Thankyou for your great reponse, yaqh.

Thankyou for your great response, yaqh.

The river chapter is absolutely fantastic.

I am trying to understand more clearly what sort of hand distributions are likely to make block betting beneficial for the BB.

1) How about in the case where either player can have the nuts but BB's range has a much greater percentage of strongish made hands (hands that want to provoke a bluff raise) and a lower percentage of air hands (which can bluff small)?

In the same case it therefore true that if BB has relatively little air in his range then block betting is a good idea because he can balance by bluffing small with all his bluffs and block betting small with a block-bet/call value range?

2) How about a different situation. Assume either player can equally have the nuts but BB's range is a bit more polarised than SB, so BB has more near nut hands and air while SB has more bluff catchers.

Assume too there is just over a pot size bet left on the river, is block betting or betting small likely to be a good idea in this case (I guess not?). What sort of bet sizing is likely to be beneficial at equilibrium?

Thanks again, these river solutions are really thought provoking!

I realise you must be a busy man, just another question.

So, after reviewing a river spot I was in, I came up with this.

Villain shoves for 1938 chips on the river, into pot of 1234 (I cover). So basically I gota call 1938 to win 6k.

call/lose stack= 890

call/win stack= 6000

fold stack= 2828

Presuming we know we have 48.6% equity against villains range

(6000x0.486) + (890x0.514)=3373

3373>2823 so we call.

I started the hand with 3415 chips. Does this imply that playing the hand this way (ultimately getting into this spot otr) has less EV than folding pre flop?

I realise you must be a busy man, just another question.

So, after reviewing a river spot I was in, I came up with this.

Villain shoves for 1938 chips on the river, into pot of 1234 (I cover). So basically I gota call 1938 to win 6k.

call/lose stack= 890

call/win stack= 6000

fold stack= 2828

Presuming we know we have 48.6% equity against villains range

(6000x0.486) + (890x0.514)=3373

3373>2823 so we call.

I started the hand with 3415 chips. Does this imply that playing the hand this way (ultimately getting into this spot otr) has less EV than folding pre flop?

I have a very simple question. I apologize in advance if it's gonna sound stupid, I am still a poker dwib. So here goes.

On page 32 there is a simplified example of EV calculation. Villain and hero sit behind 100bb deep each at the beginning, there is already 40BBs in the pot, each invested 20 BB, so they both have 80bb behind, villain now ships his 80BB in the pot, making it 120BB, hero has AcQc facing a decision to call or not to call. Hero esimates that villains range consist only of 76s and AA. So there are 7 combos of hands, 3 combos of AA and 4 combos of 76. So we combined the equities of those hands which totals to 40,49 % equity against his range. Then we calculate the EV of a call, so we multiply the total pot when the call is made , which is 200BB with 0,4049, to get 80,98 BB. So on the long run we win 80,98 BB if we make this call, which is a little more thant the amount of BB's we have to invest when we call ( 80 BB). I understand all of this, but here are my two questions: (sorry didn't say there were going to be two)

1. How do we estimate that willan holds 76s or AA exactly half the time each ?

2. Arent the pot odds to make this call 66 % ? There is 120 bb in the pot , we have to call 80 bb to win 120bb, making it a 66% pot...ohh..never mind, just realized that my math was incorrect here, pot odds are 40 % exactly, since we call 80 bb to win 200bb. So I had to write a question to answer to it myself...I hope I am thinking correct here. If not, someone correct me please.

I'm a noob, but I'm going to try to poke into this one. I don't get where you get a 6k figure.

The pot is 1234, villain goes allin for another 1938, making the pot 3172, you have to invest another 1938 to call.

So Ev of a call is: If you call, the pot is 5110. Then you multiply this number with your estimated equity 0,486, you get 2483.46.

So this is a +EV call since 2483.46 > 1983

You win on the long run, because you are making 500.46 chips every time you make this call.

Maybe im wrong here, but in the book yaqh recommends calculating ev using what our stack will be at the end of each outcome. So we know what our stack will be if we fold, and if we call and win we have all the chips in play so our stack is 6000. If we call and lose our stack is 890 chips.

