An introduction to the theory and practice of poker (2020)
hopkinspokercourse.com
hopkinspokercourse.com
Today, much of poker theory is driven by analyzers that are supposed to implement a practice called "GTO" (game theory optimal). There have been a lot of interesting findings in the last ~5 years that have come from these that I would be surprised to see in a course like this.
To bring someone from completely n00b level to "okay", this course is probably fine.
Where can one learn about these? Resources on fast moving areas like this is super hard to find if you're not "in the know" already.
The game these days is all about reverse engineering strategy principles from GTO simulation output. E.g. what general principle causes the solver output to say raise 30% in this spot vs raise 80%? If you come up with a coherent story, you can apply that thought process to new situations. It's a totally different game than it was a decade ago
Here is one of the solvers if you are interested: https://piosolver.myshopify.com/
Fwiw there is a significant amount of skill involved in choosing how to run simulations. I think they have some intro videos to help you
and sometimes a pretty significant amount of memory - these applications use massive amounts of it
Anyway, it's still not best to play like a robot in live low stakes games, which are probably what you're going to be playing. Exploit the shit out of your opponents. GTO has some good concepts that are easy to implement, but I'd work on studying your opponents and the mistakes they are making, and decide how to capitalize on those mistakes.
If you are going to multi-table online, ignore everything I just said and become best friends with some solver software.
Good luck.
Piosolver has several features that lets you emulate how your opponent plays, such as "node locking", that "lock" the game tree node to the strategy you suspect your opponent plays, and shows you how to maximally exploit it.
Otherwise, what is your exploitation based on? Certainly some people have great instincts for the game, but it's just untrue that solvers can't help you exploit weaker players. For example, if you're on a given board and a given river and an opponent makes a big bet, if your opponent bluffs too much you should call, if they don't bluff enough you should fold. But the solver teaches you how often they should be bluffing and thus what "too much" or "not enough" even means.
This is why I prefer the term "theory-based" to GTO, since the point of studying GTO is not to play GTO but to develop a better understanding of the underlying mechanics of the game.
I think GTO is a great way to think about the game. I don't think studying solvers is important to understand the game well, or GTO. When solvers provide an insight, it generally trickles out to the poker community and we all hear about it. It's much easier to digest traditional educational content than to futz around with a solver, and a much better use of time for a new player.
https://www.raiseyouredge.com/tournament-masterclass-starter
Some people also have to spend a lot of time working on emotional regulation to avoid throwing good money after bad.
I was once interested in going pro, and I landed on some advice that said to go to a poker house and fold every hand for 3 hours. Poker has very high variance, and you can easily have 3 hours of hand shuffled poker and not get a single playable hand. That was when I realized I didn’t have the emotional regulation to play properly, especially, since part of the exercise was to throw away the strongest starting hand even if you are dealt it during this exercise. Also, that was about the time I realized that poker is generally an extremely boring game, with the very occassional periods of high emotion.
It did teach me a lot about going on tilt though, it’s very easy to throw away a lot of profit after a big loss.
I was gonna'say "patience," but your response is better.
I was a complete blackjack noob until a few months ago when I got interested in my states online casinos.
I would check literally every position (even obvious ones) to see the expected value for each decision and quite quickly built up an intuition when I was playing without the aid (the live dealer games sometimes move too fast to input and get results back in time).
Now its like second nature and only in rare situations do I double check my judgement.
Do you know how you can tell everyone is largely full of shit when it comes to poker?
No one ever talks about the rake. They are a winning player no matter what the rake and that obviously can't be true.
The other issue is the variance is so high in no limit that to converge to a true win rate in live full ring poker takes years of playing full time.
you just need to grasp the basics.
Phil Gordon's Little Green Book and The Theory of Poker (Sklansky) are common recommendations.
Q: As a noob, what’s the quickest way to become better than breakeven, then better than breakeven including the rake/seat charge?
A: Find a way to play against the worst players you can find, or at least players worse than you. There are likely some tough games near you; avoid those. They might be some soft games; play in those.
Game selection and exploiting opponent weaknesses can easily turn a player with a grasp of the basics into a winning player.
If you can play even a little bit - eg you know some hand rankings and don't get too drunk - you're better than some players, and you can find a game you can beat.
If you're the 20th best player in the world, but instead of looking to play against weaker players you yearn to challenge yourself against the best, or in general if you move to bigger and tougher games every time things are going well, you will lose money in the long run.
It's not quite that simple in practice. You might be one of the worst players in your local cardroom, so your only winning move is not to play. Or you might be one of the best, but you don't travel to other games, so you win in spite of your self. I've seen so many people like this! If you play on the Internet, however, that's effectively not possible.
