Heads Up No Limit Poker Solver. The Jupyter notebook in this repository largely represents the code from Will Tipton's Solving Poker with IPython video series. However, I have begun editing the code to add. Will Tipton Will Tipton began playing poker online in 2007. He steadily moved up in stakes in online HUNL tournaments to become a regular winner in the high stake games. He recently completed his PhD work at Cornell University and has taken a position as a software engineer in the San Francisco Bay area.
I recently had the opportunity to read Expert Heads Up No limit Hold' Em, by Will Tipton (you can find my review of the book here: https://pokernewsboy.com/reviews/book-review-expert-heads-up-nlhe-volume-1/13332) and Will was kind enough to answer a few questions on his book and poker in general.
PokerNewsBoy.com: Could you give the readers a little background on yourself and your life as a poker player?
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Will Tipton: Sure, so I started out playing small home games with friends in college. At first I had no idea what was going on, but I borrowed a copy of Harrington on Hold'em and must have finished it in a day or two. At the time, it was a great introduction to the game. It did a good job showing how intelligent decision making could lead to success, and I was hooked.
I started out online in January ‘07 with a $60 deposit and never had to reload. From there, I played the game a lot and thought about it more. I moved up much more slowly than is usually recommended. There are trade-offs with such conservative bankroll management. I'd definitely wish I'd moved up a quicker to maximize my overall profits, but there's also something to be said for keeping a high win-rate and low variance. I was a fulltime student with a heavy outside-of-poker workload, and it was nice to rarely have significant downswings that could distract me from that.
Computation has always been my default problem-solving method. In fact, when I first learned about online poker, my first instinct was to write a bot, and I made a significant progress on that project before I learned that it was a no-no and decided to just focus on improving my own play. Since then, I've developed a software package to solve large approximate HUNL games, and the things I've learned from it essentially made the book possible.
I also learned a ton from online poker forums when coming up. The level of play by the heads-up community as a whole has improved tremendously over the past couple of years, especially in the short-stacked regime since the hyper-turbo format became popular. However, there's still a lot of misunderstanding of theoretical concepts — concepts which I found to be very useful in thinking and talking about cutting edge modern strategies. So for a few months I sort of thought about how I might organize and present the ideas, and then I started writing towards the end of 2010.
Shortly thereafter, Black Friday happened, and my poker career hasn't really been the same since. I play a bit on one of the US-facing networks, but just when I feel like it — it definitely isn't the grind it used to be. That said, I study the game more than I used to if anything, and I think I'll be well-positioned to jump back into the games once we get some favorable legislation and good online cardrooms become available in the US.
PNB: What is it that drew you to Heads-Up NLHE?
WT: Well, historically I pretty much started out playing HUSNGs at the suggestion of my brother and then never stopped. That said, I think the format is a good fit for my strengths and interests. A lot of my
success in poker has come from my ability to find patterns in an opponent's game, to think hard about what various information I get actually tells me about opponents' strategies, to really figure out what
they're doing in different spots and why, and then to come up with a good way to exploit it. I often find myself playing wildly different strategies versus different opponents and doing things that would be extremely spewy without solid reads. On the other hand, I don't think I have a particularly good sense for playing 'in a vacuum' that is, for making standard plays without adjusting. Thus, I've always felt that multi-tabling traditional formats would be a poor choice.
Also I'm not really big on folding, so a game where I can usually treat top-pair-no-kicker like the stone cold nuts works well for me.
PNB: Do you have experience with any other formats?
WT: Not at a high level, no. I started out focusing on heads-up play, and I've never really had a reason to switch. HU play is obviously the most fun, and recreational players seem to like the high-variance, quick-action nature of HUSNGs, so the action is probably better than in any format except for MTTs which have other significant drawbacks.
PNB: Early on in the book you make the point that Heads-Up games are a good place for players to get their feet wet in poker. This kind of goes against the conventional wisdom, and as a person who loves contrarian thinking I was hoping you could you elaborate on this a little bit?
WT: Really? I don't know that I've heard that conventional wisdom — it seems like a no-brainer for me. I am mostly referring to HU S&G's by the way, not HU cash. HUSNGs work great for the two things a beginning player (and, you know, everyone else) wants to do: learn how to play and build a bankroll.
Will Tipton Poker Club
It's a good way to build a bankroll for a couple reasons. The games run online down to very low buy-ins, and on many sites, the rake is pretty reasonable, in contrast to some micro-stakes cash games. The level of play at the lowest buy-in levels is generally atrocious, and pretty much anyone actually trying to play well and educate himself about the game should become a winning player very quickly. Additionally, there is actually significantly less variance in HUSNGs than in many other formats which is good for impressionable new players.