I'm not that far in the book yet, I've read and worked through first 40 pages. But I think you should be looking at effective stack size here, which is the smaller stack at the table.

Yea your right actually, thanks!

Ah blockbetting, yea it's tricky. I discussed this a bit in the context of the SB bet-or-check game, but basically whenever you use multiple bet sizings in a spot, solutions pretty much never break down into clearly-defined action regions. There ends up being a lot of mixed strategies and balance going on that can make it difficult to see quite what's happening.

This is one of the reasons I suggested that players turn to the example solutions to see when blocking might be reasonable/unexploitable, but to otherwise focus on using the move exploitatively. The other reason is that I've found that different players' response to block bets vary extremely widely, and they're very often quite bad (probably for a lack of having faced many good blockbettors) so again an exploitative approach makes the most sense.

But as far as distributions where its show up at the equilibrium -- let's think about why blockingbets work and what conditions that implies for the distributions. Let's assume the 1 full bet left behind case, so any bet on the river is all in except for the BB's blockbets.

So first of all, facing a block, the SB has to not-fold a ton, or else the BB can print money with his bluffs. (So, here's condition #1 -- BB needs bluffs (of course, these don't have to be pure air)). Second of all, the SB can't raise a blockbet as much as he can bet all in when checked to. Why not? Well, if he did, then the BB's nut and strong value hands would all start blockbetting, since they would get all in just as often as if they checked, but they would also get extra value from all those hands the SB has to call with. But, BB playing all his nut hands with a blockingbet would certainly incentivize SB to not be jamming so much at all. (So, condition #2 is that the BB needs some strong value hands he can sometimes blockbet with. (no sort of betting is going to work well for him if his range is capped low.)) So now we know that, when facing a blockbet, the SB is calling a ton and jamming, perhaps pretty often, but not as often as if he faced a check. This is a perfect environment for the BB's weak value hands! They can block out, also get a bit of value from the SB's wide calling range, and not get jammed on as often as if they had checked. And not getting jammed on is great because it's generally going to make them indifferent between a call and a fold, i.e. it makes it really hard for them to realize their value. And of course the BB does need his blocking range to be comprised primarily of these hands, because if the BB just mostly blocked with the nuts and air we mentioned earlier, the SB isn't going to be raising much at all, and BB will just lose value with his nuts. (So, condition #3 is that the BB's range contains a lot of these weak value hands).

Hope that helps, sorry for the wall of text .

Yes, calling beats folding by 3373 - 2823 = 550.

At the point when you're facing the all-in, you do expect to end up with less than you started the hand. This doesn't necessarily mean that you made an incorrect decision at any point in the hand. It could just be that you got a bit unlucky either in the cards that came out or in Villain showing up with the top of his range.

Looks like you guys are both right here, except for the bolded which appears to just be a transcription error:

2483 - 1938 = 550.

In general, I agree it's easier to work with effective stacks. Carrying along the extra chips when you cover here essentially just amounts to adding the extra 890 to all of Hero's EVs. Of course, this cancels out when you take the difference in EV between two options which is what you need to do to make a decision, so both ways are correct. I show both ways in jimmyjesus's EV calc thread in Poker Theory this morning:

http://forumserver.twoplustwo.com/15...g-pre-1297849/

Ah, well we assumed that Villain plays this way if and only if he holds AA or 76s, but that was definitely just for the sake of giving a simple example. In general, a preflop 5-bet shoving range will have a variety of different hands in it. (Also, as you mentioned above, we don't assume that Villain holds 76s and AA half the time each -- we assume he has AA 3/7 of the time and 76s 4/7 of the time.)

Right, you need 40% equity to make the call here since 80/200 = 0.40. Notice that you'll never need 66% equity to make a call. The most you can ever need is 50% -- if you win the pot half the time at showdown, you can call any size bet. So, if you ever do a calculation and find that you need >50% equity to call all-in, you know you've made a mistake.

