19 Dec 2024 Advanced This material is for experienced players distance equity EV GTO probabilities variance In today's article, we'll cover the top 10 most important poker concepts and topics about how poker works. It's designed to help you overcome common leaks, improve the way you learn, and change your mindset to more reliably achieve success in the long run. The article will be useful for both mid-stakes and low-stakes players. However, micro-stakes players will also be able to learn some crucial mechanics which they will use later on. #1. Mechanics of game theory Learning how game theory works is one of the most misunderstood topics in poker. In general, you should start learning poker from the absolute fundamentals (as well as returning to poker after a long break). The problem with poker is that the «feedback loop» only works over a long distance. The overall graph as the sum of all your tendencies is, of course, representative even over 100,000 hands, but if you are interested in more specific spots, then the distance should be really long. Here you can get rewarded for bad plays and punished for perfect play - all because variance plays a very significant role in poker (more on that later) and the advantages between players are very small. I will tell you this: If you decide to learn entirely from your own mistakes and go your own unique way, focusing solely on your personal experience, then you will suffer in poker: you will waste a lot of time and money. We haven't even gotten into what kind of desire you will have to play it in the end. Therefore, if poker for you is primarily a tool for making money, and not just a game, then you need to master fundamental mathematical concepts as quickly as possible: EV, Equity, Exploitability, Combinatorics, Equity Realization, Indifference, Minimum Defense Frequency, Pot Odds, SPR and a number of others. It is clear that you will not always have to figure them out right at the table - but it is important to pump up your intuition of how it all works. Here are some examples: When a live opponent bets big, it should be intuitively clear to you that you need to continue the hand narrower than if a solver or bot bet the same way. When the SPR (stack to pot ratio) is low - that is, there is already a lot of money in the pot relative to what is left in your stack - you need to play with a wider stack than when the SPR is high. And indifference means that the available options for playing the hand have the same EV or they are close in expected value. This often happens on the river with a medium or large pot: the opponent makes a big bet, and you need to decide how to play your medium-strength hand - call or fold. They will have a close EV, or (more often) a fold will be slightly more plus than a call. But you do need a sense of how this game’s mechanics actually work to become successful. You need to understand what hand strength (relative to the board texture) is appropriate for what line you’re taking. Stacking off in a 20 SPR pot with top pair no kicker is seldom warranted. Folding a set just because a two-card straight is possible is almost never going to be correct in a low SPR situation. You need an idea of what is appropriate. How do you develop these senses? Well, start with thresholds! And this will be in the next point. #2. Thresholds One of the fastest ways to become a solid player is to learn the limits (thresholds) of ranges. Thresholds / limits of ranges are lines of indifference. You can also simplify the orientation in this concept - the weakest hand from a stronger range or the strongest hand from a weaker range. The boundary of the continuation range (its threshold) looks like the line between the strongest hand of those that you fold and the weakest of those that you continue in the hand. You can shorten this definition as simply the weakest hand in the continuation range in this situation - it will remain understandable, but is written several times shorter. The threshold of the value-bet range will be the weakest hand within this range, with which you will still bet for value and expect to be ahead of 50+% of the opponent's continuation range. In this picture, the colors indicate 3 ranges and clearly show the thresholds between them: Red is the value-raise range in response to a bet, Green is the call range, and Blue is the fold range. Understanding where these boundaries are between different ranges (raise / bet / check / call / fold, etc.) in different conditions: On different textures, Between different positions, With different stack sizes, etc. It is extremely important when determining how and with what to act first or react to an opponent's action. For example, You are planning a third thin value bet with TPTK (top pair + top kicker) Against a tight reg in early position who is unlikely to pay you a 3rd bet with worse hands than your actual TPTK, the threshold of the thin value bet range will be this TPTK (sometimes OverPair / lower doper). Against a calling station fish with stats like 72-8-3, the threshold of the third thin value bet range will be almost any second pair with a high kicker - depending on the bet size and other circumstances. Specifically against such an opponent, your actual TPTK will be at the lower limit of the thick value bet range (when