The bigger point is that while playing against worse players is an important skill if you want to make money, poker is still a very complex game with a high skill ceiling similar to a game like chess. If you're good enough, even pro players are "worse players" and you can "select" those games. Though admittedly even the high roller tournaments require some "recreational" businessman players for enough pros to be willing to play it for it to run.
Solver study has become essential for the vast majority of top pros, which Haxton also discusses in the podcast, and I mentioned my project in the space in my other comment.
It’s true that playing against bad players will increase your win rate but it’s also true that if you study and improve you will also improve your win rate. It’s not true that there’s no point in studying since you should only play against bad players, because “bad player” is relative to your skill.
The podcast episode I recommended is a long time pro player interviewing another long time pro player, whose widely regarded as one of the best players ever, so I think these people know better than the HN comment section of “well 20 years ago I read one sklansky book and a year ago I played a 2/5 game and didn’t win much so poker is pointless unless you play idiots”
I used to strongly agree with this (skill ceiling is so high that large edges can be found if good enough) but no longer believe this is the case - I think the edges are much narrower now in the top levels of the pro scene, much of which I'm sure is due to the rise of solvers and the game being closer to "solved" now than it was even 5 years ago.
There's a lot of complex evidence for this, but without going into too much, the degree of scumbaggery in pro scenes going on is usually a strong indicator. When edges get small, pros tend to get a little scummier to get ahead.
A guy I dealt to for years was known at the table as Hillbilly. He had a manner that just disarmed some other players. He wasn't an amazing player, but he was a lot smarter than most people assumed, and you wanted him at the table because he was fun to chat with and you thought you could beat this disheveled, ol' country boy.
When you lost to Hillbilly, it was just bad luck. When you won, it's because he's a simpleton, of course. But somehow, he always had a pretty big stack of chips in front of him.
A lot of pro players have this edge, too; just the right personality to get other people to believe their superiority, ignore their discipline, and "go on tilt" (make suboptimal decisions)
This isn’t Reddit. Don’t make lazy meme posts.
"Thinking in Bets" and "Quit" by Annie Duke
https://www.annieduke.com/books/
I do own "How to Decided" but haven't read it yet. I will say that "Bets" and "Quit" are both easy reads and are high on value and low on noise. That is, even if you have play poker you'll get something out of both.
She holds a World Series of Poker (WSOP) gold bracelet from 2004 and used to be the leading money winner among women in WSOP history, and is still in the top five as of April 2023, despite being retired from poker, last cashing at a tournament 2010.
https://en.m.wikipedia.org/wiki/Annie_Duke
So yeah, top enough to use her professional experience as context for her books. Once you read the books you'd understand.
You should now be a winning player. Most decisions will be easy. Any post-flop improvements will start to mint money.
Other players will note how tight you are and still give you action. They cannot help themselves.
I was a pro player for a number of years, just to give context to this advice. Start with playing very tightly, be instantly profitable, and add skills from there. And please, please, please, don't talk about poker strategy at the poker table.
Four to a flush on the flop? One in three chance of getting it. If a lot of people are in the hand and the flush looks like it would be the best outcome, stay in.
Same with an open-ended straight, and you should know whether others could have a better straight draw than your own.
If you see a bunch of random crap on the flop e.g. no straight draw or flush draw or high cards? If you have high pocket pair or two pairs, get aggressive as everyone else is either drawing (and you want them under the profitability threshold of 3+ other players in the hand) or playing a hopefully lower pocket pair or very ill-guided low two pairs (so watch the big blind or historically loose players).
You can usually calculate in your head how many of the unseen cards need to be somewhere to beat you: Suppose I have the best two pairs on an otherwise unspectacular board. My opponent needs a pocket pair to beat my hand. I have 8 opponents, usually a pocket pair is dealt 6% of the time. Even if I sum all the percentages---mathematically wrong but worse than the truth---it's less than 50% chance SOMEONE has been dealt a pocket pair, so I don't have to feel bad about staying in.
If you can do this quickly and make it look like you are acting impulsively or inexperienced, more money will bet against you.
You can check out my project which includes a preflop trainer at:
https://www.livepokertheory.com
I also have a lot of strategy articles that explore how to use solvers to understand live cash games, and I also just started posting Youtube videos that do solver walkthroughs of high-stakes LA cash games.
I'm also doing some unique things like spaced-repetition which none of my competitors do, unfortunately very few pro poker players have heard the term so it's not a selling point to them but HN crowd tends to have heard of it.
