$20 mystery bounty, ugh river

I don't think the river is really a problem for you; there shouldn't be much Ax in villain's range outside of A9. On the contrary, if he has 9x, now you chop with him.

I think the bigger problem is the line you took. HJ opened and bet a 9-high rainbow flop three ways; unless he's just picked this flop to bluff overcards, his value range is going to be pretty tight (and largely beat you). I don't think your hand is strong enough to check-raise on the flop. (If you check-call the flop, the turn is possibly a good card for you to lead. I'm not sure how much 4x you're calling the flop with in a multiway spot, but given the small flop size and closing the action, it wouldn't be unreasonable with a strong kicker or some backdoor equity.) I think you've kinda just built a big pot with a weak top pair and weak kicker in a spot where villain's range is going to basically all be hands that beat you. (Maybe he has 88 but I don't think he calls the turn with it at your sizing.)

I guess you could block bet like 10% and hope he has a 9x and you chop. Or you can bluff-shove to represent A9+ if you want to go nuts and try to fold TT-KK. But I think you played this much too fast at this depth for your hand strength vs. what villain is representing.

So what was your plan for other rivers, especially those not a 9 or 7?

I'd just call the flop - x/r you eliminate his ability to bluff future streets and some of his calling range is overpairs/better hands. As played by the river he most likely has an overpair/better 9 - might not be bad spot to jam it in as a bluff. Overall though you took a very high variance line that you really shouldn't take given your stack size.

Agree that you should just call flop. If you were shallower, like 20-30 BB deep, I could see check raising to get it in. This deep though your hand is not going to perform well against your opponent's range when a lot of chips go in.

As played I probably jam river as a bluff. If I was your opponent I would interpret that line as representing something like a set. The ace is somewhat of a scare card too and you might be able to get them to fold a better 9 or an overpair.

That's sort of a desperation move though. I would have preferred you just called flop and used your hands as a bluff catcher calling down on most run-outs.

Edit: Was kind of distracted when I made this post and I just realized you chop with all 9x now. This makes me lean more towards just checking river and hoping it checks through.

I usually don't c/r here on the flop because I will likely call a turn bet against a player that barrels. And we get worse hands to fold and better hands to call. The bright spot is we will usually get 2 overcards to fold and it gives us the win in a situation where we will lose about 25% to 30% of the time. If I did c/r OOP it would be closer to 4x or 3,320 so overcards will fold.

As played I probably bet the same amount on the turn that I bet on the flop if I bet at all. I usually check when the board pairs. And here it takes away our win if we hit two pair assuming Villain has an overpair if they are calling our turn bet. Also when we are essentially betting close to 33% effective stack it feels like we are pot committed.

I doubt Villain has an A in part because there were no possible flush draws. And in part because they would have folded non-pair hands on the turn. So this would be our shot to bluff on the river. It looks like we can have A9 or a set or even trips. If we check my guess is that Villain will check back and win (though we do mostly chop vs 9x). I actually don't mind the river jam which is about pot sized but because the sizing is a bit polarizing (at 80% pot) we will likely get called at least 50% of the time...

Okay so a few thoughts on the hand. I posted this in another group and it led to an interesting discussion and solver results.

Although I didn't remember this when I posted the hand, I went back into my PT4 stats and I actually have about 1400 hands with this villain. My notes on him is that he isn't positional preflop (his MP stats are laggier than his CO stats) but he's fairly passive postflop.

My rationale for the x/r on the flop is that I have a very vulnerable made hand, and if I x/call I know I will most likely end up x/folding turn or river a very high percentage of the time. I actually interpreted his bet more as a weak stab, so I figured I could rep strength and fold out his good Broadway combos. The flop is better for my range and I can apply more pressure on a lot of turn cards. When I posted this in another group, most people preferred a x/call but it turns out the solver actually does most of its x/raising here with 9x combos (high frequency x/r with the best 9x, lower frequency with weaker ones like mine). Now that is based on villain having some hands in his range I don't think he'll have here, like K6s, but I found it interesting that this was a spot where most responses are at odds with the solver response.

I think the big mistake was firing the bullet on that turn, at least for the large size. I wouldn't polarize there with a boat or 4x, and villain's call of my flop x/r should slow me down. He might continue with some of his best Ax given my x/r was a bit small, but his range should be heavily weighted towards over pairs now.

I agree the big turn bet was a mistake. If I was going to check raise flop I would likely then check turn with an intention to check call.

If you could post the solver results screenshot for the flop I would be curious to see what you're looking at. I would be surprised to see the solver check raising this hand more than 10% of the time or something. Solvers commonly mix a small percentage of the time in spots where one action is clearly preferred. That sort of thing is often for board coverage. Like in this case if your opponent knew your entire overall strategy (like a solver strategy assumes) then you would want to have some two pairs when a 7 comes on the turn. This is less relevant against human opponents that don't know your entire strategy.

In practice I could see raising A9 and maybe K9 for value, when you're dominating more of the 9x.

Also remember humans tend to overfold. So in practice when a lot of chips go in you're going to be in worse shape than you would be against a solver range.

