I am doing a coure based on Ed Miller's 1% book, and the book also just arrived today. So I haven't read much of the book, but I've read some of the introduction that the course went over, and reviewed the main ideas.

I am really struggling to understand why or how this strategy works, as presented. I have seen some folk suggest that this should be read as an 'ideas' book, rather than taking the figures seriously, but I'm not sure how to do that when examples are built around the 70% figure give in the book. (The 70% figure is what we mean whenever we see the word 'usually', in the context of the two rules (i) if your opponent bets or raises, you should usually call, (ii) if you bet one street and your opponent calls, you should usually bet the next street).

My first main lack of understanding is, where the 70% number comes from (even if we think of it as a ballpark figure). He gives an example in the book saying we should continue 72% of the time on an A85 rainbow board when we're in position facing a pot size bet. This isn't the MDF, so is he getting this number by incorporating some ideas about our/villain's range?

My other question is that on page 39, the author makes the point that you never have to 'break the rules' as it were. He also says under this heading:

"Say you somehow were granted knowledge of the perfect mathematical solution to no-limit hold'em.... It's unbeatable (over the long term) no matter what your opponents try to throw at it"

This is really leaving me perplexed and struggling to understand his point. That quote strikes me as implying the solutions in the book are GTO, which they are definitely not. My understanding is that this book tries to make us a bit less exploitable by denying the opponent from auto-profiting and realising equity as easily. Is my understanding of the main ideas of the book correct?

I am really failing to see from a strategy perspective, how this is unbeatable (read: unexploitable). In fact, if you never broke the rules, you would get crushed by anyone paying attention to your calling frequency of 70%, for example.

Ultimately I am looking for some guidance on how to interpret this book, and it's ideas. My current thinking is that the main idea is to deny auto-profit, and to play a strategy based on frequencies that give our game less obvious holes that opponents can exploit. I definitely see the value to this. However, IF this is correct, why not stick to the MDF? Why pump the number up to 70%? (I get that neither the MDF nor the 70% figure is optimal from a GTO perspective, but I can see its value in reducing the most obviously exploitative spots).

Sorry for the very long post, I am not great at poker and am really trying to get a firm understanding of the game. The book by Miller seems very valuable, but I am struggling to get a coherent theoretical understanding of the game.

I strongly agree with the part I've bolded.
Miller's book (which I found very easy/fun to read) was largely based on ideas in Matt Janda's training videos from 5 or 6 years ago. Janda used math and elements of game theory to help inform his "best guess" of what optimal poker looked like, but the advent of solvers showed that he wasn't correct on the numbers/frequencies.
The basic concept that you should often be betting or calling - rather than giving up on pots - is basically right, but the 70% number was rather arbitrary, and isn't correct (on average) for either a betting or calling frequency. Every pot you play has its own nuances. Sometimes you should bet very often (even 100% of your range), sometimes you can profitably float with way over 50% of your range, and sometimes you have to "overfold" (more than a MDF calculation would suggest).
Some readers might find the book encourages them to be more aggressive than they were previously (passivity doesn't make much money), and others might realise they are folding too often, but I would not recommend trying to follow Miller's advice literally, especially in low-stakes live games. His other books are more useful for real-world play.

P.S. Matt Berkey posted a twitter thread a couple of days ago about one page of the book that he took issue with. Judging from the replies, and the poll result in the thread, some people don't get it at all.

I have read only parts of the book because I prefer Janda’s non-dumbed down writing style.

Back when Janda’s first book was published, a lot of the concepts weren’t common knowledge even for mid-stakes players. Today, that’s stuff people learn very early on.

Janda/Miller basically answered a question that lots of break even regulars always asked: “Why do I lose to calling stations?” Today we know that those regulars massively over folded and that optimal calling frequencies are somewhere in the middle in a lot of spots.

Not too different from regulars finding out that the one-size-fits-all approach of betting isn’t the right way to do it. And that some “fish” had it (accidentally) right with their small bets (back then called ‘gay bets’) and overbets.

Ahh, yes thank you, this is basically what I was thinking was going on, but I was unsure because I don't think the nuances have been explained in the course to a great degree (probably justifiably so), and I haven't yet seen it addressed in the book either.

Ultimately my takeaway from the idea was that none of this is optimal (at least in the mathematical sense), it just reduces the obvious exploits that good opponent's would easily notice. I suppose this is why the quote from page 39 really perplexed me, because it felt like it was misconstruing two similar but disparate concepts.