In terms of where to start, I'd recommend where the game starts, which is preflop, and incidentally where my product starts, which is a preflop trainer that helps you study equilbrium-based preflop charts using spaced-repetition. It's currently about 90% free with only one set of charts paywalled (BB defend).
I'm actively developing both postflop content and a native mobile app, though the current app is a responsive web app that should work well on your phone.
I also have a Discord with a lot of professional live players that I've attracted via my content marketing and I'm happy to answer followup strategy questions there.
Some good books I'd recommend that are more modern:
Modern Poker Theory by Michael Acevedo
Play Optimal Poker by Andrew Brokos
Grinder's Manual by Peter Clarke (pre-solver but basically the most exhaustive guide to every concept pre-solver)
for Youtube channels, my own :
https://www.youtube.com/@livepokertheory
https://www.youtube.com/c/FindingEquilibrium (Finding Equilbrium, similar content analyzing live games with solvers)
I also recommend the Thinking Poker podcast by Brokos.
(btw, Hopkins Computer Science is also my alma mater so great to see this coming from them!)
If you have a table full of clowns who are playing a range of strategies (ranging from being spiteful to just all-ining every hand, to barely knowing how to play poker), you will very quickly go broke with GTO, because you didn't adjust.
If a GTO player has negative EV in heads up poker, he is not playing GTO.
You don't understand multi-player poker and I see this meme repeated on many poker forums. It's possible for GTO to be worse than other strategies, based on suboptimal strategies of other players at the table.
Ignoring the fact that there is no known GTO solution for more than 2 players, GTO only applies under the assumption that everyone is acting independently for some fairly formal and strict notion of independence. This requirement is broken in many real world games with more than 2 players potentially playing loose and wild, where they may not actually be colluding or coordinating with one another, but they behave as if they were.
Imagine a situation where the collusion was explicit, you are playing GTO against two opponents who are colluding with one another. A Nash equilibrium will still exist in that situation but your EV will be negative. Now explicit collusion is considered cheating but you can imagine a scenario where two players play in such a way that even though they are not explicitly colluding with one another, they behave the exact same way as if they were. This happens among a group of loose players where their actions as a group rewards the group as a whole against players who are acting independently.
In other words, just because a strategy is optimal does not mean that it results in a positive expectation. You might be in a situation where playing perfectly just minimizes your losses, but you will still lose anyways.
If there are weak players they can effectively end up colluding against a stronger player who is playing "More Optimally".
Understanding the table, is a key skill. There's still a human element in the ring game.
I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting.
Going back to the original parent comment:
> If you have a table full of clowns who are playing a range of strategies (ranging from being spiteful to just all-ining every hand, to barely knowing how to play poker), you will very quickly go broke with GTO, because you didn't adjust.
I feel pretty strongly that this is not representative of practical reality. I don't believe that caveats about implicit collusion against a GTO player should prevent one from calling out a harmful belief that is also provably wrong in the heads up setting (the setting where GTO is actually known to exist).
In practice, I have never seen anyone who played remotely close to Nash have negative EV against very bad players. On the other hand, I have heard a hundred times someone complain that they are losing money because their opponents are "too bad" (for their presumably excellent strategy to work as planned). This is close to ridiculous in most practical settings and also quite self-limiting.
In heads-up, no-rake, NLHE implicit collusion is not possible, so yes playing GTO has a non-negative EV.
>I agree with you that you can probably construct some pathological multiplayer situations where collusion forces negative EV on a "GTO" player - assuming GTO exists in this setting.
GTO always exists, but in the presence of implicit collusion it may result in a negative EV.
> feel pretty strongly that this is not representative of practical reality.
GTO is not representative of practical reality. Very very few people, if anyone, really plays GTO poker consistently. It's an excellent theoretical result, and using GTO solvers and simulators can build up good intuition, but the idea that there are these poker savants playing GTO poker in 6+ handed games is mostly a myth.
Also your claim that you have never seen anyone play against poor players have a negative EV kind of gives away that you are likely overconfident and possibly naive about your position.
I highly doubt you have been in a position to calculate someone's EV while playing poker, or assess whether someone is playing GTO poker against multiple opponents who are bad. And assuming you did possess this amazing power, GTO poker does not guarantee against losses against bad players over any particular night or week of poker. So if you've never observed that then you are likely biased in your observation. You forgot/underweighted the scenarios where someone playing really well lost money to bad players and overweighed the scenarios where someone playing well made money against bad players.
My experience is that talk about GTO poker is mostly used by people to add a more sophisticated and technical dimension to poker, people like to say that a poker play was GTO because it makes it sound authoritative and you can geek out over it, so to speak. People do the same thing across many hobbies including sports.
