But then big stacks play off on each other, so in order to avoid them bullying you, you also lose most opportunities to recover the ground.

Good players often take more risks as the game goes on specifically because the probabilities narrow.

Mid to late game starts requiring calculated losses and risks, and if you play probabilities then you lose to that. Will you push in your 80% AA pre flop? What if three people call behind?

That's the thing about poker. You're not playing to win a single game because that's not reasonable or possible. Luck factors will overwhelm any single outcome.

You're playing to win *more games than you lose*.

A trash player is rolling 60% return. They will get there occasionally through luck. They might even play a good hand in the mix. But over many games that 60% return is a 40% loss.

A great player is rolling a 110% return. That still means luck pops them out a lot. It means bad beats 10 games in a row. It means the occasional gamble you know is the wrong call but you can't resist it. But after 50 games your average return trends to positive.

It's not like chess or go, you don't play then decide who is better and that is that. It's more like a casino where you bring your own dice dependant on your skill level. If you're good enough then you weight the averages in your favour, if you're not then you enjoy your wins as you gradually spend your bankroll.

When you play casino games it's not the single outcome that decides, it's the weight of many. The house always wins in the end because it has a small probability advantage spread over thousands of games.

Poker bots simply cannot maintain that consistency because doing the maths isn't enough.

Because the good players have weighted their dice in different ways that matter more than playing the maths can come close to.

Because it's not the average of individual hands that makes success, but the average of outcomes that require game threatening risks to achieve.

Because weighting your coin to give heads 60% of the time by playing probability isn't useful if your payout condition

Is 10 heads in a row. What you'd really want is a coin that gives the same result as the prior flip 80% of the time instead. You get streaks of tails losing, but also a much much higher chance of 10 in a row. Yet if you counted the flips over a long period of time it'd be just a 50% chance of heads. Win conditions change the relevance of probability!

Winning 600 out of 1000 hands still earns you nothing if you needed to get 100 of those hands into the one game. You need a cluster of success to make the money, not merely be better in most hands you play.

That's why poker isn't yet a solved AI problem. Even when it is, players will adapt their games and the meta game will change and new bots will be needed. We see this effect in online video game competition already, where meta-game matters just as much or more than the quality of your individual play.

The person that solves poker, they'll be rich.