There are also a few reasons why these games are a good spot to get an education. Players can put in a lot of hands for little money. They're forced to play a lot of marginal spots. And they can focus on understanding the exploitable tendencies of a single opponent as opposed to those of a table full of opponents which can be overwhelming. In fact, there's a tendency to not even bother trying to figure out each opponent's game in traditional formats but to just categorize them as one of a few broad groups. Play heads-up, and you will see that every opponent is a snowflake…
Lastly, if a player does want to branch out, the skills learned in heads-up play generally transfer well to other games. HU players usually become especially skilled at identifying and exploiting opponents' strategies. I think it was Aaron 'aejones' Jones that said he couldn't take his 6-max game to the highest level until after he started playing heads-up. In particular, a good understanding of HU play can make a huge contribution to your win-rate in MTTs since the biggest money is at the end of final table play where most MTT players have the least experience and in traditional cash games where it gives you the ability to start new tables.
PNB: One area of the book I touched upon in the review was the length of the 'River Play' section. Is this simply an aspect of the decision tree's exponential growth, or is a heavy emphasis on river play something that is specific to Heads-Up play?
WT: Interesting question. First of all, I'm not sure that the river will get more attention than other streets in the end. It's just that it came first since I decided to cover the streets from the end of a hand back up to the beginning. I discuss the reasons for this a bit in the book, but basically, the way you make any decision in poker is to think about all your options, estimate the size of your average stack at the end of the hand if you take each action, and then go with the biggest. But many of your options on the turn will involve going to the river. So, to even start to make turn decisions, you have to know something about the value of having a hand in various river situations. Similarly, to talk about strategizing on the flop, you have to know the value of various holdings on various turns. So it makes sense to work from the end of a hand to the beginning. The heavy emphasis of this book on river play is kind of a coincidence — I wouldn't say that river play is more important than the other streets in HU play, and the other streets will get plenty of discussion in Volume 2.
That said, I do think that the river is particularly interesting. I think most people play it the worst of all the streets and it's also generally when the biggest bets go in, at least outside of very short-stacked situations, so it's a great place to look for an edge. Basically, it's really hard to just 'get a feel' for opponents' river play like it is their early street tendencies, since river situations come up rarely and can be drastically different depending on the board and early-street action. Also, early-street play is often a poor indicator of players' river tendencies. Plenty of people will make copious moves to try to take away small pots but rarely put in the last bet unless they have it. Others rarely make moves, but when they do, they're taking it all the way. There are big edges to be found on the river by training yourself to pay special attention to what your opponents are doing there.
PNB: What do you have in store for Volume 2 of Expert Heads Up No Limit Hold' Em?
WT: The split into two books wasn't planned from the beginning. I set out to write one, but it turned to be too much material to fit into one book. So, the second volume will pretty much pick up where the first one left off. After a quick refresher of the main lessons from Volume 1, I'll discuss pseudo-optimal and exploitative play on the turn, flop, and pre-flop streets. I'll make heavy use of all of the tools we developed in the first book and introduce some new ones for managing the complexity of multi-street situations. After that, I want to say a bit about the process of gathering and using of new information (i.e. making reads), which is obviously an important part of the game and also a strong part of my own game. And then, I think it will finish up with a chapter which essentially answers the question, 'When does it make sense to pass up a +EV spot in order to wait for a better one versus a weak opponent?' We don't have a publication date set, but I've made a good bit of progress on the second book already, and I'm really happy with how it's coming along.
By the way, I'm also working on a video pack with www.HUSNG.com which will essentially supplement Volume 1. I'll elaborate on some river-specific topics such as: range merging and leveling on the river, play from the BB with one pot-sized bet left, and play in spots where significant amounts of players' ranges are chopping. I'll also have videos on more general topics such as reading your own hand and the right and wrong ways to use 'non-auto-profit' calculations. That should be available relatively soon.
PNB: Any plans on turning the books into your doctoral thesis?
WT: Haha, I wish. Unfortunately, I don't think there's any way I could convince my committee to go for that. I'm a computational materials engineer, so basically my work revolves around the use of computational methods based on quantum mechanics to design new materials for technological applications. Optimization problems and Monte Carlo methods are a big part of my research, so there's actually been a lot more overlap than you might think between my academics and my work on poker theory. I don't know, my professor's a fairly easy-going guy. I guess it couldn't hurt to ask, could it?