you are willing to get it all in). Similarly with the thresholds of the calling ranges for 3 barrels in a single-raised pot on a safe final board. Against 3 barrels in SRP from a nit, the threshold of the calling range will be approximately TPTK-OverPair. Maybe, a doper - depending on his tendencies and stats. And against a maniac fish, whose 3-barrel range will be overflowing with bluffs and total trash by the river, the threshold of the calling range will be almost on the third pair without a kicker. Or just on A-high. Similar ratios are between other ranges: raise / check / fold / donk and other actions at the table. Not very experienced players are constantly confused in these thresholds and often either overplay medium-strength hands, or underplay them. They either overfold where it is still too early, or overcall when it is already brings a loss. Regular training in working out the feeling of your thresholds and boundaries is one of the most effective and ... easy ways to become a better player. #3. It's not about your hand, it's about your range We assume that your opponent is a reasonable and thoughtful reg, not an amateur who came to have fun. Instead of thinking about how to play your specific hand, always choose an action based on how your entire range wants to play in the current situation. Zoom out and look at the whole picture - this is your range, where your specific hand is just a part of it. How to play a specific hand is of little importance. What is more important is your entire strategy in the current situation. For example, you should not triple-barrel on your opponent's board just because you could have a semi-mythical gutshot there, which is 1% of your entire perceived range. If the range needs to check and lose the hand - so be it, because this is the maximum plus against the background of other options (or the least unprofitable, in other words). One more example: When you triple barrel, you should have appropriate hand classes that match the amount of money you put into your barreling. The proportion of bluffs to value should match the bet size. For example, if you open 86s as part of your entire range, then the frequency of opening that particular hand becomes unimportant if the range is generally balanced and your opponent is just as likely to run into AA as he is to run into 86s. What would matter here is what percentage of hands you open preflop. Too many hands - you can be exploited expensively by 3-bets (and 5-bets to your counter-4-bets). Too few hands - the top of your range will get much less value. And in a narrow range, it takes up a larger share than in a medium or wide range. The general conclusion of this point: what matters is what your entire range wants, not what a small part of it wants. #4. Maximize EV, not how often you win the pot Winning the maximum number of pots does not mean maximizing EV. In theory, this may coincide, but in human reality, everything is much more complicated, and the desire to maximize your EV will often mean losing a specific pot. The human brain remembers losses much better than wins, And this creates a tendency for new and inexperienced players to strive to win every pot at the cost of maximizing EV, which takes a different place. The player tries to take the pot at any cost that he is willing to risk, but to take the pot as quickly as possible, before the situation gets worse, and not to play as +EV as possible. That is why they begin to overplay medium-strength hands, overfold where they have large implied odds, when, for example, this means that they will lose a small pot more often than they want, but at the same time completely refuse the opportunity to win a huge pot, etc. Example with a dice Let's imagine that we are throwing a 6-sided dice. If it comes up from 1 to 5, then you give me $10. - How do you feel before I specify your risk reward? - I guess you don't want to lose 5 times out of 6, and also pay ten for it, right? And now the main thing: if it comes up 6, then I give you $100 right away. Well, will you fit into the game now? - Definitely! - Your EV will be as much as +8.33$ for each throw. That is, now you agree to lose 5 times out of 6, but at the same time play with a good profit in total. When you clearly understand what expectation such and such an action has, you will agree to it without problems, even if it promises frequent losses, but a large profit in the sum of all situations. In poker, it's all the same, but in thousands of different situations that invariably repeat themselves over time. It's just that some more often, and others less often. - Bet on those that will be more +EV, and it doesn't matter what frequency of losing the bank they entail. #5. Stop overvaluing big cards How many amateurs and inexperienced micro-limit regulars overvalue hands with high cards: any Ah, broadway, etc. - for them these are strong hands regardless of the current situation. Preflop For example, they get a 3-bet or, God forbid, a 4-bet - and they can't fold a hand like AJo or KQo, although in the realities of micro-stakes - on these nitty fields - you shouldn't defend with a call out of position even with suited versions of these hands - extremely narrow ranges will destroy you by kicker, and you still won't clearly understand what to do: calling