Yaqh, on page 135 u talk about hand distribution charts. This might sound really dumb, but could you explain exactly what you mean by 'fractions' on the vertical axis of the charts? I just cant seem to grasp it

Thanks.

Oh sure, so the idea there is that hands can be fractionally in a range when a player plays a mixed strategy (that is, when he takes more than one action with a hand sometimes).

For example, suppose that when you are facing a 3-bet with AA preflop, you flat-call half the time and 4-bet half the time. Then we'd say your range for flat-calling includes only 50% of AA. And if we wanted to visualize your flatting range with a hand distribution chart, the fact that that hand is only 50% in the range would be indicated by plotting it halfway up the vertical axis.

Yes very helpful, thanks! Can't wait for your follow up book!

Congrats on the book, Will. It came in the mail today. I cracked it open and said, "Oh...now this looks interesting." Looks like some rich material. It's been a while since I've been excited to get into a poker book. Putting together something like this is a real achievement.

I'm only in the Game-theoretic strategies section, but I've enjoyed your writing style so far.

My thoughts on GTO have always been quite muddy. Most of the stuff I've read and heard sounds off to me (or just ridiculously impractical), but I'm not in an informed position to really reject anything.

I do have a question for you. On page 11, you talk about how you rarely use single hand examples or discussions. You say doing so encourages and reinforces an incorrect approach to thinking about the game. "Correct poker strategy involves keeping in mind all the hands with which you take any of your possible actions."

That didn't sit well with me. Perhaps I've something to learn or perhaps I'm taking it out of its context. To my understanding, using the idea of correct and incorrect there isn't accurate. If we're talking about balance (which you say is the main thrust of your book), then I can agree with that statement.

However, sitting in a game like a $1/$2 NLHE live game at a typical casino, I'd say your statement is inaccurate. If my opponent isn't adjusting to my strategy or I'm a step ahead of his adjustments, why should I keep in mind anything outside of my specific holding?

I understand I'm talking about exploitive play here. It's just your statement sounded like a blanket statement rather than an attribute of GTO play, so I wanted to make sure I'm not in the dark on some larger concept.

Thanks for your book and your participation in the forums.

Thanks Owen,

Yea, maybe "correct" wasn't the best word choice there, at least without more context. But consider this -- the defining characteristic of strategic situations is that your pay-offs depend not only on your own actions but also on the actions of other people. This is in contrast to many other decision-making situations where your results depend just on your own choices and maybe some unknowns/randomness but not on the decisions of other thinking, self-interested people. The break-through of game theory as a field was in effectively modeling the interactions of intelligent decision makers, and it allowed people to understand and plan for these situations much better than previous decision theory.

What does this mean in the context of poker? Since your results depend on your opponent's strategy, and your opponent's strategy depends on his payoffs, then you have to think about his pay-offs in order to make decisions. And since Villain's pay-offs depend on your ranges, you have to keep those in mind. So this is a pretty fundamental thing when it comes to strategic play.

I agree that we can sometimes be successful by modeling poker as a traditional decision problem by just thinking of an opponent's frequencies/play as sort of unintelligent randomness. And perhaps that's a reasonable approach if his strategy is either fixed or changing slowly enough that you can always be on top of it, but I think the right way to play games is in the paradigm of game theory. In practice, I think that you put yourself in a much better position to make smart adjustments versus bad players and also develop the skills necessary to be successful against good players if you get in the habit of keeping your whole range in mind when you play.

Cheers,

Will

You say here Will, that villains strategies depend on his payoffs. I dont quite understand this. Surely his payoffs depend on which strategy he is adopting? Also, if you are playing against a low stakes player who regularly checks back the flop with different parts of his range somewhat equally, and Cbets also with the same frequencies, how much of a sample do u think will be needed before we can determine which parts of his range he does an action with most of the time? (obviously he will not be able to be completely random here). Do u think its even feasible to exploit somebody who is doing something as simple as checking back the flop with all parts of his range equally? I mean I see these guys do this at $20 HUSNGS.

Thanks.

I mean that when Villain makes a decision, it will depend on how much money he expects to make from each of his options. Presumably he'll go with the one where he expects the most money. Nothing too deep here, I think.