Since solver responses are based on opponents having hands in their range that most human opponents will not the responses should be different. Solvers win by not being exploitable while humans win by correctly exploiting.

Post some stats and let us assess this assumption.

I'm seeing 55-88, A4, A3, A5, A2, 76, 65 in his range. It's a disjointed flop where both ranges have as much, or more, high-card combos than pair+ and so no reason why AK, AQ can't bc here or worse for that matter.

Your high cards vs my high cards means high cards are actually pretty "strong"; it's exploitable to not realize this.

It's particularly true now that BTN has folded and subsidized the pot.

It's even more particularly true as IP defender.

Y'all both really "should" be seeing turns with a bunch of stuff that others likely--and exploitably--classify as air. It's not; you're just exploitable.

I see no reason yet to assume a high degree of exploitability in the flop strategy. What exploitability I do assume incentivizes raising.

Nor the turn. What exploitability I do assume incentivizes barreling.

Nor the river really. Check and see what happens. Assess what he'll do with 77 and 66. Mostly folding when he floats river.

I would size down turn to moderate sizing say 55%. Otherwise I like your line.

No considerations for the bounty aspect as I don't play them.

He's fairly passive postflop, yet he's betting multiway here and you still check-raise with weak top pair?

The solver is analyzing this as a heads-up spot, right? I don't think there are many, if any, that have the power to calculate multiway spots. And, again, going multiway to the flop should significantly tighten his c-betting range here.

Wouldn't the exploitability of the population incentivise raising more as a bluff? Sure they have a lot of those hands you mentioned. The problem is they're (over?) folding them. So when they do call the check raise and then call the turn barrel we're left OOP against a strong range (that also includes some bluffs) and have no idea what to do. If we fire another barrel on the river we're usually beat when we get called. If we check and he jams he's probably not bluffing enough for us to call, but we can easily be getting bluffed off the best hand. We're just hoping he checks back with 77 or something? Seems optimistic.

I see no reason to turn top pair into a bluff and that's what we're effectively doing when we take this line. It's a classic overplay of a relatively strong hand.

If you wanna assume people are such "passive" pussies (whatever "passive" means; without any precision--that word is MEANINGLESS) that they never call with worse--you be you.

I would strongly disagree with that assumption.

I would also strongly disagree with the assumption that he never has "air" (again, whatever that means--one man's air is another man's highest EV bluff). And it's not congruent to think that if he never calls with 77 he doesn't also always/mostly always fold AK, AQ, KJ, etc.

So I think a few things here:

• You're completely underestimating the protection incentive.
  
• I flat out disagree with your assumptions
  
• Let's say he is "passive" (whatever he means). There is NO UNIVERSE where he never has less than a better 9 or better. None. No one is that "passive" (whatever that means). So even if he is "passive"--you raise. You stick your tongue out at him while he tucks his tail and folds and virtually never (under these assumptions) lets his "air" (whatever that means; one man's air is another man's, oh IDK, double-backdoor with an over to the 4 and winning like 10-30bb/100 hands) move ahead of your vulnerable pair
  

No, speak for yourself. I bet you $20 bucks I can:

• Compute the entire equilibrium flop to turn
  
• Layer on data-based assumptions (approximate frequencies) for IP response
  
• Do that in under 15 seconds
  

This is BB defense. The poker equivalent of a free throw. These computations need to be automatic. Y'all are all not even close to being unexploitable--and not even because you yourselves are trying to exploit, you're just getting it wrong--and you need to train more.

Your equivocation here--There is an extraordinary (and exploitable) amount of fear (of being "shown up" and being "wrong") and ego ("What if he shows 77?!?!") embedded in this sentence. There is certainly no confidence in this sentence.

There certainly is no confidence in this statement because I don't typically take that line in this spot with 97o (check raise flop with weak top pair vs multiple opponents 68 bb deep, then bet turn big).

I'm pretty sure if I ran it through a solver it literally wouldn't exist (97o being in a range that check raises flop 3 ways 68 BB deep, then bombs turn big). There's a good chance that combo is supposed to fold pre after button calls so it's likely not even in the preflop range.

How about you use your superior solver skills to whip up a screenshot to support your case? Unlike you I am not confident enough to think I could calculate the entire equilibrium strategy of a 3-way spot within 15 seconds.

The problem with check raising this hand on the flop is not that there's not value to be had on that street (there is). The problem is that across additional future streets as more money goes into the pot you're funneling your opponent's range down tighter and tighter until you're ultimately in horrible shape when the hands are flipped over on the river. Your hand is just not strong enough to stack off here and you need to exercise some sort of pot control.

Anybody else find EggsMcBluffin's posts are like reading Confucius?

In any case, I'll tie up the loose end here. River went check-check and villain showed AK.

So my read was correct that the flop bet was a stab with a missed hand, but I was wrong in my expectation that he would fold hands like AK to my line. I can see him peeling my small-ish x/r on the flop with AK but I was quite shocked that he called my larger turn barrel with it.