Hi, the book have interesting ideas for toy games but they are not solved. Are the solutions in the the book number 2 ?

I think the author he tries to make the problems simple by explaining into words but the problem is you can not make things more simple than it is.

Honestly I'm very angry I bought this book. It's like, complex toy games, but explained using words, as if to make it simpler. That might be a good thing for the people who should not have bought the book in the first place.

But for the people who bought the book with the idea to get into the toy games, you can not make things more simple than they are without losing the essence.

I would just like to see how the toy games are calculated so I can understand. I mean yeah I will ask questions in the forums, hire a coach if I have to. But if you will sell a book you should not be so lazy and solve your own math problems.

Hello Kingkong. This is Andrew Brokos, the author of the book. Thanks for checking it out, and I'm sorry you were disappointed. To be honest, though, I'm not sure which toy games you're referring to that I did not solve. Could you provide an example?

Also, if you'd like to DM me your Venmo or Paypal info, I will refund you the cost of the book.

@kingkong, is your complaint that he showed the computer's answer but didn't show the 10 pages of math needed to derive it? Do you think seeing those calculations would improve your poker game?

If you're interested in how a solver gets the answer, read Noam Brown's thesis. If you wanna improve at poker, it's more valuable to understand (in words) the conceptual reasons behind the solutions and the broader conclusions that can be extrapolated from them. The POP books are great imo, two of the best poker books written.

This is astonishingly generous especially as under consumer law the poster would have no remedy as extracts of he book were openly available and the poster would have had some idea of what he was buying.

Sir, you are a class act.

I actually like the book. One tip though for those who are going to buy the paperback - there is a normal print and a LARGE print. I didn't realize this and accidentally purchased the large print which is in a bit of inconvenience.. so ensure you pick the proper print you want instead of clicking too quickly and taking the default choice.

Hi,

In the chapter about complex ranges, there is no way to really know why the equilibrium is the way it is.

Like I said, it is explained using words, but I think this makes it more simple than what is required to understand clearly.

I meditated for a while on this toy game and I can see that when I use the equilibrium you give it is better than if instinctively I tried to solve it.

But still the answers to 'why Opal can bet a J' and 'why Ivan can bet a T', at the end of the day the real answer is because that's what is written in the equilibrium.

But if I look into the words to understand, for example why can Opal can bet a J, then I can see the EV of betting a J is easy because I understand why Ivan calls 2/3. But how can I compare it with Ivan's betting range I can not really know, because I have no way to understand how thin will Ivan bet.

I understand Ivan will bet a T because Opal checks enough strong hands to make it possible. But I don't understand why Opal checks so many strong hands and what happens if she don't.

But I tried to test the equilibrium that you give and I see that if Ivan plays at equilibrium, checking the strong hands for Opal has same EV as bet, but I guess if she checks it too much then Ivan won't bet T, or not even J if she checks it all, so then the EV of check would go down with strong hands, but a little up with T but proportionally less. But I stopped on that page for more than one week.

So with the same idea I still don't really know Opal overfolding vs a bet. I understand the theory why, that if IP has more value bets, and can have more bluffs, and 6 is a +EV check and it is used for bluff, so to make 6 indifferent Opal overfolds. But I don't understand how to find the exact frequency by myself but only by using the equilibrium that you give I can know.

I understand that Opal can bluff with a 5 or a 6 because a 6 never win at showdown, but I have no way of knowing by myself how many bluffs really she should have (or value bets...), I just take the equilibrium that you give.

I find this very annoying because of course I try to compare with the first toy game. I tought it's very interesting that Opal can check or bet the A vs K,Q as she wants and it doesn't change EV. Then at first I tought ''oh so interesting, so when OOP in river spot it's the same EV anyways....'' So of course when I see the toy game in complex ranges I'm thinking like... ''wait... what is the difference here... '' but I can not figure it out if I can't calculate it.

I really appreciate your offer to refund the book. But I don't think this is fair. I still got value from this book and it got me thinking and occupy my mind for a while, and it was not very expensive. But I found it frustrating to not be able to solve the toy game.

Thank you for replying to me

And today I keep reading the exploitative part of the same toy game, and it is still a bit more of the same thing. I stopped question myself because it's never ending. For example in the part 'What if Ivan call only if he has a Q' and I see that then a T is a bluff and can not check-call. I just think 'alright if you say so...'' because I'm not really sure I guess it gets checked down more often too. But I don't really know... Well I guess it would get checked down more often... but I'm not sure how often... but if you say it's true it must be true...

Thank you for elaborating, I see what you mean now. I can see how it's frustrating not to see the mathematical derivations of these solutions, but this is what it's like to work with a solver. There's a lot more about this in POP 2, but essentially, we have work backwards from the solution. The game of poker is much too complicated to calculate equilibrium solutions for early street play mathematically. We require computer assistance to find the solutions. Then we study the solutions to extract heuristics and principles that we can apply in real time in lieu of actually solving the game on the fly.

You're right that the more complicated toy games in the book are still tractable by hand. I think many more readers would be turned off by that than be interested it, but if you're really interested in seeing how they're solved, you can find derivations for the solutions to similar (and more complicated) games in The Mathematics of Poker.

