Hey all,

I'm hoping to get a good discussion on this since I'm currently using ratios that I'm not sure at all if they're correct. Hopefully this is an okay place to post this rather than the general strategy forum...MODS: since the live 2/5 meta is different from online or lower/higher stakes and since I'll include some actual 2/5 hands in this thread, please don't move/delete.

So here's the main situation I want to focus on: multiway (3+ players see flop) pot that were either limped or raised where we are the aggressor (betting postflop or raising a bet).

There have been a few hands I played recently where I raised a very strong range preflop against limpers. I then am on the flop with TPTK or an overpair, bet flop, and everyone folds...I didn't think much about my exact flop bet range, and due to that I think they may be exploiting me by folding say middle pair or TPWK to my flop bet. Remember, if someone is exploiting someone else in poker, they don't have to consciously know they're exploiting them...

So it's already known that if we're the defender in multiway pots, we can fold a lot more hands that we should call with if heads up, and the more players in the pot the more often we can fold because: (1) the bettor's range is a little stronger than heads up since they know they must get through more players (2) if we just call there is the chance of a raise from another player whereas heads up there is no chance of this (3) if we want to try to make a bluff with ATC NOT profitable for the bettor, we don't need to call with medicore hands to do this as the defending responsibility is split with the other players. So if we are facing a bet in a 4-way pot, it's fine to fold like 70%+ of our range.

But what if we're the aggressor? If we bet flop heads up, it's already known we should have roughly twice as many bluffs as value bets (if the value bets are very very strong hands). But multiway, should we use the exact same strategy?

Here's an example of one I played last weekend:

500 effective, MP limps (seems like a loose passive player), hijack raises to 25. I flat on the button with KQ and a range of JJ-44, AKo-AQo, AQs-A10s, KQs-KJs, QJs, J10s-76s. Blinds fold and limper calls.

Flop = J85. Both check to me. If heads up, my bet range here heads up would be something like 88, 55, AJs, KJs, 76s, 78s, 109s, A10, A10, A10, KQ, KQ, KQ, 66, 77.

Since they're one extra player, should my flop bet range change? If so, which of the following is the best change?

1. Same value combos 88, 55, AJs, KJs but less bluff combos, resulting in a lower flop bet frequency.

2. Less value combos and less bluff combos but the same value:bluff ratio, resulting in a lower flop bet frequency.

This, like many theory questions, leaves out a lot of other factors (what happens after the flop if called? what if raised? Is PFR balancing check/fold, check/call, check/raise?) But it's an interesting question.

From where do you derive the result that bluff:value ratio should be 2:1? If we go back to that formulation and modify it for the 3-player game, we have a larger pot but also a lower probability that at least one of them calls. One hypothesis is that these two effects balance so you should fire with the same frequency. Is that possible?

Do you have a read on the hijack? That, y'know, matters a lot.

This is a wet board, your hand lacks showdown value, and you have several backdoor draw possibilities. All of those considerations matter a lot as well.

How does the loose-passive player behave postflop? That ALSO matters a lot.

If neither player will call a flop bet with less than top pair or an open-ended draw, you should be betting 100% of your hands until they adjust (which they basically won't in low-stakes live poker).

If hijack will check-call with any pocket pair, and will sometimes get tricky with overpairs or sets, then you should be checking almost always.

Playing multiway pots in low-stakes games requires compiling multiple player-specific reads. Your range math is far less important than your adjustments to players' vulnerabilities.

In theory the collective field bears the burden of defending against our bluffs. So in a spot where heads up a villain should defend 60%, 3 way would require each of them to defend only 36.8% (assuming the defending burden were equally shared).

In reality this burden is not equally shared but on average they are defending 1/2 as many combos individually.

Intuitively I want to say that the shared defending burden will tend to favor one of the field players since there is at least a bit of an inherent "best hand collusion" taking place. In other words we fire air on a dry board and player 1 calls, player 2 now can fold his weaker bluff catchers.

