"Your value bets drive your action. When you decide how to play your hands post flop, first think of the value bets you have. Depending on how many of them you have and what hands in your opponent’s range you are targeting as calls, you decide what size to bet and pick the required amount of bluffs to be balanced. What remains are the hands you check back because they have showdown value or because you intend to give up with them. You do not need to balance your give-up hands.".


Is the part saying you don't neeed to balance your give up hands precisely correct?

I know in multi street game theory, a perfect polarized range against all bluff catchers, start bluffing more from early streets and giving up bluffs on the way until the river where he bets with the correct bluff value ratio based on stack and geometric bet sizing. Those give up hands certainly don't need any protection because they have no equity to protect.

But my thinking is in real poker, a lot of your "give up" hands can have some equity sometimes, even just a little, so I don't find this statement totally true, and you often will have mid hands in every check you make, and sometimes strong, so you end up balancing them anyway in most spots, even if your main goal is to protect your mid hands and not your air.

What are your opinions on this?

And extra question, do we defend close to the MDF in every spot we are in poker when playing the GTO Equilibrium? (I already know we often defend slightly below it and rarely above it), or are there spots where we massively under protect compated to the MDF postflop?

Thanks!

IP on the river, sure it is correct. OOP on the river it is different. We check OOP hands because:

1. They may beat some value but struggle to get called by worse, they beat bluffs. This happens a lot in BvB where BB will bluff and value bet worse, so we are kind of check calling for value.

2. They have showdown value and we either hope to win of it goes check check, or call/fold facing a bet.

3. They are no/low equity give ups. 0 EV or close when we check, but we would have to many bluffs if we bluff this hand. Blocker potentially are bad and we choose to give up.

4. They are trapped nuted hands. This will be rare as mainly we want to fast play our very strong hands, but occasionally the EV of check raising is the same or more than check calling. Hands in this category are more likely to unblock bluffs, block value, and vs other nutted hands they are going to win a ton either way. Hands in category 2 are protected by this range. Some hands in category 2 might be used as bluffs to balance this range. They have tend to have showdown value when river checks through, but nuch less when facing a bet. IE, hands with the nutflush blocker, counterfeit 2p that block boats.

As for your second question I do think there are spots where we massively underdefend compared to MDF. Certain spots in 4bet pots as the caller when there is an A and K on the board. 4 flush runouts also come to mind.

Hey man thanks for the answer.

For the point 4 you mean the ev of check raising and betting is the same in certain river spots right? I think you made a typo there.

About the text, sure, for the river IP is simple that we don't need protection of our check range.

But I think it's not even focused only on the river but any street. And my point is, even though our main focus for protection are mid hands because they have more equity to be protected, give up hands often have equity against the trash of the opponent too, so they also benefit from the protection we give to our check ranges on any spot.

In few words, you will often win with J high, specially if rival knows you will not fold everytime you check.

You can check this article of splitsuit where the topic is touched:

https://www.splitsuit.com/gto-polari...nges-made-easy

"Scenario: Nutted equity distribution and some air, nothing in the middle.

This is the perfect example of a range that likes to bet, since we can formulate a polarized range by the river very easily. Flop ranges are not usually this polarized so soon, but we have kept the models extremely simple for clarity.

Because our range does not contain too much trash, we can bet most of it without becoming too bluff-heavy on the later streets.

The solver uses the large bet sizing with a 95% frequency and never uses the small sizing. The high betting frequency might seem surprising when we consider that the overall range only has 36% pot equity, but this is the power of a polarized range!

The 5% checking range is pure air with zero strong hands for protection. Range protection is not required in this case because our opponent never bets when checked to.

If we tweak the model by adding some trash hands into our opponent’s range, the solver then protects the flop checking range with some strong hands. The solver still bets very frequently overall, but not quite as often since some of the value hands get checked."

In this example, GTO decides to protect some of its trash against the rival trash apparently, so the claim of give up hands not needing protection doesn't sound accurate to me, even though for importance reasons our focus is on mid hands and give up hands often benefit as collateral result of we trying to protect our mid hands.

I agree on the last comment, I already checked there are spots where we underdefend by a wide margin (half the MDF).