Perhaps. I haven't seen a lot of big bluffs yet, though the ones I have seen, the players weren't giving off any obvious tells.

It did make me suspicious, but I wasn't sure of what. And his staring made me rather uncomfortable. I thought about saying something to him but figured it would only encourage him. In the later hands I would just pull up and tightened my hood and look away. He still stared but he couldn't have gotten any information.

I only saw three players (including this one) take this exact line c/c c/c ai, and the first two did this with bottom pair and Ace high (their bluffs were successful, they showed these hands proudly). I ran bad generally (particularly being card dead) but this was also unfortunate timing, as it may have led me to estimate villain's bluff likelihood as higher than it was. And I had little to go on but I did think he looked the bluffy type.

I'm curious how often this needs to be a bluff or us to call. Earlier I estimated villain's range once calling the flop bet, which I think is reasonably accurate for an unknown at 1/2.

By the river, accounting for card removal, the range becomes

{88-77, 55, TdTh, 9d9h, 9d9s, 9h9s, 6d6s, 6d6c, 6s6c, 4h4s, 4h4c, 4s4c, 87s, 85s, 75s, 53s, AdJd, AsJs, AcJc, KdJd, KsJs, KcJc, QdJd, QsJs, QcJc, AhTh, KhTh, QhTh, JdTd, Ah9h, Kh9h, Qh9h, Jd9d, Js9s, Th9h, Ah8h, Kh8h, Qh8h, Jd8d, Js8s, Jc8c, Th8h, 9h8h, Ah7h, Kh7h, Qh7h, 9h7h, Ad6d, As6s, Ac6c, 8d6d, 8s6s, 8c6c, 7d6d, 7s6s, 7c6c, Ah5h, Kh5h, 6d5d, 6s5s, 6c5c, Ah4h, As4s, Ac4c, Kh4h, 6s4s, 6c4c, 5h4h, 5s4s, 5c4c, Ah3h, Kh3h, Ah2h, Kh2h, 87o, AdJs, AdJc, AhJd, AhJs, AhJc, AsJd, AsJc, AcJd, AcJs, Ad6s, Ad6c, Ah6d, Ah6s, Ah6c, As6d, As6c, Ac6d, Ac6s, Ad4h, Ad4s, Ad4c, Ah4s, Ah4c, As4h, As4c, Ac4h, Ac4s, KdJs, KdJc, KhJd, KhJs, KhJc, KsJd, KsJc, KcJd, KcJs, QdJs, QdJc, QhJd, QhJs, QhJc, QsJd, QsJc, QcJd, QcJs, 7d6s, 7d6c, 7h6d, 7h6s, 7h6c, 7s6d, 7s6c, 7c6d, 7c6s}

This has 168 combos and we win with 110 combos, tie with 1 combo, so we are losing to 57 combos.

Suppose villain bluffs x percent of the time when he is losing here. For simplicity we ignore the 1 combo where we chop. We have

EV(call) = 314x*(110/167) - 100*(57/167)

Set EV(call) = 0 and solving for x we find x = 100*(57/167)*167/(110*314)

x = .165, so villain needs to be bluffing 16.5%

However this is an oversimplification as we believe villain is shoving a polarized range here, consisting of his missed draws and TPTK+ hands, and check/calling with his weak top pairs, rather than shoving his entire range.

So let's refine his range to {9d9h, 9d9s, 9h9s, 6d6s, 6d6c, 6s6c, 4h4s, 4h4c, 4s4c, 87s, 85s, 75s, 53s, AdJd, AsJs, AcJc, AhTh, KhTh, QhTh, Ah9h, Kh9h, Qh9h, Th9h, Ah8h, Kh8h, Qh8h, Th8h, 9h8h, Ah7h, Kh7h, Qh7h, 9h7h, Ad6d, As6s, Ac6c, 8d6d, 8s6s, 8c6c, 7d6d, 7s6s, 7c6c, Ah5h, Kh5h, 6d5d, 6s5s, 6c5c, Ah4h, As4s, Ac4c, Kh4h, 6s4s, 6c4c, 5h4h, 5s4s, 5c4c, Ah3h, Kh3h, Ah2h, Kh2h, 87o, AdJs, AdJc, AhJd, AhJs, AhJc, AsJd, AsJc, AcJd, AcJs, Ad6s, Ad6c, Ah6d, Ah6s, Ah6c, As6d, As6c, Ac6d, Ac6s, Ad4h, Ad4s, Ad4c, Ah4s, Ah4c, As4h, As4c, Ac4h, Ac4s, 7d6s, 7d6c, 7h6d, 7h6s, 7h6c, 7s6d, 7s6c, 7c6d, 7c6s}

This has 119 combos. We beat 92 and lose to 27. We solve for break-even bluffing percentage as before, finding

x = 100*27/(92*314) = .093, so villain needs to be bluffing 9.3% or more.

If we remove TPTK, then there are 107 combos, of which we beat 92 and lose to 15, making x = 100*15/(92*314) = .052, so villain needs to be bluffing 5.2% or more.

So, depending how polarized villain's shoving range is, we need him to bluff as little as 5.2% of his missed draws.

So how often is villain actually bluffing his missed draws? That is of crucial importance. But surely it is more than 5%, probably more than 10%?

It's not a blocking bet. He had no money behind. It's either a bluff or a value bet. I also don't think he's shoving many or all of his TP hands, but I accounted those possibilities above. Villain needs to be bluffing his draws more frequently the more value hands he's shoving, which maxes out at around 16% if he's always shoving exactly the hands that beat us.

What I meant by blocker bet was simply a button clicking bet that doesn't make much sense. For instance you might think a shove with top pair is for value or a shove with bottom pair is a bluff. However, if you ask a villain why he shoved he may tell you "because I didn't want to get bluffed." In other words, I believe some players make bets at times simply to avoid making (potentially difficult) decisions.

That makes sense, but if you didn't know, that's not the standard definition of a blocking bet / blocker bet. It's usually defined as a relatively small bet made when first to act in order to limit the money required to see the next card (or end the hand), and it's normally done with marginal hands, not with a polarized range.

I think villain's shove is always a big hand (2p+, maybe TP) or a bluff (missed draw). And since there are vastly more missed draws than 2p+ combos, or even TPTK+ combos, villain does not need to be bluffing often at all to make calling correct. Only 5 to 10% by my above calculations.

So the key question for this hand is how often is villain bluffing his missed draws?

you have shown strength on pre-flop, flop & turn. It is not likely that V will jam the river as a bluff. His $100 jam has barely any fold equity against your perceived range. Therefore V is very unlikely to be bluffing here and i think he will have at least two pair in this scenario.

I agree with you, but how likely is "very unlikely"? He only needs to bluff 5% to 10% of his missed draws for this call to be +EV since there are so many of them.

Is villain never bluffing? Bluffing one in fifty times? One in twenty? One in ten? One in five?

All of these you could say "villain is very unlikely to be bluffing here" yet the past three scenarios make the call marginal or substantially +EV.

And I saw this exact line (one hand in which I was playing) heads up two other times before this hand, from different players, and they had bottom pair and Ace high in the hand I played. I folded in that one, which probably made me want to call here as I have a very small sample size at this point for live hands.

Obviously though his jam has some fold equity, or there wouldn't be so many people in this thread saying fold, and I would have snap called.