I didn't see this before I made my post.

Is it clear why my entire range is fundamental to strategic play? I think it is...but I couldn't explain it well to someone else, which normally means I don't have all the pieces together very well.

Go on and set me straight! haha...I like it. My learning cap is on.

Hi Owen,

I think I see where you're coming from, and I think we're on the same page. I'm not sure what I said to make you think I was speaking poorly of exploitative play, but I didn't mean to. I'm certainly not suggesting that people try to play GTO without regard to exploitative considerations. In addition to being impossible, it would be pretty ridiculous. Of course the goal in poker is to make money, and "play exploitatively" pretty much just means "make as much money as possible" -- it's self evident.

But also, I don't think it's right to say that optimal and exploitative are two separate methods of poker analysis, although I know a lot of people make a distinction like that. GTO play also arises from a desire to make as much money as possible. Again, that's the point of the game, so if a theory of how to play poker wasn't based on the goal of making as much money as possible, at least on some level, it'd be a pretty crappy theory.

That's why I first introduced exploitative play in the book, and then when I started talking about unexploitable play, I made a big deal about how we can actually just think of it as arising directly out of exploitative play. I use examples to show that there's really no magic behind unexploitable play -- it just means that both players are playing maximally exploitatively at the same time. It's this intuition about GTO play that I carry throughout the book.

So later, when I look at specific situations, I often start out thinking about the unexploitable strategies. Basically, the idea is that this is what the play would look like if both players were really, really good. But that often doesn't take much space to describe, and the bulk of the discussion involves considering a bunch of ways one player could deviate from equilibrium play, and then how his opponent could first notice and then exploit that deviation, in order to make as much money as possible -- because that's what poker's all about.

So I'm not really sure what I said to make you think I disapprove of exploitative play. I think I do occasionally say something like, I make a certain play for "balance-related reasons," but I am always very self-conscious about that phrase. It is always meant to recall something like the discussion in Section 2.3.1 where I give specific examples of spots where not having certain hands in your distribution after taking a certain line will induce your opponent to play in such a way as to make it really profitable for you to start showing up there with those hands. Of course, if you know that your opponent has not made that first adjustment, then you shouldn't make the second.

So yea, you should definitely tell your students to try to play as profitably as possible, and you can be confident that game theory does not say that they should do otherwise.

Cheers

fmp

lol I didn't mean that to come off as snarky as it now sounds reading it back

Yea so I also don't think there's a conflict between trying to play as profitably as possible and the need to keep your whole strategy in mind when you play.

When I say strategic play or strategic decision making, I'm refering to a decision making model that explicity assumes that our results in our situation depend on the action of another (or more than one other) party who is also intelligent and goal-seeking and whose results depend in turn on our actions. It was the breakthrough of game theory in the 20th century to let us analyze and understand this sort of situation.

I think it's fair to say that poker (at least sometimes) fits into this mold. So, with this meaning of 'strategic play', it's pretty trivial to say that playing strategically requires you to think about your overall strategy, since your payoffs depend on your opponent's play, and your opponent's play will depend on your strategy.

Your point is well-taken that in some poker situations, statements like "the other party is intelligent" and "his strategy depends on our strategy" don't quite hold. I would argue that you should still practice thinking about your entire ranges in mind, for a few reasons:

- It'll help you identify spots where you're losing money and need to adjust. As an easy example, if you get to some spot with a mediocre-ish hand, face a bet, and decide it's best to fold, then that's that. But if you get to a spot with a range full of mediocre-ish hands, face a bet, and decide it's best to fold all your hands, then it's a really strong indication that you need to make some adjustments. Or at least become aware of the possibility that you're being exploited, so that if it happens a couple more times, you can realize that you need to adjust. And by the way, keep in mind that your opponents don't have to be smart for their strategies to be exploiting you. Sometimes guys' default strategies just happen to stack up well versus yours. It doesn't mean they're thinking, but you still need to be able to realize what's going on and then adjust to prevent it.

- You'll learn way more about the game. In the situation I just described, not only did you find a spot where you could adjust to make more money vs a particular opponent. You also learned something about a situation where people can be exploitable, and you can add it to your list of spots where you might be able to take advantage of other people in the future. Everyone these days thinks about his opponents' ranges, but if you get in the habit of thinking about both players' ranges and how they interact, you'll start seeing these sorts of opportunities constantly.

- It's an important skill that you'll need eventually if you want to move up into tough games, and it becomes much easier with practice, so it's best to go ahead and get in the habit as early as possible.

Interesting stuff. I've never thought of optimal play as exploitive play. Exploitive and optimal have always been two separate ideas in my mind - and I'm inclined to think that separation is the way most players are thinking about it...at least those I've been reading in forums. Looking back at MOP, I'm pretty sure I got that idea from that book, and perhaps that was just me reading it incorrectly. I've always thought about it this way.

Exploitive - my hands vs. his range and make most +EV decision

Optimal - my range vs. his range and make him indifferent

Seems this thinking may be off...

