Honestly?
Patience.
Every weakness in poker can be traced to a lack of patience. A lack of patience is why new players play way too many hands. A lack of patience is why people start getting superstitious in an effort to win sooner. A lack of patience is why people focus on recent results and not on process and math.
Patience allows you to wait for the right spots. Patience allows you to take the time to do a little reading or watch some online coaching. Patience is how you learn.
Imagine there was a version of poker where everyone played with their hole cards face up. It’s trivial to see that there is a mathematically optimal way to play this game. There’s still an element of strategy involved since you don’t know what the community cards will be but you can model them from a probability distribution and derive your chance of winning and derive an optimal better strategy. Given a fixed series of cards being dealt and assuming optimal play, it’s possible to predict the exact state of the pot after that series of hands without anyone having to sit down and play. (We’ll call this Skill Level 1)
Now imagine a variant of poker where you’re at the table with 5 AIs who can see everyone’s hands and play with exact optimal play and you who can’t see anyone else’s hand. There’s still optimal play possible, it’s just an extra level of difficult involved. You can still observe the bets made by each AI & reverse derive the hand or series of hands that is the only one consistent with that action and, therefore, what bets you should be making against this probability distribution of hands to perform optimal play. Again, there’s a derivable, mathematically optimal strategy in this scenario, even if it is computationally extreme. (We’ll call this Skill Level 2 and Theory of Mind 1 because it requires you to simulate the actions of one level of mind to implement).
Now, imagine you’re playing a 3rd variant of poker where the other 5 opponents are Skill Level 2 AIs , they will play mathematically perfect games but they assume the signals they’ve been getting from the other players must only be coming from mathematically optimal Skill Level 1 players. This is the first interesting variant of poker because this is the first one where it’s possible to get an edge. To succeed at this level of poker, you need to be able to simulate Skill Level 2 poker AIs in your head and know what they must believe if you perform any given action and lead them to believe the maximally inaccurate thing in order for you make the biggest +EV for any given hand, this is a bluff. We’re increasingly getting into deeper realms of computational infeasibility but this is still mathematically optimal play since the behavior of Skill Level 2 AIs is completely deterministic and thus your response must also be completely deterministic. (We’ll call this Skill Level 3 and Theory of Mind 2 because it requires you to simulate a Skill Level 2 player).
Now we get to real poker where you sit down with world class players. All the players have varying but generally pretty high levels of Skills 1, 2 & 3 to get to this point and this is the point where real poker begins. If person A does this action, under mathematically optimal play, that means that they must have this hand/set of hands but person A knows everyone else can figure that out so maybe the real reason they played that action is because they believe person B has X and this action is the maximally effective bluff against X but of course, person B knows this so… ad infinitum. (We’ll call this Skill Level 4 and Theory of Mind ∞ because it requires you to simulate an infinite level of minds who all simulate other minds). This is the first level of poker that moves from mechanical to artistic because there’s not any one right answer, there’s an infinite series of contingent assumptions from which you must guess to derive an edge.
Skill Level 4 is the real skill in poker, it’s where poker moves from a mechanistic game to open up in to an artistic one. I view poker as a kind of language, and the act of reaching Skill Level 4 as like, learning to create beautiful conversation in that language. The act of sitting at a poker table is speaking to each other in bets rather than words and listening to those bets and responding with your own in a way that forms a grammar and a cadence and ultimately, hopefully, something beautiful that has never been said before and will never be said since. Unlike most languages, it’s a adversarial instead of collaborative language where the beauty comes from stymying the other person but that styming can be beautiful for those who are capable of “reading” the language.
Even though Skill Level 4 is the real skill, you can’t hop up to there without mastering Skill Levels 1, 2 & 3 first. Like in English, if you want to make beautiful sentences, you first have to master the rules of grammar, you have to know what came before you and you have to know what delights people so you can produce something truly original but you learn those things so you can express some beautiful words. There is an end point of natural diminishing returns to learning more grammar, there’s a further but still foreseeable endpoint to digesting enough culture to be able to draw upon whatever cultural reference you need to communicate a point. But there is never an end point to how beautiful you can make a piece of writing, how funny you can make the next joke, how striking a turn of phrase can be, that’s a lifelong quest because the complexity is fractal and unending. Same with poker, the jump from Skill Level 2 to Skill Level 3 is TOM1 → TOM2 but the jump from Skill Level 3 to 4 is TOM2 → TOM∞. There’s additionally conceivable skills you can posit lie further on, how to manage a room and be sociable, for example, or how to extend the lessons of poker into life in ways that make you a stronger poker player etc. and we can get endlessly philosophical about it but Skill Level 4 is a concrete encapsulation about what initially enthralls people about poker and the endless depth of complexity it can plumb.
I think that’s the key. I used to play in a weekly game with 6 others. Five of us (including me) would win $10 or $15 one week and lose the same the next. One guy won every week and the last lost every week. The regular winner folded much more often than the rest of us, while the loser hardly ever folded. While we were hardly experts, we were all professors of mathematics.
Of course, just like there are tricks to sum infinite series, there are often tricks to simulate infinite-level theory of mind. For a (much) simpler example, Rock-Paper-Scissors also involves an infinite regression of bluff and counterbluff, but those levels of bluffing go in a repeating cycle, such that there are only actually three levels of bluffing one need consider. And even if you can’t find a clever trick to close the calculations exactly, also just like infinite series, it’s usually good enough to calculate just the first few terms.
yep, my apologies. I guess I was confused when you referred to the hard part as being the mathematics and the bluffing, when what you’re really talking about is the mathematics OF the bluffing. That is, bluffing, while a psychological component of the game, should really be analyzed as one aspect of of game theory. And it is the calculations of that, and optimal bluffing strategy, in light of the amount of bets on the table and the cards that are known to a player in a given hand, is what is really impossible to calculate optimally for players in real time.
