A poster in another forum asked about the following example and wanted to discuss the theory behind the actions of JNandez described in one of his videos.
I am reposting to keep the conversation going here on 2+2.

"Hey there, this will be my first post here. So Im currently giving HUPLO a go and come from a HUNLH backround.

I just watched a video by Jnandez that really threw me off and I wanted to see if anyone can explain the theory behind it.

So pretty much he was cbetting a 4k4r flop and said that he wants to only be cbetting this board 50% of the time but used a 25% cbet sizing. He goes on to list a bunch of hands that he cbets 100% of the time for which he uses a 50% cbet sizing.

Im not understanding the theory behind this. In nlh you look at the equity your range has vs your opponents range on different boards, and the more overall equity you have the more you cbet, so if youre cbetting ‘range’ from a theory perspective you need to use a small sizing right?

Is there something about PLO that makes this concept not apply? I thought this was basic game theory. Could anyone explain why he sized his bets like that? Look forward to replies, thanks

I replied:

I agree that you cbet small with a big range advantage. I don’t know which boards he bets 100% of the time, but I believe these are the ones with a range advantage, and 50% is small sizing in PLO.

On the K44 board however, only a king or 4 which makes up about 40-45% of his range, or a pair with backdoor potential will call a cbet if you bet anywhere near 50%. This is because of a well-known GTO concept known as MDF, or minimum defense frequency. In a 50% bet size, the opponent should call around 67% of the time. In this scenario, the opponent can fold some weak paired hands and ace high back-door draws where he may have very little equity. AND WE DON’T WANT THAT, we want him to be in tough spots, especially when we have position. So with a 25% size, the opponent must call around 80% of his range to be unexploitable if you don’t consider equity realization factors or are on the river. And most people don’t call nearly that often on any flop.

Does this make sense?





March 9, 2018 at 8:50 pm- Edit -

thanks for the reply though Im still confused. Putting someone in tough spots isnt game theory related, Im trying to understand the game theory reasoning that makes this concept differ from nlh, like according to game theory shouldnt our sizing be relative to our betting/raising frequency?

Also I never heard of ‘MDF’ it sounds like that is 1-alpha?

March 10, 2018 at 1:25 pm

Yes, it is referred to as 1-alpha as well. Sizing relates to BLUFFING frequency, which VARIES with the number of VALUE COMBOS in my range .

I forget how to derive it, but you can find a chart of this for various bet sizes. On a 2/3 pot bet, A=40%, B (bluff)=28.5% of total betting range (so 2.5:1 value bets (71.5/28.5)). So that would dictate a maximum of 70% Cbet on a 2/3 pot bet size (50/x=2.5, x=20 : 50+20)

I’m gonna choose bluff frequency based on how often I have a value hand, and that could be up to 50% of the time on a wet board. I won’t slowplay much on a wet board, but I don’t want to bet all 50%, because I want to keep a strong check back range so my opponent can’t donk the turn every time I check flop.

In the end PLO doesn’t vary from NLHE from a GTO perspective, only in the number of combos involved. I would appreciate anyone else’s feedback if I left anything out. Believe it or not, I am trying to keep this simple. Could be a good post for 2+2 because there is a lot to cover.


March 10, 2018 at 10:46 pm

sorry for the late reply, thanks for your answer. I know the chart youre referring to, could you please explain this part of your calculation ‘(50/x=2.5, x=20 : 50+20)’?

March 14, 2018 at 8:24 pm

in nlh I cant see situations where we bet smaller with a smaller cbetting frequency but bet bigger with a bigger cbetting frequency, this is the part im not getting about this


HERE'S MY REPLY TO SUM THIS CONCEPT UP
You are on the right track: the bigger size you bet, the more bluffs you will have to include to make the caller indifferent.

The 50% value /x (bluff)=2.5 is a way of determining how often I can cbet (maximum) on a given board. Since value/bluff=2.5, I can solve for the bluffing range that matches the value range I have chosen. Knowing this is not as useful as finding out just what hands I want to value bet and bluff with- and there are two ways of doing this, shown in 1a and 1b below.



