LukeH

Simply put, you calculate your opponents odds and then construct your range in such a way to give him exactly those odds. So you play all your AA and add exactly enought QQ to make his call breakeven.

I also liked the video a lot. I find it very useful to think in terms of equity distributions. So my question is, what other types there are besides polar vs bluffcatch and the one disscused in vid.

What equity distribution emphatisez mid size bets like 50% bets for example?

Also liked the 2-table format, a mixture of live play, HH review and pure theory videos sounds great.

I would like to aks about your HJ open, you open folded Kc9c at 2:03 and Qh9h later, which would both be opens for me. What is your take on this spot?

Agree on the 30bb-40bb range, would like to see CO vs BTN also.

Bernard: yes, thats the general idea. If he has few bluffs and many many value hands, you really cant stop him from bluffing profitably...if he has a lot more bluffs than value hands, then you need to prevent him from bluffing them (all) profitably.

No, the mdf is ok, but you have to chose the right spots, its not universal. One of the first theorems in any gto textbook is this: IF you mix between several actions in a gto strategy, then those actions have the same EV. In our case: if you sometimes bluff and sometimes not, then ev(bluff)=ev(giveup)=0. From that you derive the mdf.
The important part is the IF. When we do not have "enough" bluffs, we bet all of them, no mixing occurs and you dont have any equation to derive the mdf from.

I will try to explain what Steve is saying. What does it mean that you dont have enough bluffs? It means that there is some betsize (usually large), that allows you to bet all your bluffs and appropriate number of value hands and you still have some value hands left. If this is the case, then you can bet those excess value hands for whatever sizing you want (even 1bb or you can even check them in theory, but its stupid in real game) and you do not need to balance those (smaller) bets with any bluffs - your EV is the pot with the "nuts only" range and this is the maximum you can get. And you do not miss any bluffing opportunities, because all of your bluffs are already in the large sizing range. Now the tricky part: if the situation is as above, then you can also transfer some of the bluffs to those smaller sizing ranges, making sure you use all of them (and of course in a balanced way). This forces your opponent to fold to any bet you make. To see why, imagine this: you use all of your bluffs in the range that bets the maximum possible sizing and bet some other sizing with the rest of the value hands. What is his best response to this strategy? He has to fold to the smaller sizings and against the max sizing, he can do anything as his EV is always the same. But only the strategy that folds everything even to this max betsize is GTO. Because if he ever calls, you can exploit him by transfering some bluffs from the max sizing range to those lower sizing ranges. Your EV on the lower sizings will not change and your EV on the max sizing will go up = you exploited your opponent (while remaing unexploitable).
So there are infinitely many Nash Eqs, all of the form: he folds everything to any bet, you bet one or more sizings so that each range corresponding to a sizing is either nuts only or a balanced mix (with respect to its sizing) of bluffs and value AND you bet all of your bluffs in the proces. He doesnt want to deviate from " fold everything " because he cannot gain by doing it and he can loose, you dont want to deviate because you win the pot with every hand.

Example: My range is 6 combos of nuts and 2 bluff combos and we are 2 pots deep. I bet 1 combo of nuts for 1bb, 2 combos of nuts for pot, and 3 combos of nuts + 2 combos of bluffs for 2 pots. What will happen if you try to bluffcatch against the 2 pot range? I can change my strategy to bet 1bb with 1 nut combo, bet pot with 2 combos of nuts and 1 bluff combo and bet 2x pot with 3 nut combos and 1 bluff combo. This is balanced and exploits you. Anytime you bluffcatch against any part of my range , I have the tendency to deviate, meaning we are not in a Nash Eq. I do not deviate only when you fold against any betsize.

I would reccomend the GTO range builder for this. You cannot easily identify what the worst bluffcatching hand is. In the 1-0 games, you know there is some threshold for calling/folding, but in the real situation, its not so simple because hands arent ordered in any fixed order. As you change your range, the quality of his bluffcatchers also changes, so you cant start with assumptions about what his worst bluffcatcher is...

Maybe the basic idea is: nut blocker is important not just because he cant have the nuts, but also because he cant have the nuts blocker:) Its really easy to see with preflop ranges: if we have range of AA,KK+bluffs, its important for those bluffs to be Ax. So when he holds a good blocking hand like AK which blocks half of our nuts, he blocks all of our bluffs also.

In my opinion its more about what he blocks than about what we block, but its really both:)
I dont understand the question: if you hold the Ac, it doesnt affect how you play other hands...you just decide if you bet this hand or not.

