Thank you for running the math like that. Without detail, it's about what I figured at the time. Had to go through it three times to understand it, but it was time well spent.

Thanks.

Thanks for the good PAHWM. Lots to consider in it.

I think keeping in 3 opponents who have a combined 4-8 outs and should make big mistakes on turn is worth the risk

True.

Thanks for making the detailed calculations. I agree with all your assumptions, they’re what I had in mind..
My 80% number came from the assumption that we wouldn’t stack off if the turn 8 came, but, I guess were committed to the pot and will need to commit our last 120 even on an 8. So you’re right, 65% is the magic number (under the assumptions).
About 75 vs 53, I don’t think we need to worry as much about 53 since only the suited combinations should be present in V1-V3’s collective range.
About whether open-Enders can call our shove, I guess they can barely call based on pot odds. I ran 75 vs 44 in online equity calculator and 75 has 25% equity with 2 cards to come. That increases to 27% if we assume a K is dead. So I guess it is pretty close to whether they can call a jam.

I actually think 50% is close (maybe slightly over) to the correct estimate for how often V1-V3 will have an open ender. After they call the 15 dollar bet, their ranges are way biased in favor of hands like A6o/KQo/KJo/KTo/K9o/86o/76o/65o/87o plus the suited combos, plus suited Kx, plus 85s,52s. That’s ~120 combos of hands (treating one K as dead in V6’s hand). Then there are 20 combos of open ended draws (75,53s). 20/140~14%. So there’s an 86% chance that each villain doesn’t have an open-ender. That gives a (.86)^3~63% chance that none of the 3 villains has an openender. So a 37% that at least one of V1-V3 has an openender.

Agree, if V6 won’t call our small leads on turn/river at 100% frequency then the analysis breaks down. I guess one could insert another percentage Y in Scenario 2A and try to find a linear relationship between X and Y that is needed to make the jam/slow play lines have equal profitability.

If we slow play, and one of V1-V3 calls, I don’t think they can call our turn bet with only one card to come. They’ll be getting poor pot odds for a 10-12% equity draw.

I guess there no way we can tell whether V6 will call our jam more than 65% of the time. The truth is going to be villain/table/read-dependent.

I do also agree with the point made by QuadJ that the raise to 180 looks a lot stronger to V6 than the jam.

Good point raised in the EDIT. I guess they will have 18% equity and the pot will be about 350 before our turn bet, so they’ll call off the list 100 on non board pairing turns. But it’s not hugely +EV call, so I don’t think it will affect the analysis much.

The more I think about it, the more I think that really does matter. Whether we jam or call flop, if an open-ender stays in with us, we’re going to forfeit the entire pot somewhere around 30% of the time. That is quite a bit! So to me this really makes me think jamming is better, for two reasons:

1) If an open-ender is supposed to call us, pushing them out when folding is a mistake for them is a much bigger deal than pushing them out when folding is correct.

2) When we slowplay, we give open-enders the option to call flop and then give up on the turn if the board pairs. When we jam, even if they do call we always get their money whenever we boat up. (Admittedly this won’t matter that much, but it is something.)

Also, I have no idea why you think 75o should be part of Villains’ ranges but not 53o. They are almost entirely the same hand for the purposes of playing a big multiway pot.

I actually agree with both your points, though you stated it more eloquently than I could have.

As to the 53 not being in their range, I think you're confusing this thread with another. I went back through the thread and found that I included both in their collective range, which is what I remembered.

I don’t think these details matters all that much in the grand scheme of things. Making more complicated analyses of their turn play won’t add/subtract much in EV to the final numbers. For example, suppose we call and they call on the flop, so the pot will be 420 on turn. Suppose they miss their draw. We can bet 110 into 420. They will have to call 110 for a pot of 530. They would need 110/640=17% equity to call. Assuming board doesn’t pair on turn, this makes for a very small +EV call (an openender has 18-19% equity). They might be able to win $10 in EV from the whole $640 river pot. But this situation (brick turn, no board pair on turn) only happens a fraction of the time.

So maybe you need to add at most a few bucks to the calculation of the EV of their hand given only the one card to come.


I left out 53o because I was looking to make the most conservative assumptions in my argument against a protection raise. If you include 53o in V1-V3 range you also need to include other hands which would take the same line, namely K8o-K2o, Q6o,J6o,T6o, 96o, 85o,52o,54o,74o. That’s more than 100 additional combos of low equity hands for the 12 extra combos of 53o draws. So including 53o actually brings down the percentage of open-ender draws in V1-V3 range (the 36% estimated before) cause all the other crap they’d need to have in range compensates for the extra draw combos.

Forgot to reply to this. I don’t think Villains can profitably call a flop jam, so, they aren’t making a mistake by folding. Correct me if I’m wrong:
Ran an equity calculator and found 75 has 25% equity against 44; if you assume 1 King is dead (I guess that’s a safe assumption?) then 75 has 27% equity.
If we jam flop they need to call 175 into a pot of 465, which is 27% equity needed.
So it’s 0EV for them to call a flop jam. IOW they’re indifferent to folding.

Take two cards out, not just one. V4 is jamming with something too.

There’s no systematic rule to modify ranges/outs given the presence of V4. V4 could have 6x or Kx or 75 himself. In other words he cuts down on drawing combos and outs in a very complicated way.

If you want to count 2 Kings as dead, or 1 King and 1 Six, I guess 75 has 29% equity against 44, and call jam becomes +EV.

Not sure how that really matters since the EV of a call is still very small.

I don’t really want to go through the math again but it changes the EV of Scenario 1 and Scenario 2B above. If our jam gets cold-called—or a turn jam gets called—it should change the frequency of V6, who we assume is drawing dead against us, contributing dead money to the pot for us.

Honestly, this is interesting enough to me that I would go through it if I had more free time on my hands. My apologies to anyone on the forum who might have wanted to see this...

I doubt anyone could work through a multi-way spot by hand in the same way that you did before. Multi-way defense adds significant complications. . If V1/V2/V3 cold calls a jam, V6 is going to defend against the jam at a frequency that is much smaller than X. So you’ll have to add another frequency Z, and then speculate on the value of Z to reach a conclusion? What’s V6 going to defend with? Just AA? Who knows?

None of this discussion will be relevant in LLSNL games, though. One of the main errors of LLSNL players is judging bet sizes by their absolute amount versus as a fraction of the pot. No loose passive player is going to risk their whole stack on an open-ended draw because it’s a +$10 EV move. Most loose passive players get scared when big money goes in. It’s safe to assume they always fold 75/53 to a flop jam IMO.

Nope. However, there are some LAG's that will. When I find one, I try very hard to remember who they are (not always easy) and I'll jam into them. God bless poker.