Get Instant Access to PDF File: #4bb1e8e Expert Heads Up No Limit Hold'em, Volume 2: Strategies For Multiple Streets By Will Tipton [EBOOK. Will Tipton [email protected] () BACKGROUND Software engineer, computational scientist. SKILLS. Linux, C++, Java, golang. Editorial Reviews. From the Back Cover. Heads up No Limit hold'em is the most important Expert Heads Up No Limit Hold'em, Volume1: Optimal and Exploitative Strategies - Kindle edition by Will Tipton. Download it once and read it on your.

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Will Tipton began playing poker online in He steadily moved up in stakes in online HUNL tournaments to become a regular winner in the high stake. The right of Will Tipton to be identified as the author of this work has been asserted . sponses. Unlike many other poker books, we will not tell you exactly how. Solutions for section are obtained computationally by solving the indifference equations, google tvnovellas.info What you can.

The second best time is now. Having covered a lot of basics in Volume 1, were now ready to tackle the complexities of multi-street play. Well start with a quick review of the tools and big ideas we developed in the first volume before starting on turn play. Starting in Chapter 10, we will extend our study of polar-versus-bluff-catcher PvBC play to multiple streets. As on the river, it captures the core of poker: value-betting and bluffing versus some poor schmuck who wants nothing more than to show down. Our models will become more and more sophisticated from there.

In this book, we use the terms GTO, unexploitable, and equilibrium as synonyms to refer to such strategies. A solution for the full game of HUNL is not known, but the result of an attempt to get close is called pseudo-optimal or near-optimal play.

We have seen that pseudo-optimal play is appropriate not only against mindreading super-geniuses, but also against more run-of-the-mill opponents whose strategies are simply unknown to us. When facing a new opponent, many different exploitative strategies could be best depending on his tendencies.

When these tendencies are unknown, however, any deviation from GTO play on our part is just about as likely to hurt as to help us.

Without knowledge of a players weaknesses, we cannot expect any particular deviation from equilibrium to increase our EV. Although it is not entirely rigorous, we can think of unexploitable play as our best response given complete uncertainty about our opponent. Furthermore, understanding unexploitable play can help us recognize exploitable tendencies in our opponents and understand how to adjust our own ranges to take advantage.

For example, recall one of the simplest river situations we looked at in Volume 1: the PvBC game. One players range is made up of the nuts and air, and his opponent holds only hands that beat the air but lose to the nuts. We saw that under many conditions, the equilibrium strategies here are for the first player to bet all-in with all of his nut hands and enough bluffs so that his opponents EV if he calls is the same as if he folds.

Similarly, the second players GTO play is to call enough to keep the first indifferent to bluffing. What about exploitative play? If the polar player bluffs a bit too much, his opponent should always call, but if he bluffs even slightly too little, the 19 Expert Heads Up No-Limit Hold em, Volume 2 bluff-catcher should always fold.

On the other hand, if the bluff-catcher calls too much, his opponent should never bluff, and vice versa. Of course, too much and too little are defined in terms of the unexploitable strategies. So, our understanding of GTO play makes it very easy to understand and describe all of the opportunities for exploitative play in this situation. Despite the fact that HUNLs true equilibrium is likely too large to memorize and too complicated to fully understand and not even the best approach versus most opponents , the players with the best knowledge of game-theoretic play are also some of the best exploitative players because of their understanding of the game.

With this in mind, we have focused on learning about equilibrium strategies to develop intuition and understanding of the structure of HUNL play. In this volume, we will continue our careful consideration of a variety of spots and how we might want to split our ranges when we encounter them. Although we will describe refinements later, our general approach to match play begins by playing pseudo-optimally. From this defensive posture, Hero can observe his opponents tendencies and determine appropriate adjustments.

Of course, it is rare that a new opponent is a complete unknown. In practice, we may do well to make some pre-game adjustments based on our knowledge of population tendencies the tendencies of an average individual in our player pool.

However, this caveat does not give us a free pass to just make standard plays without good reason.

Any deviation from equilibrium play should be justified by reference to a particular exploitable tendency, whether of the population on average or of a particular opponent. Although this is a book on heads up play, its worth noting that many of the properties that make Nash equilibria so useful do not hold in games with three or more players. In particular, if we play an equilibrium strategy in HUNL, we are guaranteed to at least break even neglecting rake on average over both positions.