If I get checked to on the river, I'm analyzing a check or bet decision. If my opponent's strategy is static or predictably dynamic, I'm not seeing a reason I'd be concerned about my range as opposed to simply my opponent's response versus my specific holding. Everything I've worked on (as well as written...and writing) in the game is based on hand vs. range decision analysis. It's what I "learned on" as it were, and what was reinforced (at least in my mind) in MOP's section "Playing Accurately, Hand vs. Distribution". MOP's next section is "Adaptive Play, Distribution vs. Distribution", and seems to me an introduction to the optimal play section of the book.

Since I've always equated a separate category, exploitive play, with hand vs. distribution analysis, you can see why your statement on page 11 seemed to speak poorly of exploitive play. So I guess I need to understand things a bit more clearly. Are you saying MOP's section hand vs. distribution encourages and reinforces an incorrect way of thinking about the game? (Hope that question doesn't come across as trapping...sincere question. My books fall in the same category.) Your book is the first I've seen with almost all range vs. range analysis, so I think your statement is a pretty big one.

Also, your explanation of reference points for EV is the best I've seen. Lots of confusion over these methods, and I get caught in it all the time in the work I do away from the tables. I'm excited to see how the reference point you choose makes things simpler. Having said that, it seems your method may not have a simple relative method for comparing two choices...and that's always handy for quick work.

Thanks.

I keep making a post and then discovering you made a post while I was making mine!

I've got to head out for a bit, but I'll check out your last post when I get back.

Thanks.

Hi Al,

I do think the approach in the book could be very useful to non-HUNL-specialists, but I'm not sure I have too much to say about specific other games, so I'll try to just make some general comments.

First of all, I think it's really important for NLHE players who don't specialize in HU to spend a bit of time learning the game. I mean, people already know this, but if you're a normal NLHE MTT player, your biggest pay jump is in HU play where many MTT players have the least experience. If you're a cash player, its helpful to be able to start new tables or stick around and find an edge if a table starts to break. I've also heard a number of players say that they've only been able to take their shorthanded game to the next level after gaining their opponent-exploiting skills through headsup play. So, whether with this book or otherwise, I'd definitely recommend some HU study to all NLHE players.

Additionally, as far as other NL players go -- I think also a lot of the ideas I have about board texture, barrelling, bluff-catching dynamics, etc, will be easily adaptable to other NLHE games, even if the ranges are a bit different. Also, most of this volume focuses on river play. Plenty of hands are heads up on the river even if they didn't start out that way, so all the theory will be applicable there, even if the ranges are a bit different.

Now, it should be clear that this isn't just a book about how to play NL hands. Really, it's most notably a book about poker theory and how to break down and solve poker situations. Because of that, a decent amount of stuff is worked out in the abstract and will apply to all games. The big ideas behind GTO play, balance, etc are the same for all games.

I mean, people seem to get a lot out of The Theory of Poker even though the hand examples are drawn from all sorts of random games. And as far as theory goes, The Mathematics of Poker pretty much only covers heads-up situations, and they rarely try to give any practical examples at all! (I'm starting to think I should have just given my book a less specific title .) So anyway, I might be biased, but I think there's value here for any poker player.

Cheers

Small remark

About your raise/shove charts.
SB opening range
95s 7.7,9.1-
94s 6.5,10.8-
92s 3.7,14.2-

Imo you made a typo (had to be +) or a number is accidently not printed ...
Idem for your online charts.

Yes, those should be +'s

Thank you for this reply.

Been following the discussion with Qtip and I've gotta say this comment is just gold. Hadn't really intended buying the book but it looks as though I'm gonna now.

yaqh,

You say it is imperative to visual the equity distribution of our range vs our opponents range. Forgive me, but I dont see what relevance the equity of our entire range has vs our opponents. For example, we might be in a river spot where we have a ton of bluffs in our range, and those bluffs have 0% equity over any made hand otr, but it may still be profitable to have alot of bluffs in our river range vs some opponents (ie those who fold the river to 3 barrells alot). So, visualizing the average equity of our bluff heavy range is pretty irrelevant, as it can be close to zero most of the time, but it can still be an incredibly profitable spot vs certain villains, no?

Thanks.

Hi jimmyjesus,

I see you what you are saying, and of course you are right. If, as you describe,

1) we somehow know our opponent's strategy
2) we somehow know he's not changing his strategy (or else somehow know his updated strategy immediately when he does change it)
and 3) we have no desire to prepare to ever play in tougher games where (1) and (2) are not true

then we should just focus on playing maximally exploitatively. We can play every hand perfectly against our opponent's ranges without any thought how we might play other hands in similar spots. End of story. Don't let anyone tell you otherwise.

However, if we are somewhat less than magical or have somewhat more ambition, we will find value in strategic thinking. Tons and tons of value -- for reasons such as those I briefly mentioned above. And luckily, with a little practice, it's not even very hard.

Cheers

By the way, if anyone wants to see a player much better than myself talk about his own ranges and how he uses them in his decision making, watch pretty much any training video by Phil Galfond. He often talks about his own ranges more than he talks about his opponents'.