Also, fundamentally, multiway pots in LLSNL are typically the result of players calling too much. Unless the collective is extremely fit or fold post flop, we should be making exploitive adjustments which I think will include reducing bluff to value ratios since collective over folding is rarely going to be the weakness of the field.

From a pure game theory perspective? A mix of 1 and 2 but more 1. A couple of your weaker made hands like 87s/77/66 should go ahead and check this flop more often. You should also check your potential bluffing hands more often and your bluffing percentage should go down faster then your checking meh strength hands goes up.

The sort of hands you bluff with should also change. Heads up you should sometimes bluff with total air and check hands with back door draws. Multiway your bluffs are less likely to work and your less likely to get raised off your weak draws. So you should be bluffing more of your weak draws and less of your total air.

In practice a lot of this gets thrown out the door real fast and practical matters of playing opponents who are not anywhere near GTO dominates. What you do with draws multiway will depend on how passive your opponents are. How much you like your non-nut flush draws will depend on how much opponents like to play any two suited. Multiway at 2/5 there is a high likely hood of there being one or more very sticky villains who will generally autocall the flop to see if you continue on the turn. In a raised multiway pot it usually isn't worth trying to bluff them out of hands.

Unless you are playing only OMCs this is almost certainly not happening. They just whiffed on making a pair.

Just curious as to what is a "very very strong hand?"

Stronger than a "very strong hand", but weaker than a "very very very strong hand".

@OP While I understand the merit of GTO combo/range analysis as a thought experiment, I do not feel it's the best approach at LLSNL, or any live poker FWIW.

You do realize that if you were to play "perfect" GTO (in a game with no rake) you would be making exactly 0bb/100 right? I feel like not many people understand that...

That's only if everyone else were also playing perfect GTO. The idea is that if you play optimally and they play suboptimally you can print money. In practice I agree that a more exploitative style is more profitable at LLSNL but I imagine GTO is also profitable if done correctly. Understanding basic hand strength probably makes you profitable at a lot of card rooms.

Imagine a game of rock paper scissors (RPS). You are playing GTO, which in RPS would be randomly throwing either a rock, paper, or scissors with equal probability. Gaurenteeing that you cannot be exploited, and a 50/50 outcome.

Your opponent, a caveman-eske brute, only throws rock. He is totally exploitable; however, because we continue to play GTO, we are still 50/50, with no edge. Even if our opponent plays in the worst possible way, the edge is still zero.

That being said, in this example you are heads up, and it doesn't provide the opponent opportunities to really **** up, like calling $800 pre with a $810 starting stack, and then folding for a $10 bet on the flop with the second nuts. Also, the fancy math guys still don't know if poker (even HU) is the same type of GTO as RPS.

My point is that by focusing on GTO in a live poker game, you're not taking advantage of the huge edges available to you. You play too few hands with too many different opponents for GTO to ever come into play imo.

Playing GTO doesn't mean your playing optimally, it means your playing GTO; GTO means you are not exploitable, nothing more.

In the rock paper scissors example, the optimal strategy versus that opponent is clearly to throw paper every time, not to continue playing GTO.

We agree in general about the applicability of GTO to LLSNL but you are still wrong about many things in these posts.

When you mention GTO being 0BB/hour you are speaking of GTO equilibrium. By definition this is reached when all players are playing GTO. Playing GTO against players who are not playing GTO is not an equilibrium. It is quite likely to be a winning strategy.

It may not be optimal in the sense of optimized for that particular game and players but it is optimal in the sense of overall game theory. Hence the name.

I don't think GTO makes sense to employ at all costs in LLSNL but it has interesting theoretical concepts that can be applied to LLSNL so long as you aren't dogmatic about it. Ultimately your player reads should trump all else.

I just think the questions you are asking are not meant for this forum.. You might have better luck in the online micro or small stakes forums

I actually think this particular question is good here and in theory forum.