That is not the case in 3-or-more player games, where playing an equilibrium strategy provides no lower bound on our expected winnings. Thus, the Nash equilibrium is much less useful outside of heads up play, and anyone selling the idea of GTO strategies for 3-ormore player games should be viewed with suspicion. The equilibration exercise gives us a framework for thinking about how exploitative players adjust to each other in a particular spot.

We begin by supposing that Villain is playing a particular strategy.

Hero then adopts his best response. We then consider how Villain could readjust to take advantage of our new strategy and what Hero might notice if Villain does make such an adjustment. We can then repeat the process, alternately finding the maximally exploitative strategies for each player and answering some additional questions at each step.

The focus of the equilibration exercise is on the first few adjustments. However, this process has a lot in common with a computer algorithm for finding Nash equilibriums known as fictitious play.

It turns out that if we continue this sort of process long enough, the players strategies may converge to equilibrium. In practice, a scheme involving averaging of the players strategies in each step is usually necessary to ensure convergence. The Indifference Principle states that if a player is playing a hand in more than one way at the equilibrium, the EVs of both actions must be equal.

Consequently, his opponent must be playing in such a way as to enforce that equality. We will often use the intuition we gain from the equilibration exercise in combination with the Indifference Principle to draw conclusions about unexploitable play. For example, suppose Hero is out of position on the flop with a draw to the nuts that is fairly likely to come in, such as an open-ended straight draw.

The effective stacks are moderately deep. For simplicity, suppose Hero is restricted to two options: check-raise and check-call. If Villain is playing exploitably, one of these two options is likely more profitable than the other. However, we can make a pretty convincing argument that at the equilibrium, the two EVs are equal and Hero takes both actions with nonzero probability. Suppose Hero always check-calls with this nut draw. Then, when he does check-raise in that spot and then the draw comes in, his range is capped he cannot have the straight.

When Heros range is capped, it implies that Villains range has a significant number of hands that are effectively the nuts, and we saw that Villains best response in this case usually involves 21 Expert Heads Up No-Limit Hold em, Volume 2 making frequent, large bets with much of his range. Since Villain is putting so much money in the pot after Hero check-raises and the draw comes in, being able to show up with the straight after check-raising becomes very profitable for Hero.

Thus, Hero is motivated to begin check-raising with the draw on the flop. On the other hand, we can use a similar argument to see that if Hero were always check-raising with the draw, Villains response would incentivize him to begin check-calling it. Thus, neither pure strategy is unexploitable, and GTO play must involve doing both with some frequency. Thus, we have used the equilibration exercise to identify a spot where Hero plays a hand more than one way at equilibrium.

The Indifference Principle immediately tells us that the equilibrium EVs of the two actions must be equal. Villains play must make this true, and thus we can leverage this knowledge to learn about Villains equilibrium strategy. Indifference is not a fundamental property of equilibrium play. We have seen solutions to games where neither player is indifferent between any actions with any hands. Indifference should certainly not be taken for granted when studying a new spot.

However, mixed strategies and thus indifference often emerge when both players adjust to each other to try to play as profitably as possible. A thought process like the one above will frequently help us to identify these useful relationships. If Hero plays one pure strategy, Villains response incentivizes him to switch to the other. But when he plays the other pure strategy, Villains response incentivizes him to switch back to the first.

Since neither pure strategy is unexploitable, play must be mixed at the equilibrium, and thus the two lines have equal EV. In Volume 1, we also developed some tools for analyzing and describing ranges. You draw a hand-distribution plot by ranking all hands in a range from strongest to weakest and then plotting how often each hand is contained in the range.

This ranking is somewhat ill defined, since there is no clearly correct ordering of hand strengths before the river, nor even then due to card removal effects, but this construction is nonetheless useful for quickly visualizing the strengths of the various hands that make up a range. The shapes of these plots motivated some of the words, such as po- 22 lar and capped, that we use to describe some strategically important properties of the ranges themselves.

Of course, to draw strategically relevant conclusions, we really need to describe our hands strengths in comparison to our opponents holdings. Equity distributions allow us to visualize this information directly they are plots of the equities of all the hands in our range.

We found these very useful for our analysis of river play. We can forget about the particular holdings involved and reference holdings only by their percentile in our own range and equity versus Villains. Thus, we solved many situations in general and then mapped real hand ranges onto the results. With this abstraction, we lost the ability to deal exactly with card-removal and chopping effects.

