Ed Miller's Secret of the 1% question

tfazio

Im confused about the concept in ED's book regarding betting and calling frequencies.
It would seem to me the size of the bet would have an effect on ones calling frequencies
as well as betting. Are we calling with the same frequency facing a half pot bet vs a full pot bet.
Are we betting the same frequencies with different bet sizes. After having read the book and seen it explained
many times I think I'm forgetting something simple. I understand MDF and MBF and how it is connected to
bet and pot size. I understand the ratios on the different streets. I must be missing something regarding the 70%
percent and how it relates to bet size.

The Mule

I haven't read the book, but have studied maths and game theory in depth so will put in my 2c worth.

Pot odds require that calling frequencies must depend on bet size. You wouldn't fold a hand with 25% equity to a minraise but you'd probably fold to a big all in.

I assume that the 70% is based on a standard bet size, probably around 2/3 to 3/4 pot. Interested to hear if anyone has any deeper insight.

Betting frequency is more complicated as there are two degrees of freedom (bet size and betting frequency). I assume this is also based on a standard bet size. Again the maths requires different optimal frequencies depending on bet size.

Lafonseca

Did anyone evet get to the bottom of this?

I'm really not following where the 72% rounded to 70 is coming from. I'm sure i'm missing something obvious.

If there's anyone that could give a brief run-through of the math that helped him arrive at that figure it'd be helpful. (Surely even a PSB would only require a min defence of 50%?)

sneakyfrog

the min defense is 50% as I think he points out in the book. I never understood how he gets 72%, maybe including a few extra combos on top of the 67% calling frequency necessary facing a pot size bet getting 2:1? I always assumed it was to maximize your range's equity in relation to pot odds.
When using his formula for range construction, I always scale the frequencies in relation to the bet size and the number of people in the pot. for example, I'll call with 80% if facing a half pot bet heads up, but only 50% in a three way pot v. a pot size bet. I'm imagining the frequencies would scale like this but I've never had the chance to really dive deep into this. I wonder if Matthew Janda's book (Applications of holdem) would provide additional insight. I hear it's a pretty heavy read though.
Also for what it's worth, I find the strategies in 1% to be ridiculously inefficient for online micros. I tried it for a month and lost close to 20 buyins. Probably because my opponents are breaking the rules and I'm choosing not to break them appropriately (ie calling turn and river bets when they are never being worse than TPTK).

tfazio

It is important to remember that Miller is not talking about pot odds rather defense frequencies. A pot sized bet on the river 1:1 need only work 50% to BE 1/1+1
(Bet/Bet + Pot) and your pot odds of calling are 33% 2:1, but the MDF according
to (1-a)% alpha being BE, is 50% if you fold more than 50% he is printing money. He goes on to say most river bets are 1/2 pot so the BE is 33% and the MDF would be 66% if hero is folding more than 66% cha ching. This idea was explained a great length
in Mathematics of Poker. Miller goes on to explain how this 70% baseline is moved by the occurance of favorable and unfavorable events.

persuadeo

Poker's 1% is in many ways a very strange book. It is crucial to understand that the 70% figure is nearly meaningless in game, but is the framework for a strategy that fights auto-profit as its baseline. Key, the 70% figure is governed by "Events," which is an obtuse shortcut, covered by only a smattering of pages, to hand reading, but one which allows the author to focus on the theory and not the exceptions. It's a clever rhetorical devise as written but confuses some readers, and so whenever you read about someone saying you are supposed to just bet or defend 70% of your remaining range you can assume they have not read the book carefully, if at all.

This aspect of the book is a specific example of Ed's claim, one he used to defend against the "book burning" crowd, that you get out of books what you put into understanding them.

In other words, your frequencies will deviate massively if you follow this book carefully, to the point where the governing idea is only a principle and never a prescription. There used to be a poster and blogger, @Rello242, who employed this abstracted style in heads up sitngos - a more easy fit, as in those structures being unexploitable is far more important than in ring games. I'd think that Colldav's long thread on this subject and asking Rello, if he is still even playing, questions would be a great way to come to a better understanding.

Christian Soto

hmm

persuadeo

wait where did the ho go?

sneakyfrog

I agree the book outlines a theoretical framework for working towards GTO strategy (though it isn't), but once you swing the frequencies too far away from the 70% range vs. pot size bet, I think you would start moving into the exploitative style of play (which will usually be correct).

persuadeo

Fair enough. However, you can't agree with something I didn't say. 1% does not work toward a GTO strategy. Instead, it uses the principle of anti-autoprofit (admittedly often mistaken for GTO and/or Nash Equilibriums) toward establishing a strategy based on frequencies of actions.

I agree that you are moving in an exploitative direction once you take the Events aspect of the book, and thus the entire work, seriously. However, does this matter? If you play the 1% strategy without this key aspect of Mr. Miller's work, you end up playing, in the words of one cruel online grinder about another, "like a badly programmed bot."

tfazio

I think the difficulty in understanding the math is the grey area between auto profit and pot odds. From a direct pot odds perspective you are not getting odds to call but you fall victim to auto profit. I think millers point is to be able to navigate that grey area based upon positive and negative factors that occur.

persuadeo

What you've said is simultaneously very important, Tfazio, because it bridges many gaps - while also being the opposite of Miller's point. When a player does in fact incorporate pot odds and equities and sizings etc, he begins to approach where GTO and its solvers take poker, as he is looking for maximal equity lines against a potentially equivalent strategy. In doing this, only then does the actor move toward being theoretically unexploitable. Miller, on the other hand, takes a consequence of an equilibrium strategy and starts with its result - autoprofit unexploitablility. In this sense, then, 1% is the opposite of GTO.

sneakyfrog

@persuadeo you addressed a misinterpretation I had about the work and I thank you for that. the discussion on this post was exactly what I've been looking for so thanks @tfazio for posting. I've always been confused about the "gray area" between min defense and pot odds and trying to marry the two ideas. this post has definitely given me some food for thought moving forward.

Yosh

I haven't read this particular book, but have read several posts so I think I understand what Ed Miller has proposed in theory.

I have written and deleted several lengthy posts describing my ideas on this subject. They all seem to fall short in turning grey into black and white.

I will say that it might be helpful to draw a line in your mind and consider pot odds and defense frequencies as very distinct quantities. It seems that some are confusing these two measurements. Pot odds dictate the required equity that a specific holding needs to make a call, which is not the same as a calling frequency.