I derived the 2:1 value to bluff ratio heads up because that's somewhere in the range of what it should be if we want to make villain's EV 0 if he has a medium strength hand (bluff catcher) on the flop as well as each of the following streets. Example:

If we have 100 value combos and 300 bluff combos on the flop. If we bet .7PSB on the flop with 100 value combos and 200 bluff combos, bet the turn 71% of the time for .7PSB with 100 value combos and 103 bluff combos, and bet the river 71% of the time for .7PSB with 100 value combos and 44 bluff combos, then villain's EV of calling all the way down on the flop is:

.29(1.7PSB) + .71(.29(3.38PSB) + .71(.3(7.4PSB) - .7(6.4PSB))) = +0.04967 PSB = approximately 0

If villain knows we either have him beat or are bluffing, then it doesn't matter whether he calls or folds on any street since his EV will always be zero.

So why SHOULD we want to bet a ratio that makes his EV of medium strength hands 0? To try to increase our EV depending on V's defense strategy.

If villain calls exactly 59% of the time on all streets, then our EV is 0 and it doesn't matter what we do. In this case, it makes sense to still make the EV of his bluff catchers 0, because if we are assuming he's so good as to call at the exact correct frequencies we should also assume he's good enough to watch our frequencies to look for errors.

But if villain doesn't call exactly 59% of the time on all streets, then our strat of making his bluff catchers $0EV can outperform strategies where we have a different bluff to value bet ratio on the flop.

Examples: If villain overfolds (i.e. folds more than 59% on each street), then our strat won't be the highest EV but will still outperform a strategy of betting a 1:1 value to bluff ratio on the flop. Likewise if he underfolds.

I'm not sure if collective overfolding is a weakness in the games I play. This isn't based on a super large sample size, but I know very frequently recently I've just made a normal sized c-bet in a multiway pot (with a value to bluff ratio that's probably like 2:1 or 1:1) and everyone folds. This is why I want to work more bluffs into my bet range in multiway pots, and I figure the best starting point would be finding out how many bluffs to add per game theory.

Using game theory ratios is a great way to ensure we don't cross the line from playing good LAG (bluffs in moderation with the right hands) to bad LAG (excessive bluffs with the wrong hands).

Isn't this generally going to benefit the player with the best relative position, i.e. to the right of the bettor? They have the best information about whether any of the other people are going to choose to bluff-catch, and so can call with a much wider range than someone who still has people to act. On the other hand, the players acting first don't know whether later actors will bluff catch.

I don't have time to write a long reply right now, but I do think this is a very interesting topic.

I'll probably come back and give my own thoughts later, but it does appear that, as with most "game theoretic" discussions on this forum, there are a lot of unwarranted assumptions and people sometimes may not even be aware they're making them. Examples that I spotted right away:

How do you know that this play is exploitation? Maybe in multiway pots it is correct.

"Known" is quite a presumptive term. Very little of this seems obvious to me at all. For example, the idea that "the more players in the pot the more often we can fold" is unclear. It certainly does not correspond with my instinct, which is that we should be folding a lot more hands when we aren't closing the action, but the number of players behind us is far less relevant.

More on the bolded later.

I'm not sure why it's clear that the first thing is relevant or that the second thing is true.

This seems to me like a terrible assumption, on a theoretical level. The "accidental best hand collusion" that you're talking about surely does happen but seems like it's probably a deviation from theoretically "optimal" play, so not taken into account in any kind of GTO strategy.

...why? Again, doesn't seem obvious to me at all "from a pure game theory perspective".

The first bolded is actually technically false (sounds shocking, right? But it is). And once you leave the realm of heads-up play, I see no reason why we should assume the second bolded.

Has anyone in this thread ever actually tried to extend the usual heads-up "toy games" that all poker players know to multiway scenarios and seen what happens? Because I have one such example that may be enlightening for the thread. OP, if you want I can post it later when I have more time, but it's not a flop example so maybe it's not totally relevant to the thread...?