becomes more and more expensive, and folding becomes more offensive with each street of betting. Postflop Another example, but with a high overpair. On the preflop, of course, you almost always go all-in with a hand like QQ, except for the ironclad information that the opponent is a nit of nits. It won't always be a plus, but often it's a little more plus than folding. However, here we are talking about postflop. Imagine that you opened and bet the flop, bet the turn and bet the river - any river at all. And your opponent check-raises (or check-pushes) you on your third bet. - How often do you call here with QQ, KK, AA and top pair with top kicker? That is, with a hand of rank no higher than «one pair»? And how often did you win after these calls? And the reality is that they will mostly show you two pairs or a hand even higher. - You will draw your own conclusions. A big hand preflop does not mean that it will always be big postflop Many of these calls are due to the fact that the player believes that since he was dealt an overpair preflop, he is now obliged to win this pot - that he is guaranteed to win. The same applies to catching two pairs and higher postflop, and what happens on subsequent betting rounds clearly indicates that the opponent himself has made a hand even bigger than the one that you were lucky enough to make first. Poker does not work the way we expect it to with settings suitable for normal life. Everything that was described in this point shows those boundaries and kind of breaking points, continuing to play after which will destroy your entire win rate with such hands. The big EV that you earn by barreling with TPTK overpairs+ is crossed out by the triple loss from catastrophic calls / counter-raises when you have indicated your readiness to play for stacks. This might be acceptable in short stacks, but in full and deep stacks it's a crime against yourself. And we've already said about off-suit hands preflop against active opposition - there aren't many options there. Got a (check-)raise on the turn or/and on the river? - That's it, FOLD. - A single-pair hand is no good anymore. #6. Most of your EV comes from nutted hands I will write this point in the chain «Thesis - Explanation - Conclusion». In poker, the main part of EV comes when we «cooler» our opponents. A cooler is a situation where everyone played optimally, but the winner was the one who had an even higher hand than the others - and therefore he won. Accordingly, to «cooler» someone is to set up a situation where it is difficult for the opponent to get out of losing a large bank or the entire stack. However, coolers can be different in quality and size. Look at this chart: It shows the EV of all open hands over the distance and those that were played postflop. What immediately catches your eye? - That only 10% of hands consistently bring profit: 77+, A9s+, KTs+, QTs+, JTs, AJo+ and KQo. And this profit is more than 80% of the total EV that the entire opening range generates. Most of the other hands in the range are only for steals on BU and CO, as well as for diluting this 10% top in the entire range - so that opponents expect far more than just the designated hands with confirmed autoprofit. In fact, they have a minus or near-zero EV. And in the matrix of your tracker, you will see a similar picture. Therefore, the preliminary conclusion is obvious: Only ~ 10% of hands in your open raise bring you the main profit. The rest of the hands are here for other purposes. And that's why it's extremely important to be able to play your strong hands in the best possible way - both preflop and postflop - and to get paid as often and as hard as possible. We're talking about hitting value hands (doper+) postflop here, but we're only talking about starting hands in detail - this should refresh your perception considerably. If a player is a total nit, then he will be poorly paid by others, because his nittiness is obvious even without any statistics. However, the other extreme is also important - if you play too wide and aggressively with your weak and near-garbage hands, then although you will increase your income from strong hands, the losses from other hands can completely nullify this profit. How much real EV do different hands bring - a visual chart I want to show you a table of EV starting hands in the opening range on BU of one of my friends. He recently published it on the poker forum «2+2». It shows the EV of each hand in the range of open-raise on BU taking into account the subsequent postflop. The size and color of the cell reflect the share of expectation that a specific hand actually brought over the played distance. As you can see, premium hands bring the overwhelming share of the entire EV range. - These are AA, KK, QQ, JJ, TT, and also the hand AK. This particular group of hands brought my friend 66.37% (2/3) of the entire EV range. - In the best position called BU. - It is not for nothing that premium hands are called premium. Note that even such a beautiful and high hand as AQs is a whole jump in EV away from them. The rest of the hands, as I already said, are here in the role of decorations - they have other tasks: Profit from steals and a small autoprofit from continuation bets on the flop, as well as Help in paying premium hands - the