Thanks Will. That makes sense. I understand the value in thinking about our whole range in spots, just not why we need to consider our equity vs our opponents range in those spots. It seems to me as though thinking about the equity of our range relative to villains range is only really relevant when we are only going to call or fold and never raise/bet.

Hi yaqh, been out of poker for a long time.
However, your book really interests me, so I ordered it.
Hope to gain a lot from reading it.
Could you please show me where the extra section is located? Thanks.

Hi mazzi,

Not sure if I can post that here for self-promotion reasons, but I'll PM you.

Cheers

Don't know what this extra section is, but pm me as well please.

There's just a small bit of supplemental content on the book's website.

PM'd.

Cheers

Hey yaqh,

I love your book! Having written my thesis about combinatorial optimization and game theory topics, i always think in the terms of GTO play, so this book really fits my way of thinking.

I have a question to your equilibrium example on pages 48-52. In iteration 4 you say that if hero shoves with all 45 cards, villains best response is to call with the 98 combos you listed. This does not make sense:
a) Why should villain call with A3, but not with 44,55 or any of his weaker 6x?
b) Why should villain call with Q6s, but not with TT-77?

Ive tested the example with cardrunnersEV: if you let villain call with all hands better than Q6 (all of which are profitable calling hands due to crEV), heros bluffs become unprofitable, and we end up in the situation of iteration 1 again and never reach the equilibrium.

I'm glad to hear it

The bet is 48.5 BB into a pot of 53 BB, so the SB needs an equity of at least 48.5/(48.5+48.5+53) = 0.32333 to make the call. We can verify with PokerStove that Ac3c and Qd6d have this much equity versus the BB's shoving range:



while 55,TT, and 8s6s do not:



Card removal effects are often responsible for situations like this where hands with lower absolute value actually have more equity on the river versus an opponent's range.

Well, I'm not too familiar with CREV, but can you say more about exactly what you're doing? Keep in mind that, for this example, I fixed the ranges with which both players start the river play. So, the SB can't start calling the river shove with hands that he didn't get to the river with in the first place.

As I described above, I'm pretty sure that TT, etc. are not profitable calls when the BB is shoving his whole river starting range. If CREV says they are, you may have the stack/bet sizes or starting ranges different than me.

edit: To be clear, in most cases, the switching back and forth between maximally exploitative strategies won't find you the equilibrium. But in this case it should.

You're right, ive used slightly different ranges than you did. I wanted to save some work by grouping some of the listed hands together, for example i replaced {T4,T5,T7:spade :,T8} with T7s. I rechecked it with the exact ranges and got the same results as you.
I would not have expected this effect by minimal range changes though.

Ah, well the process converging nicely basically hinges on the SB folding enough to a jam that the BB strictly prefers jamming over checking and giving up, even with hands that never win when called. I showed that this is the case at the top of pg 53. I don't think it was too close, but it's possible that if you made the right substitutions, you could make some of his bluffs unprofitable due to card removal effects.

However, even if that's the case, I imagine the equilibrium strategies don't turn out to be too different, even if the algorithm's convergence properties are.

Hi will.

I think I may be missing the point of an important concept you talk about in the book.

Exactly why do you feel it is important to think about our own range at every point in the hand? What are the benefits of doing this? Apart from considering what villain perceives our range to be? (obviously this effects his ranges)

Cheers.

Just guessing here as I am not far into the book yet but....

You need to think of your own range because villains maximally exploitive play depends on it, and knowing what the best villain strat is means that you can better identify deviations which you can then exploit. Also, you can better identify the cases where you are (at least potentally) being exploited (eg "I never have air here so villain can safely fold his bluff catchers" or whatever).

Edit: also you need to know your range for things like determining optimal bluffing ratios and such. Again you should certainly be deviating from non exploitable strategy to punish villain leaks, but you definitely need to know what that ratio of bluffs should be to be non exploitable. This is really just an extrapolation of the above, but an important concrete example. Bluffing is a critical part of unexploitable play, and knowing the unexploitable ratio is pretty important.

Hi Jimmy,

Actually I don't think that I did talk about the idea much in the book. Almost all of the strategy discussion in the book is about how our entire strategy interacts with that of our opponent. And by "our strategy", I mean "our ranges". So, for example, I often talk about how we should split our ranges at each decision point to take advantage of an opponent's play, and then how those adjustments make us vulnerable to Villain's counter-adjustments, and what we might notice to indicate he's making those adjustments, and so on.

But I don't think you can even start to think about most of these things if you don't try to keep track of the ranges involved when you play, and thus the value of range-oriented thinking is mostly just taken for granted in the book. To be honest, I wouldn't have thought the idea would be particularly controversial -- I'm still pretty confident that most top players think about the game this way.

So, indirectly, almost all of the strategy discussion in the book is an argument for thinking in terms of ranges. As far as addressing the topic head-on, I think I've written about as much in this thread as anywhere else. Did you notice my conversation with QTip above? I think my thoughts on the topic are pretty well summarized in posts 93, 102, 103, and 113. Do they make sense?

Cheers