I dont know if this is new news to anybody but just some thoughts of mine. I'm mainly a PLO player but i see some things relating to solvers and push/fold charts that could be interesting to you guys.

Talking about push/fold charts for NL or just PLO solvers, it is just apparent that math is only 50% of the game. Exactly 50% tbh. If a computer tries to solve poker, and you ended up perfecting the math on a computer program that could play, imagine for a second this computer playing against itself. These percents are off, but say 23% vpip and say 28% pfr or something. This is only in relation to a moving part, which poker is. It is continually moving odds.

This is a big concept. Preflop vpip and pfr are relatively easy to figure out with a computer, but to balance something like this requires the other 50% of poker, which is strategy. Math and strategy are two different things. Chess uses brute math to force its lines with a bot, but poker uses imperfect information. the difference between imperfect information and perfect information is huge for bots/solvers. Solvers can tell you a guide for what the math says, but to go back to the example of bot vs bot, if one bot knows the exact odds that the other bot is using, it can use exploitative play to win by using a variation of bayesian probability.

Bayesian probability is that if you flip a coin 10k times, the result will be approximately 50% heads and 50% tails. but if you add in weight to different rolls, say one roll of the 10k is worth 5k rolls, then you will have a skewed result. This is at the heart of exploitative play, where one bot is playing a solved game, the other bot playing with the same capabilities as this math, therefore knowing the percents of play for each situation, flop preflop etc. It can then bend the odds by spiking certain situations with a knowledge of the perfect odds played by both "players" because information is imperfect. Its as simple as that. The imperfect information leads the people who know the same math as the next guy, but with a better strategy on how to deal with unknown variables, where you can rip apart a strategy where you know exactly the odds of a solved opponent would do, and play aggressively (but smart), with the goal optimally being the the most aggressive but most smart play.

They say to play aggressive in poker, and this old adage is so correct. The imperfect information of poker leads to a couple obvious scenarios, but the main one is that you can win by getting them to fold or at showdown. If you are playing smart then being aggressive is the optimal route, but this cant be solved with math, its up to player dynamics. You might argue this, but in a broader perspective if a every single player folds to a all-in preflop in NL (just say 50bb) , this player having played 1 hand will have made more profit based on a aggression strategy because you generally fold until more information is known.

Simply put, you cant call every aggression or else you run into the problem of calling every hand, otherwise you are folding until you get a good hand, in which case you would be using bayesian probability and then using exploitative play to make money. This is because you are using a model of the mind, where you assume players are using a broad strategy that can be implemented in the most possible scenarios. Shoving all in first hand, then leaving poker forever is a extreme example of aggression being optimal combined with solver info. it is just showing the point though.

Solvers solve the math component, but the strategy is to be aggressive as you can to dominate the balanced strategies of players who have the most money, but done so in a smart way with the SAME math they have. so ya, thanks for reading .

Ok hear me out...

Let's take two of these exploitative bots, and let them exploit each other back and forth! Eventually, they'll reach a point where neither can exploit the other side. Eventually, they'll reach some kind of... "equilibrium" where neither has anything to gain by altering their strategy.


Congratulations, you've just achieved Nash Equilibrium! In fact, this is an oversimplified method of how solvers work.

If it is truly solved, then there's nothing you can do to "rip apart their strategy", as a solved strategy is not exploitable. You've reached a point where both players have nothing to gain by altering their strategy. That's the definition of equilibrium.

It basically comes down to game theory.

Game theory in poker, lioterally the theory of the game is math plus strategy. If you had a bot that had perfect math AND perfect strategy it would be a stalemate. Solvers dont do this. This isnt chess where you could lioterally solve the game. By a bot that solved the game i meant math wise, it was just a long post i posted so i didnt want to get into it too much, just wordy .

You actually cant solve every scenario where there is changing variables from preflop to postflop to river etc. You run into the scenario where you just go full aggro like I said in my OP, and thats the general jist of the strategy component. Its pretty clear that solvers solve the math bit, but its pretty clear to me a aggresive strategy is better then a passive one. That last sentence alone indicates that strategy is involved, not just tactics like a chess ai would use.

Pretty trivial post of mine, its very obvious stuff that strategy is well, strategy (and useful! ). Solvers are very useful, I just wanted to get people out of the cultish mindset if they were so deep into solver ****. haha

Serious question, did you take a PHAT bong rip before posting this?

IM DIFFERENT

Before posting? I think they took a hit before and after each sentence, and 5 more before posting.

play me heads up for rolls

I would never take advantage of someone in your state. Get some rest, you had a long day.

roar

I just looked up how poker solvers work, and they mainly do a range analysis instead of pure math based, which seems weird to me. It seems better to just back analyze situations from the river expected value for each hand and scenario, and solve how much hands are based with every situation in poker accounted for. Not that hard to do. But it seems they use a range analysis, which I have a bone to pick. I don't think you can fully merge range with the actual hand that you have. This seems to only exist in some fantasy world, not on this reality. They are two separate things, but the thing is, I understand you play range vs range in the strategic sense of the word, but for the math, you are playing your actual hand.