Try this, construct your range of 33 value hands and add 16 bluffs not using the Ac. Then see the situation from the bluffcatchers point of view. Give him a hand with Ac. Now he sees your range as 14 value combos and 16 bluffs, so he can easilly call. This would be a problem - if he has enough bluffcatchers that contain a nuts blocker, you would be very exploitable to bet that seemingly balanced 33/16 range. So now go back to those 16 bluffs and choose them so they include Ac. Now when HE has the Ac, he knows that you have less nuts but also less bluffs, because he blocks both, so your ratio of value-bluff is OK...thats the idea.

You do not need to do this in every spot. It is important mainly when your valuehands are all of the "same kind" like when all of them are AcXc or QcXc, you need to bluff hands of the QcXs or AcXd type. And its even more complicated, because you dont want to bluff hands with too much showdown value at the same time.

Try spots where flush is possible. Like board is 5c6cJc2dKs, your value hands will be AcXc and so when he holds some bluffcatcher like AcJd, he knows that you have less combos in your value range. Remember that you are balancing against the weakest bluffcatcher, but sometimes even the weakest bluffcatcher blocks some part of the value range. In this case, you should bluff hands with Ac in them, so when you bet you have the key card in both your value and bluffing hands.

You are right, I believe this is one of the reasons why poker is so hard to slove by computers. We are actually not playing our range vs his range, but each hand from our range against his range (minus bloker effects). See Bayesian Games in some GTO text.

This happens very often when balancing preflop ranges: say you 7bet jam and you have AA for value and 54s as a bluff and 6-4 is your "theoretically correct" value-bluff ratio (I completely made up the numbers). Now if he holds AT for example, he knows your range is only 3 value hands and 4 bluffs and you are not balanced. The solution is to bluff with Ax hands, so when he holds Ax, he blocks your AA and Ax bluffs at the same time so that your ratio doesnt change. Its actually a bit more complicated, usually you cannot construct your range so that the ratio doesnt change for every hand he holds, but you can do it so that when he holds a high equity hand, you ratio shifts to value and when he holds a weak hand, he knows you have a bit more bluffs but he still cant call because he has too little equity. Its hard to construct such range without a software...

So on the river, its the same idea. Your range is different from his point of view for every hand he holds and you need to account for that. If both ranges are reasonably wide, you can use the standart 1-a ratios, but as the ranges get narrower, this effect is more and more significant. I studied this a lot with Combonator and GTO range builder, you can find some interesting spots if you concentrate on this. Models like 1-0 game or nuts/bluff vs bluffcatcher toy game doesnt account for blocker effects at all so the 1-a solution is only applicable when the bloker effects are neglible.

Reducing it to something like 15 would be oversimplifing things.

I think that what confuses people is that the solution to the nuts/bluff vs blufcatcher range or AKQ game is not always the same. As Steve already explained, there are two types of situation:
1)we have enough bluffs in our range so that we can balance our valuebets even if we bet the maximum possible size. Then beting this size is optimal. This is the standart "if you pot it, you should have 2-1 ratio of nuts-bluffs because you give him 2-1 odds" solution.
2)we dont have enough bluffs (=our range is very strong). Now we can find a betsize where we can bet our whole range and he cant call. Every bet of at least this size is optimal now. But we still should think about which sizing to use. It does not matter against optimal opponents, but some of the bets might be better than others against certain player types.
Extreme example: I am on the river with 100combos of absolute nuts and one bluff combo. I can pot it and nobody can call profitably with a bluffcatcher. But I can also bet twicve the pot or half the pot with the same result.

You can also find optimal strategies that perform the same against optimal oponents, but one of them is always better against nonoptimal oponents.

The idea is that in some spots there could be more than one optimal strategy (it happens often in game theory textbooks:). You might find two strategies that perform the same against optimal opponents, but one of them better exploits nonoptimal opponents of some kind. Like one exploits calling stations better and the other exploits nits better. So you choose one of them depending on the ratio of stations/nits in your game . You play balanced and exploit bad players at the same time.

Or sometimes you can, but it depends on the situation a lot.

I did not saw the Snowie hands, but consider this: The rules for value-bluff ratios are derived from simplified models (like the 0-1 game, situations when you have nuts and bluffs against bluffcatchers etc). But there might be real game situations with different range structures and hence different solutions. Your opponent can have nuts and bluffcatchers versus your range of second nuts and bluffs for example. You cannot use ratios like in the polar vs bluffcatcher case in such situations...

Bet/folding and raise/folding for value is also possible. You can reraise for value and plan to fold to 4bet for example. Thats why Steve made his comment.