range is blurred, and the opponent expects not only nuts there. On the postflop, obviously, a lot can change, and other hands can become nuts, but summing up preflop and postflop, your main "assets" are located in the top 10% of the starting hand matrix. Therefore, how you play them is many times more important than barreling and check-raising with draw hands and trash when there are big holes in the opponent's stats. And we return to where we started: In poker, the main part of EV comes from the fact that you cooler your opponents, catching top starting hands on the preflop and hitting nut combinations on the postflop + playing them as profitably as possible. And in order to get under the cooler of opponents as rarely and cheaply as possible, you need to hone your strategy. But that's a completely different story. #7. Start by mastering your preflop strategy Preflop is a fundamental part of the hand. Mastering preflop perfectly is the fastest and most effective way to dramatically increase your win rate. Good preflop play translates into confident postflop. Everything happens from street to street. Once you hone it to automatism, playing at subsequent stages of the hand will become much easier: You will be able to think less on the preflop, Dedicate resources to better thinking through the game on the postflop, You will not have to dig through a bunch of statistics, HUDs and info on websites, You will be much less tired from the game and, accordingly, you will last much longer. Numerous preflop charts, which are abundant on the Internet, preflop trainers, as well as training modes in solvers can help you with this. Really, make your preflop strategy automatic. This allows you to confidently put in more volume, make fewer mistakes, and sets you up to play well on future streets. #8. Most of your heuristics are based on lies This is a somewhat controversial point, and many of you may actually disagree with it. But we will still state our position. Heuristics are methods / techniques / generalizations that help solve a problem quickly and with acceptable quality, based on incomplete information, rather than spending a lot of time, nerves and other resources searching for the ideal solution. But there are several significant «buts» here. One of them is the already mentioned incompleteness of information and, as a result, a lot of assumptions and speculations (often illusory). Almost every heuristic you come to is inevitably based on partially false assumptions. Because if you try to improve through personal experience, then your perception of a profitable game will be distorted by the meta in which you play. As well as by such factors as risk propensity / aversion, the desire to win the pot as often as possible and others. To truly grow as a poker player, you will have to break old habits and expand your horizons, both in terms of what is acceptable in your game and in terms of new horizons in general. This will be especially true when you start practicing solvers specifically. Solvers can be very confusing. And the vast majority of people have acquired, over the years, unshakable illusions and global-scale beliefs about how poker should work in their unique case and how - therefore - they should play it. Players also have a confirmation bias - where they look for anything that even slightly confirms their current beliefs and results. They look at a strategy or move and are more likely to adopt something that fits their picture of poker. But they rarely, if ever, think about why their current view might be wrong. This is true not only in poker, but in any human endeavor in life. One last thing that supports our claim that most of your heuristics/generalizations are based on lies. You know that feeling that the more you understand something, the more you feel like you understand less and less of the big picture with each new step in your development? - The great Socrates once said, «I know that I know nothing.» - How are most of us better than people of that stature? Try to challenge your assumptions. Go out of your way to look for counterexamples to your theories. The goal is to expand your mind rather than reinforcing your current view. #9. Variance is bigger than you can imagine The so-called «Gambler's Fallacy» is an extremely common illusion among poker players, and exceptions are probably extremely rare. First, a slightly abstract example. You flip a coin. The coin is normal, without a shifted center of gravity, so the chances of getting heads and tails in the long term are identical and equal to 50%. In the first 6 flips, the coin landed on heads all 6 times in a row. And what would that mean? How did this change the probabilities that on the 7th flip the coin will land on heads again? And on tails? If you are a very suspicious player, then, like most amateurs, you tend to think that now the coin is almost obliged to land on tails, and you can even bet some symbolic money on it (and a larger amount?). But in fact, the chance is still the same as in the long term / over the distance = 50%. The probabilities of getting both heads and tails remain the same as they were before the first throw: 50 to 50. This phenomenon is described by the so-called «Law of Large Numbers». You don't have to study it all, but it is enough to learn