I agree it can be hard to figure out what opponents are doing, even in fairly common spots like flop c-betting. Start out when facing a new opponent with a guess about how he might be playing based on how people in your games usually play. Then, pay close attention to his actions and use each piece of info to update your ideas about how he's playing the game.

As far as players who make their c-betting decisions without regard to their particular hands -- to see how you make money from them, think of all the reasons you dont play this way. You miss value with your strong hands, you miss profitable bluffing spots with weak ones, you don't charge draws, you don't protect your hand when appropriate, etc.

But more importantly I would say these players are very rare. Sometimes people mix it up, but more often than not, they play the same hand the same way each time they're in a certain spot. They play it however they think is best, and their idea of the best way to play a certain spot doesn't change that often. If you think you see your opponent mix it up by playing differently in two similar situations, consider the possibility that your opponent didn't see the two situations as the same. Perhaps he found some strategically-relevant detail that changed his decision. What was it? What does that say about his play or how he thinks about the game?

I am beginning to think the yaqh knows how to play poker and has written an important book.

I am even thinking of buying the book though I don't play HU NLHE.

I am sure it will have cross discipline relevance (I play mainly limit draw, 7 stud, triple draw and hold'em) but would you (yaqh) expound upon just one.

Many thanks.

Thanks for the reply. Sorry it's been a few days. I put in over 100K hands since Friday, so I've been busy and my mind is a bit fried. I've typed and deleted for about 10 minutes here. Gonna get back to this after some rest. Just felt bad I've not been able to get back to this thread... There are a couple things here I'd like to iron out. Lots of discussion I've seen in other places that I think is a bit off - if not harmful.

Np, is it clear now why thinking in terms of your entire strategy is fundamental to strategic play? Post your other questions when you get a chance, and I'll do my best to set you straight.

Will:

Maybe it's best if I lay out my thoughts a bit more clearly. In doing so, perhaps I'll expose gaps in my understanding as well as make sure we're on the same page.

We're comparing two different methods of poker analysis: exploitive and optimal. Exploitive looking at a particular decision point and moving forward, analyzing the most +EV decision using our best assumptions regarding the opponent's strategy. I understand it's important to consider the expectation of a hand distribution against the opponent's strategy as well as thinking about how our range impacts the opponent's thought process so we can make accurate assumptions. Having said that, in exploitive play, the analysis is using our particular hand vs. the opponent's strategy and determining which betting decision has the highest EV.

It sounds to me like you're giving exploitive play a lashing - condemning it as an inferior method of analysis. I hear what you're saying when you talk about how a more complete understand of game theory will aid in a better understanding of exploitive play; however, I don't think it's correct to view exploitive play as an inferior method. Indeed, I would argue it's the superior method for most of the poker audience. Small stakes games are still littered with opponents against whom you can employ a maximally exploitive strategy with little concern of your opponent adjusting well.

I've found players trying to apply optimal play in the wrong situations. They add certain hands to a betting strategy that simply don't belong in that betting decision verses an opponent who is not adjusting well. I ask them why they're making that betting choice with that hand. "I have to have these types of hands in my range in order to balance." It's nonsense versus these opponents - and it hurts a win rate. Applying optimal play in these types of situations is sacrificing profit in order to accomplish an unnecessary goal. In these circumstances, thinking about your specific hand versus the opponent's strategy isn't a "sometimes successful model" or a "reasonable approach"; exploitive play is the correct and balancing is the inferior choice.

I love the idea of learning about game theory and I definitely see (probably more dimly than I should) the value in understanding optimal play. I see the value in applying it as well - especially when we begin entering the infinite regress of "he knows I know he knows...", i.e. we're against tough opponents. I concede your understanding of game theory is well beyond my own; I couldn't have written this book. Perhaps I'll see things more closely to what you're saying after I've given your book a few readings. However, at this point in my understanding, it's been very frustrating for me to hear so many students of the game talking about balancing their ranges and attempting to play GTO as if it's where the real money is made.

Thanks again.