Vern, isn't it pretty much impossible to establish an early street b:v ratio given the number of potential branches in the decision tree between river and flop?

Heads up the flop ratio is arrived at by assuming bet sizes on river and turn. Since multiway we don't know how many villains will be calling and thus what port odds we will be offering on this later streets how can we arrive at a theoretical ratio for the flop?

And if still multiway by the river on most boards it's likely ranges are stronger in an absolute sense, perhaps less so in a relative sense, but stronger nonetheless. So the polarized range vs a bluff catching range model would seem to give way to a more exploitive approach considering the usual stuff like board texture, ranges and tendencies.

I went back and read both Janda (applications) and Miller (1%) and both have a "multiway pot" section in their books.

Both note that all the principles still apply but then completely ignore this subject and talk about shared defending burden, ranges, position etc.

Edit: I posted this question in Janda's book thread. He's pretty active there. I'm curious his response.

This (bolded) is exactly how I feel too--it's pointless to try to work out what GTO is supposed to be, because we almost have to play exploitively.

Nevertheless, I think it is extremely interesting that if you try to use the polarized range vs. bluff catching range model, where you give multiple opponents identical bluff catching ranges, you almost immediately arrive at the conclusion that all the bluff catching is supposed to be done by only one opponent--the one closing the action. And once you have that, you see that using this model, the "desired" ratio appears not to change from heads-up to multiway. Of course, as you point out (though for a different reason), it's probably better to conclude that the model is totally pointless to try to apply to real life, as I've been saying in this forum for years.

Agreed. But the early position caller *should* have the stronger range thus when he calls post flop the player closing the action should fold his bluff catchers (best handing).

In reality at LLSNL that player with worse relative position frequently won't have the range strength he should pre and will have lower standards for calling post than he really should which is why there are so many multi way pots at LLSNL in the first place.

I don't want to be misunderstood to imply we shouldn't be bluffing. In fact cbetting / barreling loose passives / fit or foldies and the like on the right boards can be very effective 3 handed for these very reasons. The bets look bigger in an absolute sense because the pot is bigger. Betting into multiple opponents looks strong and the above exceptions not withstanding the player not closing the action will have to worry about the player behind and thus defend less with his pure bluff catchers.

But I think from a theoretical standpoint the larger point is that the fundamental imbalance in our opponents that leads to multiway pots in the first place is the thing that should be causing us to deviate. And I think that is just me agreeing with your larger point.

I think that's probably true (that you're agreeing with my larger point). I guess I'm saying, if in some future timeline you were playing against people whose tendencies you didn't know, in a world where GTO was known, and you raised preflop and got multiple callers, and then you kept up the aggression on the flop, and someone called you OOrP, then you would be unsure whether they were playing a GTO range (which is supposed to be very strong not to be folding OOrP) or whether they were deviating by calling you wider than they're "supposed to". In real life, of course, we almost always assume (correctly in my opinion) that it's the latter. And another point about GTO in multiway games is that when you know someone is deviating, sticking to GTO is potentially losing (which is very different than heads-up which I feel is how most people get their intuition), so you basically have to start deviating once you get reads.

I won't pretend to understand all this GTO stuff but it is interesting so I'll stick around.

GTO has absolutely no relevance in the games I seek out. My games have at least 4 players who will, during an applicable hand, say after it's all over: "Damn! I had bottom pair on the flop! If I had called down to the river [outrageous price applies] I would have got runner, runner flush or str8."

"Dammit! I woulda' flopped two pair with my T6o! You all woulda' never seen it coming! I almost called" Outrageous price applies.

etc., etc., etc.

This is a really good thread with good info despite that. Thanks to those who contributed....AND: It doesn't come in a book with a $50 price tag!

Here is Janda's response:


In other words it's "messier and trickier".

Ha ha At least he didn't say "it depends", though of course how much messier and trickier it gets will depend on a large number of variables that are all impossible to pin down....