Tags: Background, Decision Making, Default Problem, Fulltime Student, Game, Good Job, Harrington, Home Games, Instinct, Intelligent Decision, Online Forums, Online Poker, Poker Player, Profits, Software Package, Success, Trade Offs, Variance, Volume 1, Workload
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Will Tipton Poker Results
Playing a toy poker game with Reinforcement Learning
Reinforcement learning (RL) has had some high-profile successes lately, e.g. AlphaGo, but the basic ideas are fairly straightforward. Let's try RL on our favorite toy problem: the heads-up no limit shove/fold game. This is a pedagogical post rather than a research write-up, so we'll develop all of the ideas (and code!) more or less from scratch. Follow along in a Python3 Jupyter notebook!
(more)Games, Strategies, and GTO Strategies
This is Part 1 of 6 of an adaptation of my chapter 'Game Theory Optimal Strategies: What Are They Good For?' from Excelling at No-Limit Hold'em edited by Jonathan Little.
Much of the reason I wrote Expert Heads Up NLHE was to explain the ideas of game theory, poorly understood in the community at the time, to the average poker player. Heads up no limit (HUNL) is my game of choice personally, so it made sense to use it as the primary example. However, HUNL is something of a simple case, and there's a bit more to be said about how game theory applies to other games. In this chapter, I'll give a quick introduction to game theory as it applies to a variety of common poker formats. We'll see when it's useful, and more importantly, when it's not – when it's appropriate to use game theory-inspired strategies, and when it just can't really guide our play. I promise to cover a practical skill or two as well.
(more)Solving the Shove/fold Game with TensorFlow
Google recently open-sourced TensorFlow (website, whitepaper), a software package primarily meant for training neural networks. However, neural nets come in all shapes and sizes, so TF is fairly general. Essentially, you can write down some expression in terms of vectors, matrices, and other tensors, and then tell TF to minimize it.
I ran through a couple of their very well written tutorials and then decided to try it out on one of my standard toy problems: the HUNL shove/fold game.
(more)Running it up, Part 3
We doubled up twice – time for round 3!
(more)Running it up, Part 2
We doubled the roll once, can we do it again?
(more)Running it up, Part 1
Tonight, Carbon was down, but Black Chip Poker gave me a few dollars to play with, so I'm going to try to run it up.
(more)Value categories in C++11
One of the most important additions to C++ in the C++11 standard was the introduction of movable types. This feature has consequences for many common programming tasks such as assigning variables and passing arguments to or returning objects from a function. Move semantics are a bit subtle, and when reading documentation, it helps to understand some vocabulary: value categories.
(more)EDVis v1.1
Changes from v1.0 to v1.1:- Control fractions of individual hand combos- View and set fractions of hands of a particular suit- Account for card removal effects when drawing the distributions
(more)Debugging
Pretty much any nontrivial piece of software will have bugs during development. Fixing bugs is thus an unavoidable part of programming, and it's important that all programmers have some skill at the task. I recently made a video series about developing some poker-related software. The focus was on the problem domain, but much of the audience was new to programming, and I didn't talk too much about what to do when things don't go perfectly, i.e. Casino slot games that pay real money online. when there are bugs. So, this post is a quick intro to debugging methodology in general, but I have my poker audience in mind.
(more)Arbitrarily-deep nested loops
I finished a first pass at my lattice regression library over the weekend. The idea with that is pretty straightforward. Essentially, there's some function we want to model, and it's unknown, but we have a bunch of observations of inputs and corresponding outputs. So, we throw down a lattice (i.e. a regularly-spaced grid) of points over the space of inputs, and we use the data to 'learn' some values of the function at the lattice points. Then, we discard the training data but can predict new values of the function by interpolating between the values at the lattice points. For more details, see, e.g. this paper.
Code-wise, one challenge of the project was in representing and dealing with the lattice. For example, suppose the function we want to model has 4 inputs. Then, our learned values on a grid over the space of inputs might naturally be stored in something like a 4-D array,
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(more)Eclipse: Computing Git status for repository LatticeRegression
I've gotten a lot of value out of Eclipse CDT over the years, but I wish it was less buggy. And the UI could be better. Anyway, today I open my laptop (on an airplane), start a new C++ project, and soon notice (thanks to a battery indicator reading under 2 hours time left) that Eclipse is using 350% of my CPU. I check the Progress tab and see that Eclipse is 'Computing Git status for repository LatticeRegression'.
(more)Job fairs and SWE interviews
I have a different perspective on the job search thing now that I've successfully done it once and seen things from the other side. I manned a booth at my alma mater's job fair recently and didn't think most students asked the right questions. Ideally, almost all of a job fair conversation should consist of the student telling me what he's good at and passionate about in as straightforward a way as possible (there's no need to be modest or subtle). Reading resumes is mind-numbing work, if I have to use a lot of imagination to see you as a successful candidate, you're likely to be disappointed. If you do ask questions, and I do the talking, you might as well take the opportunity to try and get as valuable of information as possible.
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Will Tipton Poker Player
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