As a side note, do you recommend Janda's book on the application of no limit hold'em? I've read some of it and I quite enjoy it, it doesn't seem bad at all. I guess I'm wondering whether it's still relevant in the day of solvers? (My guess is yes, since I don't think the guiding mathematics ever goes out of style)

I'm also not quite sure I followed the polling on twitter, is the point that bluffs on the flop don't make much sense?

Yes I've been enjoying Janda's Application more; it feels a little bit more rigorous, which just means I feel less lost with a million questions.

Also that makes sense, and I can see why the general idea of the concept is actually very valuable!

Lol, I didn't know about the gay bets, interesting bit of trivia!

When it came out I thought it was the best poker theory book ever, but it's not without fault. Not all the math in it is correct and Janda himself regrets much of the pre-flop section (the ranges and sizes weren't particularly close to what the best players in the world were using). Miller's book was, to some extent, a dumbed-down, but more readable, version of the same theories.
I think Janda's second book, which was informed by work with Snowie and solvers, is much more useful than the first one.
The terms "value-bet" and "bluff" don't make much sense until the river (both players have various hands with high, medium, or low realizable equity), and even on the river the optimal betting frequency requires a consideration of how villain reacts, since his range isn't comprised solely of bluffcatchers.
As I put it in reply to someone who thought Miller's advice about balance was a "golden rule"....

Janda's second book explains it better than I can.

Ah OK thank you, I think I will finish applications and then maybe fill myself in on some of the newer developments then. And OK, that makes sense with regards to the bluffing. I am curious however, when you say

what exactly do you mean by optimal? Do you mean in the sense of playing the most profitable line?

Optimal in a game theory max-EV sense. That is to say, if villain was aware of your strategy and played in such a way to maximize his own EV against it (calling and folding with the right hands at the right frequencies) then the optimal strategy is the one that gains the most EV against him.

In real life, you're not playing against optimal/GTO bots, so you can maximize your EV by exploiting the imbalances in your opponent's strategy. e.g. Vs someone that folds too much, you should bluff more often, and vs someone that calls too much, you should reduce your bluffing frequency. When you play "optimally", villain can't exploit you (by over-calling or over-folding), because your range is balanced correctly and is therefore "optimal". To put it another way, if you take the optimal line, based on knowing villain's strategy, it doesn't matter whether he calls or folds. In the long run, you just win, because you have just the right amount of value hands that get paid, but you also have the "perfect" number of bluffs that work.
Poker would be very simple if you knew villain's range only contained bluff-catchers, as you could just pot the river with a ratio of 2 value combos for each 1 bluff, and your total EV would be "pot", whether villain calls 0% of the time, 50% of the time, or 100% of the time. But villain's range doesn't usually contain bluff-catchers and nothing else (he sometimes has some nutted hands), so it's very hard to decide which hands are pure fat value-bets, or thin value bets, or bluffs. That's why you can't just arbitrarily bet 70% of your range and print money. You have to know what your opponent's range looks like.

[I think I'm getting very off track from the original question; not sure if that's allowed so stop me if it's not, but it's a very interesting conversation!]

This is a very interesting point, one that I've seen a few times, and one that I'm not sure I follow. Specifically I'm referring to how we reference GTO play, AND villain's range. From a mathematical standpoint, if we knew a GTO strategy, then it wouldn't matter what strategy villain played. I.e.

Is this accurate? I'm not sure that from a theoretical standpoint it would matter. I have seen this issue raised a few times, but I've never followed it. To my knowledge, if we play GTO, then any non-dominated strategy (compared to GTO) that villain could use (if it exists), would be 0EV, and any dominated strategy would turn us a profit, I.e. the particular implementation of villain's strategy is irrelevant to anyone playing the solved game.

So I'm curious if when I have seen this mentioned before there is some underlying mechanism in the game that makes knowing the range of the villain important? For example, is it just that since we are not playing a true GTO strategy, range reads just inherently become more important?

If you play the GTO strategy over multiple streets, you cannot lose in the long run no matter what your opponent does. If the villain isn't also playing GTO, he must be making mistakes somewhere along the line, donating some of his EV to you.

But the GTO strategy can only be computed by simulating/calculating the best possible play of two rational players. You might bet the river in a 2:1 ratio of value:bluff precisely because the best that villain can do is call 50% of the time with his bluffcatchers. If he calls more often, your bluffs lose money, but your value-bets get paid more often, thus keeping your EV the same no matter what he does. If he folds too much, your value hands don't get paid so often, but your bluffs get through, so you still win the size of the pot on average.