Example 1: Say you don’t have many value bets in your range, like when the flop is TT4 rainbow after you raised on the button. You have a ten around 17% of the time, and an overpair 20% given a preflop 50% range. Because your opponent is a very check raisey, you decide to bet all and only those hands at 40% pot, so 22% of your betting range should be bluffs by formula (find at runitonce.com, search GTO simplified: 40% sizing is not on table but can be calculated from it).

a) You can set up an equality: how much of my range do I want to bluff at this bet size? So theoretical value/bluff = real value/bluff and 78/22 = 37/x, and I would cbet 37+10.4, or ~47.4% of the time.

Another way that I like better is to use the A%, or alpha you mentioned, which is on the runitonce table.

b) Value range * A = % of total hands bluffing, which gives 0.37*0.28 = 0.01036 or 10.36%. We have the same answer, with a small rounding error.

As a result, I might choose to only bluff when I have QJ with a bdfd (~6% of a 50% range) because this blocks his combos of QQ and JJ. Also, I can bluff any other hand with 2 bdfd’s (5%). Ok- this is close enough to 10.4% of my range required to bluff as a 40% of pot bet.



Example 2: So, going back to Fernando setting up 25% pot bet with 50% of his range. Knowing this, we can determine the ratio of bluffs to value. Using the table mentioned earlier, bluff/value ratio is the same as the A in 1-A=MDF form: so here, 0.2 or 20%. This is because a 25% pot bet size corresponds to a 16.7/83.3 ratio found in the link to “GTO simplified”.

So its easy enough if you understand example 1: Let’s assume Fernando is not nitting it up and will play 50% of hands while on the button in the example. Given that he is betting 50% of those, knowing his bet size, what % of THE TOTAL PLO HANDS is he betting for value and bluffs ? Now we have to work from the ratio given, x/y=50%.

Long post but the problem is it looks like there are just heaps of game theory misconceptions in it.

- "MDF" is not a GTO concept. That is not how GTO works in actual poker. For example ...

... no.

- Hands in actual poker aren't neatly divided into "value bets" and "bluffs" pre-river, not even on ultra-dry boards.

- Even if they were, the ratio of "value bets" to "bluffs" wouldn't be determined the ratio required to make your opponent indifferent between calling a bet with a bluffcatcher unless calling would end the hand. After a flop c-bet there is still the turn and river to play.

- The way ranges are constructed there is just bad, given all of that.

- And more. Unfortunately it seems like almost every paragraph is wrong about something.

This info is counterproductive and actually applying it will lead to bad strategies. Would suggest ditching it for now and relearning from scratch.

Yes, you are right about MDF only applying to the river because of equity realization. I should have clarified that. I don't see how the majority of the post regarding bluff/bet ratio is incorrect. What other way do we have of making the opponent indifferent to calling without a supercomputer? How would you improve the ranges under consideration?

I see there is a big mistake here.
"As a result, I might choose to only bluff when I have QJ with a bdfd (~6% of a 50% range) because this blocks his combos of QQ and JJ. Also, I can bluff any other hand with 2 bdfd’s (5%). Ok- this is close enough to 10.4% of my range required to bluff as a 40% of pot bet."

I forgot to convert 6% QJ w bdfd to 12% of the range (.06/.50). Taking away the QJ's with overpair and tens which we would value bet, that alone would consist of about 10.4% of the range for bluffs. No need to find more bluffs at that bet size.

So if I'm understanding this correctly, on that TT4r board, the c-bet range you gave has about 3.7 times more "value hands" than bluffs? That is a preposterously strong range, and conversely the checking range is incredibly weak. Villain should exploitatively fold with anything that isn't pretty good itself against that c-bet, even against a 40%-pot bet. KKxx is the weakest hand that can even think of continuing. A random fish will have a c-bet range closer to GTO than that.

I looked at my post again and overthink this. NOW IM SURE The original post was correct with respect to the QJ w BDFD bluff because we are looking at a % of betting range, which is irrespective of the range you hold

you are understanding me correctly Rei, and you have a point with the strength of the ranges. I would only like to do this against a ABC opponent- the example was hypothetical.