In reality the best advice for playing poker if you want to be profitable is to find fish and play against them. The sad truth is that there's no shortage of gambling addicts to take advantage of, or people who overestimate their abilities but lack discipline, or heck are simply rich and play poker socially and have no problem losing money and have fun doing so.
That's far more likely to yield profitable results than pretending that you can play an incredibly volatile and dynamic game like poker with anything remotely resembling game theory optimal.
I see good poker players lose to bad players in a single session all the time. Even if you are crushing with a +15 BB/100 hand winrate you’re still going to lose 30-40% of your sessions. That is not an indication of negative EV.
I’ve never seen someone who understood poker very well have a losing record over a long period of time against bad players. I don’t disagree about humans never playing actual GTO, which is why I use phrases like “remotely close” to optimal. My point is that the bar is low enough that any reasonable deep attempt at learning and approximating optimal play should clear the bar to be +EV against bad players.
Parent comment says “if you’re playing GTO against clowns you’ll go broke because they are too bad and you are too GTO.” I strongly disagree with this - the reason you have negative EV is not because you are “too GTO.” If you losing money in expectation you are just not very good at the game yet. What is needed is to understand the game better (and moving closer to optimal play is a reasonable goal). I suspect you agree on this - any reasonably good player should have positive EV against fish, regardless of whether they go out of their way to exploit.
If I were teaching poker in a university setting I would generally work with a bunch of toy games to teach concepts of polarization, MDF, indifference, and so on. Those are the fundamentals of poker theory in the modern environment.
I'll give you a concrete example. In lecture five at 15m he starts talking about donk betting, which is when you lead out with a bet on a street into the aggressor from the previous street instead of checking to them to let them bet (for example, you're the big blind, you call a raise from the button preflop, and then when the flop comes you bet directly yourself instead of checking). He mentions that this is unusual, which is true, because normally you would just check and let the person with the betting lead bet into you if you have a good hand, and so the donk bet is typically weak--but then he goes on to say that advanced players may exploit this perception by donk betting with a strong hand knowing you will interpret it as weak, and then you can exploit that line of thinking, etc.
A more modern view of donk betting is this: the "betting lead" is not anything inherent to the game but just an artifact of the range of hands each person has. Typically when you call preflop from the big blind, you'll have a wider range of hands than the person raising preflop, because they can't raise too wide profitably due to players left to act after them, and you get to both close the action & also get better pot odds on your call from the big blind. Not only do you have a wider range of hands, then, but you also lack the strongest hands (AA, KK etc) because you would have reraised (3bet) them preflop. So overall, on most flops, the preflop raiser will have a stronger range of hands and can thus be expected to "take the lead" betting.
But! There are some flops that can neutralize or even reverse this range advantage. The flop 654 rainbow is now better for the big blind than for an early position (EP) raiser, because the big blind will have many straights, sets, two pairs, and pair+draw hands in their range, while the EP player will generally not have these hands. The EP's big pairs (AA, KK etc) are less strong, and some of their other strong hands preflop like AK or AQs have totally whiffed too.
As a consequence, it is correct for the big blind to have a donk betting strategy in this situation--the way the two ranges interact, the big blind is now incentivized to put money into the pot directly, and in fact, if the big blind does not have a donk betting strategy on this flop, the EP player should respond by virtually never betting themselves. The big blind is incentivized to bet frequently with a small sizing and put pressure on EP's overcards; if you have, say, 86s, and you can get a hand like QJo to fold, that's a pretty decent result on the flop, because QJo has six outs to improve to a better pair.
Anyway, sorry that this example was probably hard to follow if you don't play poker, but it's probably illustrative of some of the ways in which poker theory has evolved over the years--more focus on the specifics of range vs range interactions. There are many more complicated and intricate examples on turns and rivers that solvers are very good at finding but may or may not be obvious to humans.
source: semi-professional online cash game player
Note that most poker games were very easy in those days. You'd log in and enter a couple of tables where most of your opponents were going to take the name 'Hold'em' very literally, also some of them were drunk and you could basically expect them to bet with anything without paying any attention to your table image.
So the optimal strategy in those days was to simply wait for solid hands, you would get paid for them anyway even if you had been folding everything for the last hour.
Solvers love completing the sb. They also occasionally like to open limp on the button against certain strategies - another thing that would have been sacrilege not that long ago that’s completely commonplace now. The “donk bet” once belonged there too.