If you know your opponent is unbalanced/sub-optimal/exploitable, you can alter your strategy (i.e. deviate away from the GTO strat) to make the most of his mistakes in order to maximize your EV.
If your opponent was an idiot that folded every hand on the river, including the nuts, you'd obviously make even more money by betting 100% of your range, than by following whatever the GTO solution would be.

Hence EV maximization occurs when you know exactly how your opponent plays. And the GTO strategy arises when your opponent plays the best strategy. To maximize your EV against a perfect/optimal opponent, you have to play perfectly yourself.
If you don't know your opponent's strategy, you'll still win if you play optimally/perfectly, because GTO at least breaks even (but usually wins) against every possible strat. It's just that you can't maximally exploit his mistakes if you don't know them.

In real life, the top players use strategies informed by GTO solvers, but they still deviate from them in order to exploit players that they know/believe have leaks/imbalances in their game.

Thanks for the reply, this was a great and succinct post!

I am wondering if this is strictly true:

Technically any non-dominated strategy could be played and they would all be zero EV? I suppose this is purely theoretical, I doubt this has any practical application to any poker player at the moment...

0EV would mean they are breaking even, when if you play a perfectly GTO villain you would be -EV no matter if you underbluffed/overbluffed, undercall/overcall, etc.

Balanced play works vs any opponent because if they are deviating in any way, they are getting wrecked by the other side of the coin your range is on. For example, if a GTO villain's opponents are underfolding, then a GTO villain will make money off of value, and if they are overfolding, the GTO villain will make money off of bluffs. It's a sort of pick your own poison type of thing.

I will never stop loving this fact lol, and I also love how it maybe wasn't even that accidental, but fishes somehow realized that small bets with a wide range
were actually a good way to set up a polarized river overbet while we all thought that it was a fishy move; sure, sometimes they would do it in wrong situations but the point still stands.

This makes intuitive sense, but I am wondering if this is truly known/proven, in the mathematical sense. There are simpler toy games where the nash equilibrium does no turn a profit vs some non-gto strategies; I'm not sure whether such strategies exist in hunlhe, but if they did then any such strategy would break even vs a gto strat.

Yes, it's proven. The Nash Equilibrium arises because "GTO play" maximizes EV against an adversary also trying to maximize their EV by definition.
https://en.wikipedia.org/wiki/Nash_equilibrium

Poker is essentially a zero-sum game. (Rake is a complicating factor, but if one player is making a profit, the other is making a loss of equivalent magnitude.)

I'm not aware of any zero-sum games between two players where following the Nash equilibrium loses. If the strategy was beatable, it's clearly not optimal, so it can't be at equilibrium.

Sorry, what I meant when I said is there a proof, I meant proof of whether any non-gto strategy necessarily has a negative expectation (vs a gto strat), not whether a nash equilibrium exists in hunl.

I also didn't mean the nash-equilibrium loses; I mean that it is just not necessarily positive expectation. In RPS, and you can choose any non-dominated strategy (i.e. any strategy) vs the gto strategy with equal expectation (0)

If we play a zero sum game, we know that every strategy is at best 0EV against a GTO strat because the latter one wasn’t GTO if it would be-EV in said game.

So if we have one strategy that we know is GTO and 0EV and another strategy that is also 0EV, it’s hard to argue the latter one isn’t a GTO strategy too.

Besides that, I’m not sure if it’s worth discussing something that’s mostly hairsplitting.

I don't think it would be; for example in RPS if you threw rock 100% of the time thats a breakeven strategy vs the gto strat, but it is itself definitely not GTO.

Yeah haha. I have always wondered though whether it has been proven that any non-gto strat in poker is always minus EV vs a gto strat. But I agree because it certainly doesn't affect me, it's just a curiosity!

Yes, there are non-gto strats that are breakeven vs the gto strat in nlhe. You can play pure frequency with any mixed frequency hand and you'll have the same ev vs a villain playing gto -- for example, as the river bluffcatcher, you can purefold or purecall all your indifferent hands and you'll break even vs villain executing a gto strat. In that sense, you aren't losing additional ev by choosing any option with a wide variety of hands. This seems pretty straightforward.

However, just like in RPS playing a non-gto strategy in a spot, though it may breakeven vs a gto bot, opens yourself up to exploitative adjustments by villain that will gain them a bunch of ev. On the other hand, there's nothing you can do to increase your ev vs villain.