Thanks again,
Andrew

What Andrew did with the "Play Optimal Poker" series is to simplify the complex works of authors like Bill Chen and Will Tipton, which is no small feat. In fact, having read and thoroughly enjoyed both volumes of Play Optimal Poker, they have clearly become the preeminent books for any player looking to learn the foundations of GTO.

My only criticisms are tiny:

Paperback volume 1, page 94:
Andrew threw that in to make sure the reader was paying attention, but it's wrong because Ivan's EV doesn't change. Given the answer to #3, one doesn't need math to deduce this: if it's (co)optimal for Opal to check her whole range, then of course being forced to check wouldn't decrease her EV.

Page 91 typo: "is now 1/2 instead of 1/3" (bolded should be 2/3)

Cheers

Andrew,
Great job with both books. I have pio and I replicated your ranges and bet sizes from Chapter one. My frequencies are close but not exactly matching. Can you repost the full pio tree inputs please?
Thanks,
Joe

Thanks, asif. The info on pages 11-13 (the ranges and bet size, etc parameters) should enable you to replicate the solver outputs. If you're getting slight variations in frequencies, that's just an artifact of the degree of exploitability to which you ran the sim. If you're getting a big deviation, like an output that pure checks a hand I'm showing as a pure bet, then something has gone wrong. But if it's just that the book shows 87.3% betting and you're getting 88.2%, that kind of variation is going to occur because the solver isn't running to total unexploitability.

Thank you for a quick reply. I have both books and they are excellent. Can you give some advice on best way to extract heuristics as you did extremely well when I run pio on different flops? Were some of your heuristics "educated guesses" since no definitive way to disassemble the pio solution?

It’s been a while since I’ve cracked POP1, but having worked through POP2 a couple times recently, there are far less “toy game” examples/principles. Andrew did a great job of taking reader feedback from POP1 and making POP2 more relevant to actual poker examples that are far easier to follow. Highly recommend OP to read POP2 instead.

Thanks, asif. I think you can look at the POP books, the second one especially, as a template for how to derive heuristics from solutions. To break down a little further, I have a workflow that looks like this:

1. Identify a situation I find a tricky or where I have low confidence about the equilibrium solution.

2. Make some predictions. These are akin to the questions from the book: how does equity and nut advantage break down, roughly how often do I expect a given player to check/bet/raise, which hands do I expect to be pure strategies, etc.

3. Identify surprises. Run the simulation and evaluate your predictions. Note where you are off. Look over the results for other things that surprise you or that you can't explain.

4. Find explanations. This is the hardest part, of course. It requires a good understanding of concepts from POP 1, in particular indifference and equilibrium. If you're surprised that a player checks at a high frequency, take a look at which hands are pure checks, as those are the ones driving the strategy. Take a look at how the solver expects the opponent to respond to a bet, how it expects them to play the turn after the flop checks through, etc.

5. Formulate a hypothesis. We're essentially back at Step 2. Your answers to (4) are new predictions you can test. Once you have a tentative heuristic like "do more checking when you have a large equity disadvantage", you can design experiments to test them. Run some other simulations and see whether your hypothesis holds true. Revise accordingly, rinse and repeat.

Hope that helps!

Andrew

Thank you for taking the time to give a detailed answer. Any plans for pop 3?

Hi Andrew,
Should the pot be 15 instead of 13 on Chapter 10 of pop2? The dead small and big blind added.
Thanks.

i meant 16 since 1/2 blinds

15 would be correct (the SB was accounted for but not the BB). Maybe this was a raked game? ;-)

I wanted to change as few variables as possible between the simulations for the sake of comparison. So even though 15 would be the more "realistic" pot size, I wanted to have the SPR be the same as in the example where the original raiser was IP. Of course I should have explained in the text that was what I was doing - sorry for the confusion!

No confusion. I assumed that was the case but asked just in case I missed something
Thanks again for being so receptive to questions. Will start second reading of pop 2.

Hi Andrew,

Is reading POP1 a prerequisite for reading POP2?

I am currently reading POP1. It is an excellent read and cheaply purchased on Kindle.

Albert Einstein said: if you can't explain it simply you don't know it well enough.

Well, the author knows it well enough as I am understanding it.

Al,

Thanks so much!

Josh,

Yes.

Hi Andrew,
If you have time to answer. If you have two identical ranges (about 30%) in a raised pot btn vs bb, gto will effectively calculate positional EV advantage. Is that true and can you derive any additional information from identical ranges?
Thank you.

Asif,

I think not really. There really is no "value of position". There is the value of holding a certain range in position against another range on a certain board at a certain stack depth. I think what you're trying to do is subtract out the variable of range advantage/disadvantage by keeping them the same, but the result you get is still going to be specific to those ranges. If you used a different range for both players, you'd get a different result.

Hi Foucault:

Let's do a statistical trick by looking at an extreme of the starting hand distributions. Suppose the range for both players is aces or kings, nothing else.

Now an ace flops and no king flops. If the first person has aces, he will know that since three aces are accounted for his opponent cannot have aces. But if the first person has kings, also notice that his opponent can still have kings even though his opponent is six times more likely to have aces. So even though both players now started with the same range, their range will not be the same anymore which I suspect should lead to a different strategy for both players.

(Also, just to be complete, notice that if a king flops and the first player has kings, then the second player's can't have kings.)

Please correct me if I have this wrong.

Best wishes,
Mason