I think you are missing the role that bet size plays in this. As I explained, the value-heavy bet range is inversely proportional to the bet size, AS NECESSITATED BY GTO.

Added a few more sentences to my post (everything after the first one).

I suppose a good plan on TT4 is to cbet QQ,JJ and all tens which is around 27% of the range. Then, multiply by appropriate alpha (MDF) value for bluff range, which for 40% size is 28% (.28*.27= .075), see example 1b above. This can be represented by bluffing QJ (10%) with bdfd (~72% on rainbow board), where .10*.72 ~=7.2% of range

The ratio you are using doesn't apply since there are future streets of betting possible. For a pot-size bet you wouldn't be "bluffing" with 13.5% of hands either. The whole approach is wrong, and the resulting ranges are bad.

I never said anything about a pot sized bet or 13.5% of hands. My understanding is that this ratio does apply, regardless of future streets, IF YOU ARE THE BETTOR. If this is wrong, would you please tell me what is right?

The psb/13.5 was an example to demonstrate that you don't use the same ratio you'd use on the river, which is what you are doing now with the 40% psb.

Look up Will Tipton's books on HUNL. Reading those should teach the right approach.

This one? Expert Heads Up No Limit Hold'em: Optimal And Exploitative Strategies (Poker Series) Volume 1

Im the guy from other forum, appreciate you delving deeper into this, perhaps im a lost cause but Im just as confused as before lol.

Can you give a direct game theory answer as to why we'd use a smaller betting frequency with a smaller sizing but a bigger frequency with a bigger sizing? Sorry for annoying questions but im not following lol

could you please tell me from where you were able to get these odds/ precentages?

To figure the odds of anything PLO in RANGES, you need to get pokerjuice for a month, or just odds oracle for 90$ lifetime license. Otherwise, it is combinatorics and /or some guesstimating to get most any data you want.

You must have the proper ratio of value bets to bluff, and your sizing depends on what? The board texture , right?

So , let's say I want to bet 1/2 pot on a paired board. Well, now lets say I choose the SAME % OF VALUE BETS AS WHEN I bet bigger. Because of the alpha principle, I will have less total cbets ON THIS BOARD because less bluffs are required as per game theory.

On the river vs a 100% pot bet we need to be continuing 50% of the time so that our opponent wont be betting with impunity vs us his whole range(hence he will not have an incentive to overbluff as by doing so he will be losing EV).
Being on the aggressors shoes deciding to bet full pot on the river we are offering our opponent direct odds 2:1 which will be identical with the ratio of value:bluffs we need to be using if we want to be bluffing with a balanced frequency (which means that our opponent will be indifferent between calling and folding to our bet, hence every time we will be betting we will be winning the pot).

For the above to hold true requires the simplification that the caller has a range consisting of only bluff catchers, and the aggressor has a range consisting of only bluffs and value hands.

On that premise we can continue the analysis for prior streets:
So for 100% pot size bet on the turn the value:bluff ratio becomes 1:1, and on the flop it becomes 2bluffs:1value.

But as we cant be simplifying on the flop ranges to only value hands , bluffs and bluffcatchers this analysis has little value for spots other than the river.

In my opinion though it can be used to approximate GTO solvers behaviour. Things like how many bluffing combos they are using in comparison to their more nutty hands, and how frequently they are continuing vs a particular bet size for a cbet etc.

Coming now on the Jnandez board K44r it would be best to provide the remaining info for the hand , SPR, position or maybe link the video , maybe it was something you misunderstood but generally we want to be cbetting such boards with a small sizing (1/3 pot or even lower) so that we will be able to bet our full range there. That way opponents are forced to continue kinda light which most of the time i guess they dont.

Not sure if this was really touched upon, but that's because there's a difference between polarity advantage vs general equity advantage, right?

I understand there are some spots like CO vs BTN on AK6r where the correct sizing is more than pot and low frequency, so we don't do that range advantage = bet everything small thing.

I don't really know how to resolve these two different approaches. Anyone help?