Over the last decade or so, Andrew Brokos has become well-known for his valuable poker content. He makes training videos, writes articles (many of which have appeared in this magazine), coaches, blogs, and, with Nate Meyvis, co-hosts the Thinking Poker Podcast. Last summer was an especially productive one for Brokos: he finished 125th in the 2019 WSOP Main Event and published Play Optimal Poker: Practical Game Theory for Every Poker Player. After finishing the book, Brokos and others couldn’t help wondering: is it possible to play optimaler? (and is “optimaler” even a word?)
In this email conversation, I asked Brokos about his much-anticipated sequel Play Optimal Poker 2: Range Construction. We discussed key takeaways from the book, using solvers as an educational tool, creative writing, pessimism, and America’s future.
Ben Saxton: Your first book nicely bridges the gap between theory and practice, introducing readers to a bunch of toy games that illustrate key poker concepts. Why did you decide to write a sequel?
Andrew Brokos: The new book covers equity realization, equity denial, and board coverage. Game theory is about incentives, and so often in poker we have competing incentives. We want to bet marginal hands to protect them, to deny equity to opponents who could draw out on us. But we also want to avoid inflating the pot in case we don’t have the best hand. And we don’t want to open ourselves up to a raise. Maybe we’d also benefit from giving opponents the opportunity to bluff.
Play Optimal Poker 2 is about how to sort all that out: how to recognize the different factors in favor of one play or another and how to weigh the advantages and disadvantages of two competing options.
The original Play Optimal Poker was, as you say, an introduction. It illustrated some key poker concepts, but there were others I chose not to cover. I wanted to limit its scope and make sure I thoroughly explained core concepts like equilibrium and polarized ranges. I didn’t want the book to be too intimidating for folks who are new to game theory.
In the first draft, I had some material that delved into more complex topics about early street play, but it soon became clear to me that to do them justice would require a different book. So I cut that material entirely. I didn’t want to cover them in a half-hearted way that would raise more questions than answers. That was when I decided to write a sequel.
Mason Malmuth gave Play Optimal Poker a glowing review in this magazine, which was of course very flattering. His only criticism, which was fair, was that the book didn’t say much about multi-street play.
I’m glad I wrote the sequel to close that gap. The fact that hands can change value, that we don’t know on the flop what the nuts will be on the river, is what makes poker so interesting and exciting and complex. That’s what Play Optimal Poker 2 is about.
At 339 pages, POP 2 is a lengthy book. What are one or two key takeaways that you’d like to share?
I want readers to learn to think in terms of ranges and range construction. I try hard to keep the focus on the big picture, to emphasize that even when we look at details, that’s only an example. The point is not to memorize which hands to check-raise at which frequency on a specific flop; it’s to understand WHY we have a check-raising range at all, why it’s the size it is, and why some hands are included in that range while others are not. You need to be able to take that information into other, less familiar situations, and use it to find the right play.
My goal is for readers to understand poker, to learn to think for themselves and find the best strategies for any situation. That could be tournaments or cash games, short stacked or deep stacked, in position or out—honestly, most of the theory isn’t even specific to hold ‘em, though those are the examples I use because it’s the game I know best. I want readers to see the beauty of poker, and get more comfortable in situations that currently make them squirm.
Given your interest in optimal play, it’s unsurprising that you rely heavily on solvers throughout the discussion. I’m wondering—and here I’m recalling a “debate” between Chris Kruk and Charlie Carrel—how solvers might function as an educational tool. Do you think that everyone, including complete beginners, would benefit from using solvers? Or should they be reserved for more advanced students?
I think everyone can benefit from solvers, but that doesn’t mean they should use them, in the sense of buying their own copy of the software and running their own simulations. Most people are going to learn “downstream” from solvers, meaning they are going to read a book like Play Optimal Poker or they’re going to watch training videos or in some other way learn concepts derived from working with a solver.
In 2020, you shouldn’t be taking strategy advice from anyone who isn’t game theory-aware. I want to be very clear that I’m not saying everyone should “play GTO” in the sense of trying to imitate what solvers are doing. My books emphasize how to use game theory and solvers to craft exploitative strategies. But the best exploitative players are still game theory-aware.