Making $25 an hour on average isn't just hard, for the overwhelming majority of players it's impossible, and for the group for whom it is possible, it will take a lot of time, and a lot of hard work to get to that point. And even when you get to the point where you can make that kind of money, variance will still kick your ass from time to time, and it can completely drain you emotionally.
If you do want to try, I suggest you learn how to play the game, find some games (either online or live) and see how you do. Keep track of your results. Reflect on your play. Be honest about why you're winning and why you're losing.
I think poker is best played for fun, and if you manage to learn and play well enough to the point where you're consistently making money, that's a bonus, and perhaps an opportunity to take it to another level.
But again, if you want to find out just play the game and see how you do. Find stakes you can beat and try to move up.
- https://github.com/elliottneilclark/rs-poker
- https://docs.rs/rs_poker/3.0.0-beta.7/rs_poker/index.html
Future Goals:
- Complete CFR bot
- Create training corpus of full ring to heads up play
- Train a model
It's free, no ads, we don't sell (or even collect for the most part) your information, etc.
Back in the day I did some work on fast hand evaluators in C and wrote in Objective-C the first software to deal multi-table poker tournaments (on IRC) on the internet.
I understand that these are people who are willingly coming to play the game and putting up their money but I just don’t feel comfortable intentionally seeking them out to take it from them.
Pretty sure that means I’m simply not cut out to play the game but the theory is definitely interesting.
It's typically older people who have "a system" and are trying to implement it, losing their savings in the process.
Also of note, at JHU, an "intersession course" is a kind of mini-semester taking place late december-early january (hence intersession, between fall and spring). you may take one or take a break as you please. if you take the course, usually they are cute and interesting as we see here, and count for 1 credit.
The future of online play will be catered more toward teaching, solving, and tracking hands, rather than playing competitively for profit. I recently started a side project in Rust to do just that, mainly for love of the game and desire to learn the language.
Hoping to release later this year and perhaps productize if it gains traction.
Referencing a solver while playing (what people call real-time assistance or RTA) is definitely a problem in online poker and is always prohibited. Solvers however play in a fairly predictable way and poker sites can detect if people are using them, though I'd imagine imperfectly. Saying that 99% of online poker is vs AIs is a hilarious overstatement.
But it feels to me a bit awkward that I can't use all the tools that could help me play a better game. But of course rules are rules. In Formula-1 you can only drive a specific type of car. But the car-machine still helps you move faster. The car has a cockpit and I assume it is much computer controlled.
The prevalence is an open question, though. I imagine it's rather high since there's a huge incentive to cheat.
I'm trying to work on this myself in my spare time.
No we are not. Poker skills (even at a high level) go beyond live tells.
People spend thousands of hours trying to grasp it.
In a 100BB 6-max game in a single raised pot BTN vs loose player on Bb, who called your raise: is the J83r a good flop for a small bet? Maybe a bigger bet is the proper size? This is a simple question that has often a correct answer and the question is different for each flop, for each preflop spot and potentially for different opponents.
Now once you have figured out betsizes on the flop - go figure out which actual hands you are supposed to bet. Hmm, you should play most hands with mixed strategy of check and bet, but with different probability distribution so that your distribution of good hands / bad hands on the future streets after called is right on a variety of turn cards.
You can spend all life mastering that part alone and we are talking only about the first decision on the flop in single raised pot.
Tldr; poker theory is not something easy and quick to master.
There's certainly a part of me that wants to go thru this curriculum just to say that there's no way it could help someone to be better than an 'average player'.
Perhaps if the population on which the average is based is...the world?
Further, I disagree with your point that the mathematics of poker (implicitly top tier highest level poker) are not complicated.
(edit) to your top line point: > My intuition having played recreationally is that the absolute optimal move in poker is relatively trivial to calculate compared to chess/go.
While the branching factor of Go is between 10^250 to 10^361 (and chess is ~35), poker is 10^17 to 10^165 depending on the game variant: ""Thus, the game tree for no-limit has a much larger branching factor and is significantly larger; there are 10^165 nodes in the game tree for no-limit, while there are around 10^17 nodes for limit (Johanson 2013)" - Sam Ganzfried, Reflections on the First Man Versus Machine No-Limit Texas Hold ’em Competition
...though it's the hidden information component which ratchets up the complexity and leads to a game tree size that's many orders of magnitude higher. If you're curious about that, there's some great info here on other aspects which add complexity: stack depth, multiplayer scenarios, etc: https://poker.cs.ualberta.ca/publications/billings.phd.pdf
That said, I do agree with a relaxed version of the point you're getting at: some subset of high level poker skills can generalizable quite well to other jobs.