just its basic axiom, which sounds like this: The probabilities of an event over a distance and in a specific case remain the same. And if there are deviations in a short sample, then over a distance they will still level out to the true probability. After a conditional 100 thousand tosses, the numbers of heads and tails will be very close. Imagine that we continued the experiment and tossed a coin 1000 times. Over a distance of 1000 tosses, it turned out that heads came up 6 times more often than tails: 503 heads against 497 tails. What conclusion can be made based on this sample? Compared to a sample of only 6 tosses, we got a probability realization very close to its mathematical expectation. It was 100 / 0 in favor of heads, and now it is 50.3 / 49.7. If we extend the tosses to 10 thousand, the results will converge even more strongly. Up to a million - almost 50% and so on. But on a segment of specific 5, 10, 100 or even 1000 times the deviations can be huge. Tails can easily overtake heads on the next 1000 throws, for example, appearing much more often than heads appeared during the first 1000. I don't know how and why it works this way, but in the world the realization of probabilities works in such a way that the long run will inevitably equalize all this. Back to Poker Just because you’ve had bad luck doesn’t mean you are «owed» any good run. The deck owes us nothing. Each hand is an independent event without memory of how we got our aces cracked. The fact that you were unlucky for 1 hand, 1 session or 1 month does not mean that the RNG owes you. Of course, you can think of it this way if you want, but the EV realization will not happen any faster because of this - it is not in your power. The opposite is also true. Just because you’ve run well doesn’t mean you’re owed any bad run. So, if the opponent completed the draw and coolered you for the 3rd time in a row, the probability that in the next hand he will be lucky to complete the draw again has not changed - all the same 18-20% per one street. The truth is that variance in poker is far beyond what humans are capable of truly conceptualizing. If you’ve ever played around with a poker variance calculator, you’d find that it takes tens of thousands of hands before you can see a statistically significant edge materialize. We’ll discuss poker variance calculators more in future articles. The way of the play, as well as the perception of what is happening, will be in your power. The cards themselves and the RNG do not have a memory and understanding that due to their trick you lost money in a very offensive way - it just happened. There is an extremely high variance in poker and it is everywhere, and its manifestations can be described in more than one article. For example, You were dealt AA? - You got really lucky here. The opponent was dealt KK? - He was incredibly lucky relative to your entire range, but incredibly unlucky against a specific hand in this particular hand at the same time. A fish entered the pot with a pocket pair? - He was unlucky with his hand against your hands, but ... he flops a set => If all 3 of you go all-in preflop, then for you with AA this will be a badbeat (while the community cards are dealt after you open your holecards), for a player with KK this will be a terrible cooler (vs your AA), and for the fish - a reason to play poker a lot more often. If you go all-in on the flop, then the cooler will be for all of you except the fish, because you both run into a set with such equities: Well, if one way or another you dealt the turn and/or river with closed holecards, and an A or/and K or/and 8 came out, then you can come up with your own names for all of this. In general, in poker, a lot of things that concern the perception of success/failure are relative and depend on a lot of variables and dozens of conventions. However, what should be important to us is not the quality of luck, but something else - the quantitative influence of variance, the swings of up and down streaks, as well as the probability of ruin. Therefore, we need to properly configure our brains and - most importantly - the perception of the magnitude of variance and prepare for it in advance. It was here, is here and always will be - but our actions will be in our power. Online tools such as variance calculators will help you. They calculate several consequences of variance based on the parameters you enter and visualize its work to illustrate what can happen - as well as with what probability. Primedope One of the most popular and authoritative variance calculators is available via this button. Choose a cash game variance calculator if you are interested in this poker format. If tournaments - then tournaments variance calculator. But we will limit ourselves to several illustrative examples of cash games. Visualization of the consequences of variance Let's enter the player's parameters and click the «Calculate» button. Let's assume that you have a good win rate of +5 bb/100. We will set the standard deviation (variance of the game) as 100 - this is the norm for TAGs who are able to bluff, but do not play as widely and wildly as LAGs. We will first set the distance at 1,000 hands. And what do we see? The most important thing we should pay attention to is the probability of getting