> I am familiar with virtually all the topics you are discussing, so you can skip the citations.
I really can't, because other people might believe you if I don't; I don't hate them. I want them to know the truth. So I'll oppose you strongly, for their sake, so they can discriminate between my counterintuitive truth and your rejection of the truth on that basis of confusion.
Go read page 173 of Artificial Intelligence: A Modern Approach. I'll quote Norvig here. "Because calculating optimal decisions in complex games is intractable, all algorithms must make some assumptions and approximations." Now go to page 172. I'll quote Norvig again. "One way to deal with this huge number is with abstraction: i.e. by treating similar hands as identical. For example, it is very important which aces and kings are in a hand, but whether hand has a 4 or a 5 is not as important, and can be abstracted away."
But, the discerning might ask, what of the talk of the infinite? Why does Josh speak of such an absurd thing? Isn't it irrelevant? It is not. Go to page 611, "Non-Cooperative Game Theory". I'll quote him again for you, "With this observation in mind, the minimax trees can be thought of as having infinitely many mixed strategies the first player can choose." The thing to notice in this quote is that we have a simple game - very simple. Yet Norvig just explained that in this simple game we have the quality of a tree of infinite size. This growth to infinite is actually very normal - mixed strategies are continuous and we have proofs that mixed strategies are the solution for a variety of different games involving imperfect information.
I really can't, because other people might believe you if I don't; I don't hate them. I want them to know the truth. So I'll oppose you strongly, for their sake, so they can discriminate between my counterintuitive truth and your rejection of the truth on that basis of confusion.
Go read page 173 of Artificial Intelligence: A Modern Approach. I'll quote Norvig here. "Because calculating optimal decisions in complex games is intractable, all algorithms must make some assumptions and approximations." Now go to page 172. I'll quote Norvig again. "One way to deal with this huge number is with abstraction: i.e. by treating similar hands as identical. For example, it is very important which aces and kings are in a hand, but whether hand has a 4 or a 5 is not as important, and can be abstracted away."
But, the discerning might ask, what of the talk of the infinite? Why does Josh speak of such an absurd thing? Isn't it irrelevant? It is not. Go to page 611, "Non-Cooperative Game Theory". I'll quote him again for you, "With this observation in mind, the minimax trees can be thought of as having infinitely many mixed strategies the first player can choose." The thing to notice in this quote is that we have a simple game - very simple. Yet Norvig just explained that in this simple game we have the quality of a tree of infinite size. This growth to infinite is actually very normal - mixed strategies are continuous and we have proofs that mixed strategies are the solution for a variety of different games involving imperfect information.