To make a extreme example of this, say you were dealt 7-2o for the rest of your life. You would have to play this occasionally based on advancing preflop edge based on position game theory wise. Post-flop, your range would be dominated by ACTUAL HANDS. Its not the same thing as range, but seeing as that example, even if you extrapolated to every hand over a regular sample, you would still get this variant of Bayesian theory where some hands are worth more value then others. Not even just hand rankings, but in the complete analysis of the hand where you may have got one outed for a 200bb stack. This situation is obviously different then a situation where you one outed somebody, but this is where it gets a bit complicated, concerning my proposed alternate Bayesian theory.

Someone of equal skill who played perfect up until the river who gets one outed obviously has some expected plus ev for the play. Someone who played less perfectly would have less expected ev. But if they played the exact same way, using ranges vs actual hands, the range would matter for both the better play and for making money vs opp because ranges DO matter. BUT the actual hand matters in a non-skill sense, because of this math i proposed in my first paragraph. maybe we could bring in some solved math of what spot are worth given a weighted value for strategy and ranges proposed by solvers..... thoughts?

I'm not sure if you're being serious or trolling, but what you said makes no sense.

Solvers work using pure math. A solver has no idea what a "betting lead" or a "range advantage" is, they simply maximize the value of each combination relative to their opponent's strategy.

Analyzing your opponent's strategy involves knowing how they play their range on different streets, runouts and against different sizes. So 72o will pick actions that maximize value against that entire strategy.

Strategically, poker is played not as hand vs hand or range vs range, but rather hand vs strategy. You can't optimize your hand vs their strategy without examining their range. They can't optimize their hands vs your strategy without examining your range.

What do you mean they 'do range analysis'?
Strategies are well defined everywhere using regret matching, and then both players traverse the entire game tree. Values at terminal nodes are then passed back up the tree and regrets are updated. This is 'pure math based'.

Actual solvers implement vector form cfr, which deals range vs range instead of hand vs hand to use an algorithm for terminal nodes that has lower time complexity, but it gives the same values as exploring a tree that is dealt hand vs hand.

Vector form cfr and scalar form cfr both give the same results, one is just much faster than the other.

If thats true then you have a bot that can play perfectly? If you are correct, you could win alot of money. But strategy is incredibly hard to analyse for computers.

Example: two hands, one is a JJKK on a two tone board being bet into with 200bb stacks. Another is K876ds on 872 flop with 300bb stacks. If you extrapolate this to infinite hands, it seems pretty clear to me that strategy is a part of the game. Tell me how to code for infinite hands with differing ranges and values using just math. You solve the game, its set in stone boom. Someone else who knows this exact solved strategy can manipulate it. If you dont understand this your probably bad. Phil ivey is they greatest of all time because he has good strategy. Some 180iq math guy would never beat phil ivey.

This really comes down to range vs actual hand. This dichotomy is why solvers are imperfect. You cant play your range and hand at the same time. They are valid but completely differing concepts. Like white and black, or night and day or some other bs haha.

Range is the abstract meta system in poker, where youre playing he thinks, i think game.

Hand vs hand is solvable by math, but range is as important as hand vs hand. You cant bring these together, the best you can do is 99.99999%.

I meant solvers use range vs range because if you arent using a game tree for ranges, you solve the game by giving weighted values to hands using some sort of symbolic system, like giving red to some roullete colors and black to others. This is a spectrum of good hands vs bad hands, but it cant be solved.

Yes, cfr converges to a nash equilibrium. There are not infinite hands. Someone that knows your exact strategy can not beat it.

bro, its a imperfect information game. You can solve it to the best of your ability, but a better strategy will always win out.

quick search on the internet brings me this from carnegie melon university "Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice,
fastest approach to approximately solving large imperfectinformation games" APPROXIMATELY. it will never be solved. THEREFORE there is some strategy to the game. if you play poker i dont know how this isnt the most intuitive thing youve ever seen in your life.

i just googled this "Can a game not have a Nash equilibrium?
Nash's theorem states that every game with a finite number of players and a finite number of pure strategies has at least one Nash equilibrium. As a result, a game with infinitely many strategies might have no equilibria." thing is with CHANGING VARIABLES LIKE BIG BLINGS THERE IS NO SOLVING

just to change the pace really quickly...what do you guys think of giving values to hands based on endgame river bb value to your pocket which is solvable based on starting hands then adding a strategic structure on top of that. seems gto. LETS DO IT WOOOOOO

cfr converges to a nash equiibrium. the longer you run it, the closer it gets. you can measure the distance from the equiibrium by calculating the best responses, all solvers already do this. it will never be solved to a nash distance of literally 0. what distance would be acceptable for you? 0.1bb/100? 0.0001bb/100?

there are a finite number of players and a finite number of pure strategies, at least one nash equilibrium exists, and cfr converges to a nash equilibrium - those are not debatable facts

if big blinds didnt exist you would be right. Look your arguing a pretty trivial point, but its going in the wrong direction. My original post stating poker as a whole is 50/50 math and strategy is way broader then your perspective because big blinds are infinite. Is that debatable?

Poker is finite because you can't bet infinitely small fractions of the pot. It's well known that Nash Equilibrium exists in poker.

You realize there are GTO bots have already destroyed the best humans right?

And yes, GTO real-time assistance is actually a huge problem for online poker right now.

Your argument about strategy being different from math relies on fluffy human terminology. Strategy and math mean the same thing to a computer.

I bow out here at the stupidity of your arguements, your unwillinegness to listen, and your lack of insight. thanks. read it again maybe it wont be over your head. bye now

also tombos your lack of computer programming skills frighten me. read a book or something bro.