I'm somewhat skeptical any time anyone references "the fundamental theorem of poker" (like that wiki page), given that Sklansky definitely doesn't understand game theory and the "fundamental theorem" is just wrong. This Morton's theorem shows one example of that.
For people who don't know the so-called fundamental theorem of poker[1] was proposed by David Sklansky who was definitely more mathematically-minded than most poker players of his generation but was not really a mathematician. It's gained a lot of mindshare even though it's clearly at odds with game theory. Probably this is because it's very simple to state and seems intuitive. It is usually stated as something like "Every time you play a hand differently than you would have if you could see all your opponent's cards you lose and they gain and vice versa, and conversely every time they play a hand differently from how they would if they could see all your cards you gain and they lose and vice versa".
This is one of those things that sounds sort of obviously correct and so is very seductive as an idea, but it completely fails if you just think for a second about the fact that you can't see their cards and they can't see your cards. In that world (actual poker), we know that the optimal strategy is a Nash equilibrium in mixed strategies(we know this is true for all games of hidden information). By definition that means you are sometimes doing something different from "what you would do if you could see their cards", because you have a mixed strategy (ie you don't do exactly the same thing every time but choose options with some randomness). The same is true for the opponent. Therefore we can see that it follows trivially that the "fundamental theorem" can't be correct.
For people who don't know the so-called fundamental theorem of poker[1] was proposed by David Sklansky who was definitely more mathematically-minded than most poker players of his generation but was not really a mathematician. It's gained a lot of mindshare even though it's clearly at odds with game theory. Probably this is because it's very simple to state and seems intuitive. It is usually stated as something like "Every time you play a hand differently than you would have if you could see all your opponent's cards you lose and they gain and vice versa, and conversely every time they play a hand differently from how they would if they could see all your cards you gain and they lose and vice versa".
This is one of those things that sounds sort of obviously correct and so is very seductive as an idea, but it completely fails if you just think for a second about the fact that you can't see their cards and they can't see your cards. In that world (actual poker), we know that the optimal strategy is a Nash equilibrium in mixed strategies(we know this is true for all games of hidden information). By definition that means you are sometimes doing something different from "what you would do if you could see their cards", because you have a mixed strategy (ie you don't do exactly the same thing every time but choose options with some randomness). The same is true for the opponent. Therefore we can see that it follows trivially that the "fundamental theorem" can't be correct.
[1] https://en.wikipedia.org/wiki/Fundamental_theorem_of_poker