a loss (not losing the bankroll, but getting a minus of any depth), playing with the same parameters / manners / opponents / at the same limit. Even after 1,000 hands it is as much as 44%. - A high chance that you will finish this particular sample of hands at a loss (and this is only 1 session or even shorter). After 10,000 hands, the chance to end up in the red = 31%. After 100,000 hands, you still have 5.7% to see a minus in the cashier. And this is with a good win rate of + 5 bb / 100 and Std. Dev per 100 units. Many people do not play so much even in a year. And a typical average regular plays so much in about 3 months - and still has about 6% to play at a loss (excluding rakeback and other external payments). - What desire will you have to play after this, if you are in poker purely for the money? After playing around with variance calculators, you will see for yourself the magnitude of poker variance - especially in tournament poker. We cannot imagine such a number of hands in our minds, and even more so that it is in the minus - so you just need to be mentally and financially prepared for this. But the opposite is also true: you can crush your stake by +25 bb/100 over a distance that seemed good and post graphs on forums / in social networks / send to friends in messengers, but in reality you - really - can be doing so well. You will not study your entire distance under a microscope and count and compare different manifestations of luck in thousands of hands, will you? - You will not, therefore it will also be wrong to unequivocally state that you break the limit purely on skill. The reality is that Poker is a game of both skill and luck There is a common belief among high stakes players that a poker player's career is largely determined by variance. And to a large extent, this is true. Not 100%, but to a not insignificant degree either. Recently, the results of an experiment on the game of 6 GTO bots with each other at the same table, which play perfectly and according to the same program, were even published. The result is that even at a distance of 5+ million hands, they have minimal differences in actual win rates, although mathematically it should be the same for all 5 bots - 0 EV. But some play with micro-profit, others at zero, and others - micro-loss. And we, living people, also pay rake. Therefore, in order not to be slaves to variance all our lives, it is most profitable for us to play as often as possible with those players over whom we have the maximum advantage in skill, and as rarely as possible with those who are at least close to us in skill. Not to mention those against whom we have a clearly negative EV. That is, ideally, this is 100% of hands with the worst fish in the world and 0% of hands with regular opponents. The influence of variance (randomness) is generally great in life: starting from the stock market, which is the closest to poker in terms of generating profit, and ending with completely human affairs. You can take risks and act perfectly everywhere, but still not get the result you expected. But we are talking about poker here, and we should just be ready for the worst that can happen in it. Just like the greatest upstreak, the most unimaginable downstreak in poker will always be ahead of you. And sooner or later you will get into it. Have you already gone through more than one terrible crisis? - There will be an even more terrible one. So get ready for it! The longer you play, the more guaranteed this is... and your most phenomenal upstreak is also waiting for you ahead. #10. Stop overplaying medium hands This is a very common leak at low stakes. Most ineffective but aggressive players have only two ranges: Which they give up right away, And with everything else they press the gas pedal. They win too rarely at showdown with medium hands because by betting too often / too much with medium hands they either knock out weaker hands or go to showdown against a range that blows them to smithereens. - This is a bad way to distribute equity across a range and the entire game in general. The problem with overplaying medium hands is that you often just end up folding out worse and getting called by better. It’s a very inefficient way to organize your equity. This style really only works well against calling stations. It’s easy to exploit. It will be much more effective if you have 2 clear poles of hands in terms of their strength - value and bluff - and also a gap in the form of these very medium hands. Then with each bet you make, your opponent will only be left to guess what you are betting now - with a value hand that he does not want to see at the showdown or this is just a powerful bluff. You need to have a range in almost every postflop situation that has a lot of medium and SDV hands that you can confidently check back / pot control / call probets from your opponent on the next street. And when your medium-strength hands check more, they will more often showdown (check or call) against the hands that they beat. Believe me and check - such a strategy will bring you much more profit than persistently playing for knocking out and pressing, not allowing the opponent to reach the showdown. This article was written by Vladimir ABIVPlus based on the 10 Most Important Concepts for Poker Players video.