I don’t feel bluffing is really a mathematical issue.
If a person has four clubs showing, for example, along with a hole card and starts betting, he’s not doing this on the basis of percentages. He knows what his hole card is and whether his hand is a flush or worthless. If his hole card is a diamond, then he knows with one hundred percent certainty that his hand will lose.
I suppose there is a trivial amount of math performed by the other players. (“There’s a twenty-five percent chance he has a fifth club and a seventy-five percent chance he doesn’t. Math done.”)
What the other players are doing is considering the psychological issues of the situation. Is this person betting like he is because he has a winning hand? Or is he betting as if he has a winning hand in order to convince the other players that he does when in fact he has a losing hand?
If I’m following you correctly, and referring back to my earlier post, what you saying is that above a certain level all of the players at the table will be able to do the math. So the difference will come from who has the best psychological skills.
It’s essentially this. It’s all about watching how everyone else bets and noting what they had if showdowns occur. The best players are consistently inconsistent, completely unpredictable.
Everyone loves a player who sees every flop, bets high when they have something, folds when they have nothing, and never ever bluffs, like the way a robot would play if you only gave it the basic rules. Still, an astounding number of people play more or less exactly this way.
As in many other games, I would expect a computer these days to effortlessly outplay and defeat any human, and that every pro uses those programs to practice and sharpen their skills.
Yes, exactly. If you’ve ever played a social deduction game before like Mafia/Werewolf, there’s a lot of similarities. There’s the “surface meaning” of any sentence you say but the art of the game is that everyone is deploying the surface meaning as a weapon to hide their underlying goals. The best way I’ve found to understand poker is that through this lens of language, the main difference is that Mafia uses English and poker uses bets. But once you can learn to “read” bets as a language, the core gameplay is very similar.
Probably most players don’t treat it as one, because we humans have devoted a rather large proportion of our intelligence to the problem of figuring out when other people are bluffing, without consciously doing the math. In the same way, an athlete who’s positioning himself to catch a ball isn’t consciously doing trajectory calculations. But both can be treated mathematically, if you dig down into them, and the mathematical result is more precise and more reliable than the instinctual shortcut.
I still don’t see it. Can you outline for me how a person can mathematically figure out that another person is bluffing?
If you wish, use the example I gave. You’re playing an opponent who has four clubs showing and a hole card. If his hole card is another club, he has a flush which you both see can beat your hand. If his hole card is not a club, he has nothing and you both see your hand wins.
He is betting money, which on the surface is an action he would only take if he has the flush. But he could be pretending to have a hidden club in order to deceive you into folding.
Now mathematically, as I said, you can figure out there is approximately a twenty-five percent chance he was a fifth club and a seventy-five chance he doesn’t. (The real odds are slightly different because of the other cards that are showing.) But I don’t see how you can use math to get past this point and know what his hole card is in the way that you can use math to know where a ball will land.
No, because that’s impossible. What you can calculate is the probability that they’re bluffing, assuming that they’re playing optimally, and then use that and the other known information to determine your optimal play (where an “optimal play” can itself involve probabilities, like “Fold with a 25% chance, or see the bet with a 75% chance”).
Except I can’t even do that here, both because you haven’t given us all of the information (the exact values of all of the known cards, what bets everyone else has made, the sizes of all of the stacks, how much the opponent is betting). And even if we had all of the information, I, personally, couldn’t do the calculation, because it’s a really, really hard calculation. But there are computer programs that can do it.
I mean, just the fact that the best poker computer programs beat the best human players should be enough to illustrate that it’s ultimately all math, because ultimately, math is all a computer program can do. And computer programs were beating humans even before the current AI trend of creating programs that even their creators can’t understand: These superhuman poker programs were created by programmers who understood what they were doing.
The math is based on previous betting patterns along with pot odds. Even forgetting what was played earlier in the evening, was how they played the flop consistent with a hole club? The hand isn’t just the current state of the game, but also how you arrive there.
Also, with the talk of bluffing, don’t forget the value bet, which is sort of the inverse of a bluff. The idea being that you have the strongest hand out there, but you want to convince everyone still in to keep raising by convincing them your hand is weaker than theirs.
And then of course you can make a big bet with a good hand, hoping your opponent(s) will think it’s a bluff and therefore call you. Or conversely, make a relatively small bet with a poor hand, as a bluff, hoping your opponent(s) will think it’s a value bet and fold. But your opponents know about these possibilities too.
Here’s a thing I’ve always wondered: what level of math skill is necessary to be better-than-average at poker? My math skills are best described as “rudimentary,” and that might be generous. I can do simple arithmetic and whatnot, but other than that… Oof.
For whatever it’s worth, my brother-in-law is a math genius, and during the pandemic he put that to use via online poker and was making about $5k a month before my sister put the kibosh on that. I’d ask him to teach me how he does it, but I get the sense that he doesn’t like me (he’s been married to my sister for years now but still won’t accept my FB friend requests lol).
You need very little math skills to be better than average. Drawing odds you can just use the “number of outs x 4” rule of thumb. Then you need to be able to calculate expected winnings of a pot. Then you just need to know what hands are reasonable to play and in what positions.
Now, better than average is still someone that loses money, especially with a rake, so don’t quit your job just yet.
This is what I don’t get. If poker computers can beat the best human players now, how is it possible for a human to still make money playing online? I would have thought the bots would have completely hoovered up the internet by now.
He was playing against other human players. At least, I assume – do online poker websites put in bots to win all the money for the casino?