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 .