However, it allowed us to deal with many situations at once and see connections between them. Our convention for drawing equity distributions might need a bit of explanation. Suppose we have a hand from the hth percentile of our distribution.

The equity distribution is a representation of a function, EQ h , which takes a percentile and tells us our equity. However, we plot equity distributions by drawing this function backwards. In effect, the function we care about is EQ h , but we plot EQ 1h. This was done for historical reasons and is perhaps not the clearest choice.

For consistency, we will keep the same convention in this volume. However, since equity distributions do not account for the possibility of changing hand values i. In many settings, the answer may be as simple as the identification of a weak player at the table, and it may be reasonable to make an extra effort to play pots with that player.

As sophisticated players in a HU game, we might think a bit more deeply what exploitable errors is our opponent making and what are we doing, exactly, to profit from them? To address these questions, we generally focus on analyzing the EV of each of the options available to us in individual situations. However, we can gain some important insights by taking a more holistic view of things.

So, where does the money come from in a hand? Well, payoffs come at the end of a hand: after a fold or at showdown after the river. After a fold, our payoff is the whole pot or none of the pot, depending on who folded. After an all-in or a showdown, our payoff is essentially just our equity in the pot.

In a big picture sense, our early-street actions can be thought of simply as attempts to guide play to leaves of the tree where we have the largest payoffs, on average.

Identifying the spots from which we are profiting in a match is important, because it is the first step in developing a plan to get there.

Understanding where it is valuable to have some hands and not others can help us organize the play of our whole range, especially on the earlier streets. In particular, we are about to study turn play, and a solid understanding of the values of holdings in certain river spots is necessary for evaluating our options on the turn.

Consider all the types of hands you might hold at the beginning of river play. How valuable is each of them? It is not immediately obvious. For example, we have seen situations where a complete air ball is just as valuable as a legitimate value hand at equilibrium.

In other spots, good-butnot-excellent value hands are essentially bluff-catchers, and they expect to capture little more of the pot than a good high card.

Perhaps we should try 24 Preliminaries to play earlier streets so as to get to the first spot with more bluffs and to the second with fewer marginal value hands. Let us look at the value of various hands on the river in the context of pseudo-optimal play.

Of course, a particular holding cannot be considered in a vacuum. The value of taking an action with a hand depends on how Villain reacts to it. That, in turn, depends strongly on the entire range with which we take the action.

So, the value of an individual hand on the river is strongly tied to its place in our range and how that range stacks up against Villains. Suppose we start river play with remaining effective stacks S and a pot size of P. Call the size of a first river bet B and additional money put in by the first raise C. Remember first of all that we need never play a strategy that gives any hand an EV less than S.

We can always just achieve at least that by simply giving up and putting no more money in the pot. Now suppose that Hero bets, putting Villain to a decision. If Hero is in the SB, his betting range facing a check on the river should generally be polar.

That is, his betting range is composed of some amount of his strongest and weakest holdings, and if he does check back with any hands, it is those in between. These conclusions about the structure of the SBs strategy in this spot came out of our study of river situations.

Of course he wants to bet his strongest hands to try to get called by worse. However, if those are the only hands he bets, Villain folds a lot, so that Hero is incentivized to bet his weak hands, too, to avoid a showdown. We saw that, at the equilibrium, Hero can only get away with a limited number of bluffs, so he might as well use those that win the pot as little as possible at showdown.

If Hero is in the BB, however, he usually cannot get away with so extreme an approach. If he only checks mediocre holdings, he must contend with the possibility of a SB bet, and the SBs play will generally incentivize him to start checking some strong hands, for balance-related reasons.

Playing well in the BB is much harder than playing well in position! A correctly balanced polar betting range has a clear effect on Villains distribution. It splits his range into three portions: those ahead of some of Heros value-betting hands, those that lose to even some of Heros bluffs, and those that are stronger than all of Heros bluffs but weaker than all of his value-bets. The hands in this last group are all effectively bluff-catchers and are, up to card removal effects, indifferent between calling and folding.

At the equilibrium, some of these will call and others will fold. Either way, they have an EV of S when facing a bet they are no better than complete air! Bluff-catchers do perform better than air in general, since they can show down and capture some of the pot if they do not face a bet.

