of opponents are bluffing here - the previous hand was a big semibluff on the flop which is a different thing to a big river bluff when you could have a K.Honestly if he's bluffed you off nh.
V can have plenty of Ks with this action - given they are SB they are mostly going to check the flop with Kx

I don't think this is a bluff much.

There are two value possibilities.
1) SB has 4Xs and didn't want to bet the turn because he thought you and the BB would fold because you checked the flop.
2) SB has Kx and is afraid that BB has 4x so he checked the turn. If SB bets BB will either just call or will jam with 4x. Either way it's awkward. If SB checks then he gets to see if BB bets and BB will bet with 4x because why not?

In general good players will always bluff the turn with a draw from SB because it is clear that you don't have Kx. SB can also bluff with air to pretend they have 4x. The only hand you can possibly have with a K on that flop is KK. And even then you should bet because one or both blinds can have a straight draw/gutter.

Given that you bet the turn, SB has to call with Kx because you didn't bet the flop and BB didn't bet the turn. It's true that SB could c/r here but then nobody would call.

The river jam is just an attempt to pretend that he is bluffing so that you will call with Ax or any PP > 44.

I don't think SB would call the turn bet with an A unless it was exactly A7s. I think A7 has showdown value and wouldn't bet the river especially because it blocks your Ax hands. So I don't think SB is bluffing with Ax to get you to fold (and not chop).

Now I don't play online anymore. It can be that online players in $11 tournaments suck. Or they may be playing a bunch of tournaments at the same time so bluffing here just wouldn't be a thing.

My opinion is that you played the hand very very well. Betting this flop against 3 opponents is risky. Against 1 or 2 opponents its a must bet (to get Ax/Qx/Jx hands to fold). You could have bet the flop as a sort of value bluff but its good to see if the guy in position bets because then he likely has Kx because its not a clear bluff spot given the SB and BB could have Kx. Betting the turn is probably very good because everybody has checked at least once so it is likely nobody has a K and you can take it down (or at least get some J, Q, and/or A to fold). I think I have to give up on the river. I might call a small blocking size bet (like 1/5 or 1/4 pot). But I wouldn't ever call a jam.