Denying equity on earlier streets is an important reason, but it's often justified exploitively; and little to nothing is talked about raising at equilibrium.

As with most things in poker, raising should be used when considering a number of possible factors. But with as little bias as possible, what are these factors, and how do they interact to predict when raising is an important strategic option at equilibrium?

Some of these factors include:

Positional value: Dynamic/static boards, SPR, Tempi-betting

Polarization:Spread of draws (equity spread), High/Mid/Low value polarized,
bet sizing

Range advantage:High/Mid/Low equity advantage

Balance: Blocker prevalence, Unique hands


And less of a concern at equilibrium:

Barrel frequency: How often hero or villain continues to bet on future streets.

Heavy equity distribution: Villain is too equity driven.


Example: Why does equilibrium check/raise often on boards like 883s as BBvsBU?
IP is pushing a lot of Low/Mid-equity on 883s, so much so that he still wants bets into a relatively polarized OOP range.

OOP has a Mid-High value polarized range, which prefers to continue with a beefy C/R range consisting of trips, mid hands like 77-22, and various types of draws. And on most turns OOP checks 50-70%.

So in this example, IP still wants to bet the majority of the time into this polarized range, and OOP prefers to make it a size to his 'liking' (2 bets, mid-high value preferred), instead of donking (1 bet, low-mid value preferred) and calling (villain pot controls too well).

So take a look at some of the factors above and try to use these to analyze a spot. Feel free to comment on, or add any relevant concepts.

I don't consider these factors in this way anymore... I simply consider what my perceived range will be when I make the raise, and then how he will react with the different hands in his range, and, how much money I expect to make from that reaction in the end.

I don't understand all the terms you used just then, but from what I can tell you didn't consider your perceived range in any way, which is a massively important factor.

To me, the only reason I would raise is if I make more money that way. I might do it to represent a strong hand to force folds from his range. Or I might do it to build the size of the pot against hands that are weaker than mine which I think will continue. Or a lot of the time, I do it for both those reasons. I don't think Poker needs to be any more complicated than that. Everything is covered.

I like you dissected all the options. And in my opinion this information is what gives us the knowledge to who we raise/defend/fold wider or tighter.
But the main one is to get the dead money from the pot.

In a flop JJ5 you can x/r a loose player and call a re raise with a wider range than vs a nit player

Sent from my computer at home.

Well what I'm saying is that this sort of info doesn't directly lead to the decision. There are an infinite amount of these types of reasons and all of them lead us to change our understanding of the ranges and how much we will make in the end. And then that's what leads to our decision.

I don't understand this either, but I think it be fun to discuss (Please feel free to point out errors in my understanding and let me know why I'm a dumb dumb). I don't have any answers, but am seeking clarification too.

Why does equilibrium check/raise often on boards like 883s as BBvsBU?

If two opponents are playing at equilibrium, then neither opponent is able to unilaterally increase their EV. This is accomplished by playing your all your various postflop ranges in a way that is maximally +EV against a equillibrium strat, and minimally exploitative against any opponent who deviates from a equilibrium strat (right?).

So it must be that on the board listed, it is maximally +EV to x/r at a high frequency. So then we have to figure out what is driving the EV behind that aggressive x/r strat as opposed to a strategy that emphasizes more check-calling. Is there a way to quantify this or explore this?

I think that reviewing equilibrium strategies helps us discover when raising helps us 'make more money'. I agree that perceived range and judging how our opponent plays against us dominates the EV difference in real play. But these issues are subjective and are not relevant in studying the equilibrium. I'm trying to learn more about objective and theoretical play, so I have a better default strategy to then employ more exploitative play and whatnot.

If you're interested in working with and understanding equilibrium play, owning Piosolver is a must.

I never got too deep into the game theoretical properties of GTO play partially because I don't think there's much incentive to do so. But I simply think of GTO / equilibrium as a strategy where its nemesis is not +EV.

So you can at best be 0EV against equilibrium strat in a symmetric game, and there's no requirement for it to play 'minimally exploitative' against deviations. The only requirement is that its strategies against sub-optimal opponents don't make larger mistakes than the sub-optimal opponent. But whatever.

I do think there's value in exploring why equilibrium strategies have certain properties. It's a tricky thing to do though, since there's not necessarily a relationship between things that stand out in frequency, and things that stand out in importance (or EV difference).

Denying the realization of equity by raising is just as important a concept in optimal/theoretical play.
Matt Janda wrote about "denial of equity" quite a lot in his first book. He's presumably written more in his second.

There are so many merits to raising preflop.

1. By raising preflop, you lessen the amount of people in the pot and thus creating better chance of you winning your hand.

If everybody had a random ahnd and was dealt any 2 cards preflop, raising is going to be a winning play. In this case if you dont raise and it checks around, the chance of you winning this hand before anybody seeing their cards, is 11% or 1/9. If 2 players call, then it is 33% and if you are heads up, you are 50%.


2. You protect your hand from getting a bad beat.

Nobody wants to lose with AA against 94o. By not raising and having somebody call with any hand, you are not protecting your premium hand. You want to make the opponent pay to see the flop since at the moment, you have the best hand.

Most of the time, AA will still be better than 94o after the flop. And when you C-bet and they fold, you didn't make any money since no pre flop bets were made.

3. You can attack the blinds and also take dead money.

If you are playing against tight players, why not bet preflop and take down pots and win money? if they call, its not over, you still have a chance to win money anyway.

4. You apply pressure.

When you raise preflop, you're opponents will be making bigger decisions on later streets. If you raise to 15 in a 1/3nl game and you go heads up, there is about 30 dollars in the pot. If you make a c-bet, he will be calling a bigger bet since bet sizing is in relation to the size of the pot. If you didn't raise preflop, well he is calling a price of a hotdog and it applies no pressure.

5. Preflop bets will tell a story.

If you raise preflop, you are the boss of the hand and it likely will get checked to you on the flop. Unless they have anything at the flop, they will be respecting your raise and proceed cautiously. If you bet on the turn after a C-bet on the flop, opponents will definitely respect your hand. Maybe you don't even have a made hand but since you raised preflop, middle pairs and small draws may fold to you hand.

6. Adds unpredictability.

If you feel like the time is right, perhaps raise with mediocre hands like suited connectors and small to medium pairs. Especially if you are in position, raising will be a great plan. Its also nice to showdown at the river with hands like these because the opponents will now be playing the guessing game as well. This may lead to more players calling C-bets on flop so you might want to lower you C-bet percentage with hands like AK. However, wouldn't it be nice for opponents to be calling or jamming all in with draws when you actually have a monster.

7. Make Money

Make more money with big hands. Simple as that. If you are just calling and never betting or raising, you will never win at poker and make money.

I'm confused what you are asking. Do you just want to discuss what factors an equilibrium strategy uses to pick raising candidates post flop? Because if that's the case the answer is because the algorithm "learned" that some hands made more by raising than by any other strategic option.

I think the only quality that matters is range/board interactions between player's ranges to determine which strategic options will be avaialable to a player and hand/board interactions when determining what to hands to use to construct those ranges.

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value, bluff, equity denying, futureEV (bilding pots with nutmaking handz)