However, finding oneself with a range composed primarily of this type of hand is unfortunate, especially when Villains range is sufficiently strong that he can bet and put us in such a spot with high frequency. In practice, exploitative call-or-fold play with bluff-catchers involves figuring out whether an opponent is bluffing too much or not enough in a particular spot. In the first case, bluff-catchers all become profitable calls, and in the second, they are all clear folds.

In Chapter 7, we discussed common river decision-making thought processes to try to understand situations in which opponents are likely to bluff too much or too little.

What about the two other types of hands Villain might hold when facing a bet? With holdings worse than bluff-catchers i.

Thus, when facing a bet, these hands also have an EV of S. Again, however, these hands do not always face a bet, and if they have some showdown value, they may occasionally win at showdown. I'm not saying that a HUD can give you all the info you need to know about an opponent, but there are some pieces of information a computer is good at gathering anything involving incrementing counters and some that a human is good at patterns based on gameflow, texture, etc.

I let the computer do what it's good at, so I can focus on the other stuff. There isn't a release date set. It'll be a few weeks at least, but possibly a decent bit longer -- getting it done right is more important to me than getting it done fast. Thanks for your interest, though -- I'm looking forward to getting them out, too. Nice man, and yea i agree with you abut getting it done right: So no rush also because i'll get my 2nd book anyway only on 30th May: J7o of course is a little bit better so its maybe 91 percentile hand i dont know.

Hey Will. Just wondering should i download Mathematica. I don't plan on any more supplemental content that uses Mathematica. My next video pack will use the freely available iPython software. Ohh and that question i asked about Mathematica - I wanted to know if there will be ways to solve SB river bet or check game and "big river game" like you did using Mathematica in this video pack but this time using iPyton So is there gonna be ways to solve these games using iPython instead of doing it in Mathematica.

Your new book is very good, probably best poker book ever written, but here are couple of things that I don't like:. I really dont like so many questions with no answers like this one: Why is this? I did so in the 1st book and only tried to answered them after the 3rd reading of the book. The problem is that even if we try to answer them we have no way check if our answers are correct or wrong It would be nice if you could publish a short workbook, where we could find answers to all bolded questions from both books.

I would be willing to download such a workbook and I think it would be very helpful for many people Yea i would also snap download them but anyways if u read carefully and ask questions on forum u can get the answers. For example, in exploring such questions, the nuances and limiting assumptions you need to make will become more explicit in your mind.

As such, you will become more adept at realising where particular models are not applicable and being able to appropriately adjust your approach to solving new problems you encounter. Rather, the typical approach is effectively to learn how to learn. Poker is a game that evolves at a rapid pace because it is market driven. The advice of books and videos that were considered cutting edge in yesteryear are in many cases laughable because the game has moved on.

Most of Will Tipton's book is related to the interaction with the structural elements of the game which won't change within the confines of the specific game it is related: Heads Up No Limit Holdem. I'm really torn because I would also like a solution manual. Figure It is kind of big error, two full pages. I don't know if the same error is in the printed version of the book, don't own that one. If SB never jams facing a c bet, how than there is tab in equilibrium that describes "BB fold to raise all in"?

Log in or register to post comments. Last post. Charles Hawk. Yea the feedback in general has been really great, and I've really enjoyed talking to readers. Do you have any plans for a volume 3? Anything else in the works? No plans for any more writing. Starting out, I just meant to write one book! What is the best compliment you've received about the book?

Maybe this is a favorite: How has school gone? Where do you see yourself in 10 years? Do you ever sportsbet or prop bet with friends? What kind of hobbies do you have? They suggest that poker is actually rather easy and that anyone with five minutes to spare can quickly gain expertise in the game. To achieve mastery of poker is not easy — it requires a great deal of deep thinking.

The author Will Tipton, a PhD candidate at Cornell University, demonstrates how decision trees can be used to model complex poker decisions. Starting with simple preflop-only situations, he moves on to consider deeper concepts such as balance, the analysis of ranges, and the theory behind optimal bet sizing.

Why study Heads Up No Limit? Because a deep understanding of this format is crucial for the modern poker player. If you find yourself playing for first prize, you will be playing heads up for a great deal of money. Perfecting your play will give you the edge to maximise your expectation whether you are competing for the big money or grinding out your profit in heads up cash games or SNGs.

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