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Sorry, can't help myself...if I was a 'theorist in the field' of zoology, I wouldn't necessarily know anything about trees. Now, if I were a botanist...(sorry for the nit, but it kind of goes with my point).
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Oops, meant botany.
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But it would be pretty easy to explain to someone confused about it that (I think..I'm not a botanist) hardwood versus softwood is an issue of rigidity, not of strength.
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I don't agree. In any way an average person could measure, balsa, a hardwood, is softer, weaker and less rigid than pine, a softwood.
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But the key thing is the definition of complete information isn't open to interpretation.
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That's because you're a theorist.
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Are there hidden chess pieces?
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In various ways, yes indeed. Very often you hear a player say "I didn't even see the bishop!" So literally the piece was not seen. And then there are more subtle forms of it.
http://www.101chesstips.com/hidden-attacks.jsp
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Do the pieces move in a different way that isn't known to both participants?
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This often occurs with newer players. They do not know they can't castle through check, or can't remember how to castle queen side, believe that a pawn must always be queened when it makes it to the ultimate rank, and sometimes don't even get en passant pawn captures wrong.
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This makes your definitions useless, since now you need to specify the complexity of the thinking of the participants.
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This makes about as much sense as saying you don't need to account for your opponent's knowledge of the game when playing poker.
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If you want to use a new word, fine. But when you take an established word with a concrete meaning and use it for something else, you muddle up the interpretation and argument.
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Someone as educated as yourself really shouldn't have any problem allowing words to mean different things in different contexts. Hard woood, for example.
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I'm guessing a bit of trying to get chess called a game of incomplete information is that you're trying to show poker is a game of skill. That is, chess is a game of skill, and then by calling chess a game of incomplete information, those games then can be games of skill and thus poker is.
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That really has nothing to do with it. You're too intent on definitions of words. It doesn't matter that chess is a game of complete information if it doesn't play that way in real life. This would be like saying Newtonian physics breakdown when I get into my space ship and start flying near the speed of light. Well, what I'm trying to say is that we're all just sitting here on Earth, so it's a moot point. You are going to do a whole lot better sticking with Newtonian physics to get all your work done because it works, even though physicists know that it doesn't work in general (it does not describe the universe accurately). I'm not trying to say that Einstein's physics are wrong (or that quantum physics is wrong). I'm trying to put some perspective on the problem by saying that if you're a mechanical engineer here on Earth, you still need Newtonian physics to do your job. It doesn't matter that it isn't a unified theory of physics.
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As I said, sorry about the zoology-> botany quip, just trying to be slightly humorous. I know it wasn't too good.
The 'hidden piece' isn't information that's not there. That's not the game--that's the players who play the game. The game has in it's rules that all the pieces are visible. And 'hidden check' isn't because there was something that wasn't observable previously suddenly materialized.
But, what I've said before, the game is the game. If people aren't playing optimally, you can't play the NE strategy and expect it to be the best. So yes, you'd have to adjust your chess, your poker, whatever, to exploit fully your opponent's mistakes. But a game is defined by it's rules and payoffs, and nothing is hidden from players. Yes, it's complex, so noone knows the NE, but that doesn't change the game.
And I think the better analogy is a mechanical engineer using Aristotlean (I'm sure I spelled that wrong) physics--there are changes to equilibrium concepts for exactly the problem you're describing, where people don't always play the NE strategies. If you're interested, check out 'trembling hand equilibrium' or 'cursed equilibrium'. Those can keep the information in the game constant while at the same time accounting for people's non-equilibrium actions.