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I'm a beginner, sorry if this question is absurd.
If a player simply bets with probabilities in mind, and always made the correct move for every action, would s/he become rich in the long run? If this is the case, what kind of a sample size is "the long run?" Or is the meta game overwhelmingly important in poker?
This is an interesting question.
I think a big reason why these players are not rich is because of exploitative play. Theoretically, if a player played perfect theory-optimal play then they would be able to make the most money and lose the minimum in every pot they play. This is called GTO and it is based on things like odds, ranges, combinations, and implied odds.
I think there are 2 reasons value players are not rich.
Variance
exploitative play
Variance simply means that sometime you will get unlucky in an uncontrollable way, even if you are playing perfectly you will run bad sometimes.
Exploitative play is more interesting. Exploitative play is when players follow lines to exploit weaknesses of other players. This is the main reason why I think not all value players are rich. No player is perfect, therefore every player can be beaten with the correct exploitative play. It is not easy to play this way especially against very good players, but there is always someone good enough to do it.
At the end of the day, poker is a very complex game with an infinite depth of strategy (reverse psychology etc.). Value players should win money, but it is impossible for them to play perfectly enough to always win (or get rich quick).
Rich? It's extremely hard to be "rich" just by playing poker, but it's simple enough to make a living off it. The reason being that you have to be vastly superior to the field to make steady money off poker with a rake (like at Casinos). For example, in order for you to "break even" with a 7% rake, you need to be a 53.5% winning player. If you eat fancy casino food or take an uber home, your winrate goes even higher. In the end, you need to be around a 58-60% winner (against the field) to make money. At high levels, that winrate is difficult. It's only possible against a field of fish / tourists (lowest level, so $1/$2 or maybe $2/$5).
I was a cash game grinder. In fact, before my current job (that made enough money to make poker money no longer that attractive), I lived off poker for about 1 year. I was making around 1.5k a month doing 2 days a week (so probably 8 days).
My style is mostly pure math/logic due to the fact that I am casino player and most of other players (non-regs) are total fish. I only play at $1/$2 and usually each session is 5-6pm to next morning 5-6am (12 hours). I would do this Friday / Saturday. I average about 8 bb (big blinds) per hour overall (I performed much better in the last 6 months than the first 6 months). Keep in mind that live game deal cards much slower than online, so we are talking about maybe 30 hands per hours (so 8 bb per hour is doing quite well). I make about $200 a night and I am one of the better earners at the $1/$2 so I doubt you can make much more unless you play everyday (non-weekends are harder due to lower fish percentage and less action) or even you have a good bankroll to go higher ($2/$5).
Near the end of the year, I slowly saved up enough and I wanted to go to $2/$5. The competition was much harder at the level. First of all, there was one table instead of like 12 at $1/$2, so you play with all the other regs/sharks often. At the 1/2, usually you get 2-3 regs and the rest are either casuals or tourists. This makes all the difference in poker earning. I would say 90% of my poker income came from fish, there's literally no point playing against a decent player cause your winrate is shit (with the 7% rake, you basically need a 60/40 advantage again the player to make it remotely profitable). So imagine if you are sitting at $2/$5 with 6 other good/decent grinders facing like 3 tourist fish, that's way less opportunities than sitting at $1/$2 facing basically twice the amount of free money. So after playing about 2 weeks of $2/$5 and breaking even, I decided that my poker dream isn't worth it... I need to pay rent and eat so I moved back to $1/$2. I suppose if you live somewhere with A LOT of tourist (like Vegas), maybe the $2/$5 or even $5/$10 "could be" profitable, but you would need such a big bankroll to even endure the variance, so it's not something you can hope to do quickly (it would take like 1-2 years of saving at a lower level to move up one level).
All in all, you can only get "rich" in poker if you play at high levels. At those levels, the variance is too high so you better already be rich or else you live on the edge the whole time (any bad string of cards will make you unable to eat for that week).
The moment I got a good job that paid more than poker, I stopped pokering. Sometimes I do play a bit for fun, but it's different now cause I can afford to lose. When you are doing poker professionally and feeding yourself on it, the stress is intense and it's just not worth it (unless you like the thrill, but I am not really into that. I literally only play because I am good at it, I kind of hate playing it professionally).
Well, sure. If someone always made the optimal decision they would be a very profitable player. The problem is that poker is very complicated and it's not at all obvious what the correct decision is at each point. You have to take into account what cards could come in future streets and your opponent's actions thus far among many other things.
Hypothetically, yes, if a person made all the correct moves he or she would become very rich. What makes it less realistic is the assumption "always made the correct move for every action." It's important to realize that poker is a game of incomplete information, unlike chess where you can see exactly what position every piece is in or even roulette where you at least can know the odds of any event happening.
With poker, you can know your cards, the amount of money in the pot, how big everyone's chip stacks are, even the odds of certain cards to hit the board--but you don't know your opponents' cards or what they'll do next.
The best poker players get better and better at being able to make good inferences about these unknown factors and can incorporate those inferences into what they do know (their own cards, size of pot, position, etc) for a good decision, but it's impossible for anyone to really ever be perfect at it. Combine that with the fact that other aspiring players get good at making inferences from incomplete information and your "edge" isn't as big. That's where what you call meta-game comes into play: throwing other players off from nailing down your strategy (so they play less perfectly against you). However, it's more important for a new player to get the basics down first before thinking about that; plus it's not even worth thinking about with bad players who won't figure you out anyway.