There’s no excuse for basing strategy advice solely on “feel.” “Feel” is just assumptions that you haven’t made explicit. Make them explicit, and then you can use node locking and other solver features to test them and find the best exploits. I guarantee you that, no matter how good a “feel player” you are, a solver will show you new things about how to exploit any assumption you make.
You’ve dabbled in creative writing (even penning some rom-com between Ivan and Opal, POP’s main characters). How does your approach to writing fiction compare to writing a strategy book about poker? Do you have plans for other creative projects moving forward?
“Plans” is a strong word. But I am doing a lot of writing, both fiction and non-. I’m not a very good fiction writer yet, so I don’t know when, if ever, I’ll do anything with that. But I enjoy working on it. And I think it makes me a better nonfiction writer.
The more interesting thing I’m seeing, really, is how much my approach does not differ between the two. When you’re writing for an audience, when you’re asking other people to invest time in reading your work, you have an obligation to them. In nonfiction, that’s obvious. If I’m writing a poker strategy book, I need to address material that will be useful to readers in a way that makes sense, is accessible, and, ideally, is entertaining, or at least not dry. People will forgive that last point if the material is good enough, but it’s always what I’m striving for.
Fiction is the same way, though. If you’re writing in a diary or journal that’s just for you, then of course you write whatever you want. You don’t have an obligation to anyone. But if you want people to read what you write, then you need to offer them something. That can be an engrossing story or a moving experience or beautiful language or a wild experiment, but you need to know what you’re offering. And just like with a poker book, you need to think about your audience and how best to deliver what you’re trying to deliver.
That’s how it seems to me right now, anyway. Like I said, I’m still not very good at it.
“Game theory,” you write, “teaches us to make decisions under conditions of uncertainty, and never in my lifetime has the world felt more uncertain. Never has it been more clear that my outcomes—payoffs, in the parlance of game theory—depend not only on my own actions but on the actions of others.” Have you discovered any valuable life lessons during this pandemic?
No.
These days it’s easy to dwell on questions about America’s future. On the spectrum of “meh, everything’s fine” to “ZOMG, we’re doomed,” where do you fall?
I’m pessimistic, but I’m skeptical about my pessimism.
The main thing I’m pessimistic about is climate change, which is not specific to America. Indeed, that’s the problem. In game-theoretical terms, the threat of climate change presents a huge collective action problem. No one person or company or country can single-handedly solve the problem. Reducing carbon emissions requires actors at each of these levels to pay costs for which the benefits are distributed. In other words, everyone benefits from me reducing my emissions, but I’m the one who pays the costs of reducing my emissions.
I don’t think there’s much precedent for large groups of people, and certainly not for the entire world, to take action in this way. And the way the US has handled the Covid pandemic certainly does not make me confident about our ability to solve this much larger collective action problem.
Game theory teaches us to think in terms of incentives. The situations that worry me the most are those where influential people, those with the most ability to directly influence things like carbon emissions, are insulated from the consequences. If these people know—or even perceive, rightly or wrongly—that issues like homelessness or mass unemployment or rising sea levels won’t directly affect them, then unfortunately their incentive might be to invest in insulating themselves from the problem rather than in solving it.
I also know that pessimism is easy and lazy, so I’m skeptical of it. If we adopt a “Why bother, we’re all screwed anyway?” mentality, then that’s a self-fulfilling prophecy. It becomes a justification for not making change for the better. It’s like the tournament player who takes a bad beat and then just goes all-in blind the next hand because he doesn’t want to play a short stack: in his head, he’s already decided he’s lost, so he doesn’t bother trying to make the most of what he has left.
Can we expect to see POP 3: Play Optimalest?
A workbook, maybe. Beyond that, if I were to write another poker book, and I very well may, I think it would be something different rather than a continuation of this project.
Is there anything else you’d like to mention?
I always enjoy reading your interviews in the magazine, and I’m flattered to be the subject of one!
