[QUOTE=Little Nemo]
Actually, I figure it the opposite way. With the revealed information in a game like stud or Texas Hold’em, mathematics becomes a factor. In traditional poker, you have no knowledge of your oppoents’ hands except what you can deduce from psychology.
[/quote]
I think this would be quite a good game, just not poker.
Start with two cards, say Ace of Spades and two of clubs. Ace always wins, two always loses.
One player takes a card secretly, looks at it - then the players start betting. The player with the card has to ‘trick’ his opponent, the player without the card has to ‘read’ his opponent.
[QUOTE=Little Nemo]
Again, I disagree. To me, the players who memorize the “book” are the ones who are getting by on “tricks”. They’re relying on their memory of what other players have done rather than any genuine originality of their own. It’s the kind of chess playing machines excel at.
On the other hand, tricks generally don’t work in chess variants. None of them have the extensive history of play that would allow a book to be developed on them. People playing these games are forced to think about what they’re doing rather than follow plans developed by past players.
A player who can swap the positions of the bishops and the knights and still play a good game of chess is demonstrating that he understands the underlying principles of the game rather than having aquired a memory full of precedents.
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[QUOTE=Trunk]
You know, everyone I’ve ever known that was into chess variations wasn’t a very good chess player. Instead of “deepening” their knowledge of chess (which is time consuming and subject to the law of diminishing returns), they would rather just learn a crazy variation, figure out a trick or two, and then talk people into playing those variations. Breadth, instead of depth.
[/QUOTE]
Aha, my area of expertise! 
Opening variations (such as the Ruy Lopez or the Monkey’s Bum) are studied by good players, not memorised. You need to be able to cope with a new idea that your opponent has discovered and can only do this with understanding.
The Ruy Lopez (1. e4 e5 2. Nf3 Nc6 3. Bb5) is considered a top quality opening, with deep strategic ideas.
The Monkey’s Bum (1. e4 g6 2. Bc4 Bg7 3. Qf3 e6 4. d4) looks crazy (hence the name, because when shown the opening, a player said “if that’s playable, I’m a Monkey’s Bum!”). Actually it’s not as bad as it looks…
It would be hard to be original in the first few moves, with all the computer records of games. Perhaps the only ‘modern’ innovation in the first 4 moves is the Benko Gambit (1. d4 Nf6 2. c4 c5 3. d5 b5), which is an astonishing positional gambit.
Note that I don’t play either side of this gambit, but I have seen / analysed say 100 games using it. I understand the compensation. No doubt I could do well, with either colour, against a player who had never seen it before.
Chess computers do have extensive opening books. But they don’t beat humans because of it. Humans get tired and emotional, machines don’t. I remember Kramnik sacrificing a piece against a top computer and losing because of one unlikely sub-variation.
Machines are wonderful at calculating tactical lines. they are not so good at positional chess.
Fischer random chess (where the back rank pieces are shuffled) has been played a bit. I expect Kasparov could thrash me at that. But he can also thrash me at standard chess.
In turn, I would be very confident of beating a club player at either form of chess (or any other, such as speed chess or blindfold chess…)