This is awesome. Thanks for posting it.

I agree that it's awesome, even though I really don't understand it, lol. I sort of think I almost get what the basic concept might be, but I don't logically see how it could be true, and certainly don't have the mathematical background to make sense of the proof, so all I can do is trust that it's valid

BobJoeJim,

It's really not that complicated at all, just seems that way.

Check out the wiki link above for an example, if you haven't already.

Yeah, that wiki link that he linked is a really simple thought experiment that puts it in a nutshell and is v cool.

The thought experiments and nutshell explanations aren't what I'm having trouble with. I understand the claim, I just don't see how it could be true, and that's where the math (which I don't understand) comes in to prove that it is true. Maybe that means I don't understand the thought experiments as well as I think? The cave example from wiki is cute, but I don't see how it proves anything. It provides significant confidence, but still doesn't *prove* she knows the code unless you do it infinite times, which defeats the purpose.

you can prove it to a very high level of confidence by asking a relatively small number of questions, though. e.g. one in a trillion by asking 20 questions. complexity theorists are generally happy whenever they have an algorithm that runs in polynomial time or less -- this is the same thing in reverse.

the problem with applying the cave argument to something like chess is that there are heuristics for behaving like a machine that plays perfectly (i.e. never changes the evaluation of the position) in a vast vast majority of legal chess positions. but presumably that's what the paper is about.

Yeah, you understand it fine. There will always be some insanely low chance that the person claiming to have the proof has just gotten lucky, but then there is some insanely low chance that a grandmaster doesn't even now the rules to chess and has been getting lucky. These proofs are probabilistic, so you are correct that it is a different notion of proof than say a number theory proof, where you don't show that it is really, really unlikely for an exception to Fermat's Last Theorem to exist, you show it is impossible.

The cave example can't and shouldn't convince you that the result is true for chess or any complicated game. What the papers are doing is showing that no matter how complicated prefect chess* is,it can be mapped to a souped up version of the cave problem. But those papers are beyond graduate level and 95% of math PhDs couldn't prove it, so it's ok if it doesn't seem obvious, because it isn't at all.

But intuitively, this result should confirm something you already realize even if you haven't thought about the it directly. That some problems can be very hard to solve, but if somebody gives you the answer, it isn't nearly as hard to see that it is correct. That alone doesn't guarantee the chess result, but it is sort of an overall theme as to what is going on.

** And to clarify, as I did in the later post, the author of the paper doesn't actually construct a cave situation for chess, he proves that a very general class of problems, of which chess is an example, must always have a cave situation that can be constructed.

The paper itself actually doesn't talk about chess directly and nothing specific about chess really matters because it is known that a Turing Machine with a certain set of resources can solve chess. So even if you just made up some game that had similar complexity behavior to chess, the result would still apply, even though the author of the paper has no idea what the rules even are to your game.

Team 45 45 debut, team needed a draw to win the match. Draw agreed. Computer thinks I'm +1.05 or something in this position, but I'm like 90% sure it's drawn.

http://www.chessvideos.tv/chess-game...r.php?id=40918



[Event "ICC"]
[Site "Internet Chess Club"]
[Date "2011.02.15"]
[White "KyleMayhugh"]
[Black "kidcobra"]
[Result "1/2-1/2"]
[WhiteElo "1362"]
[BlackElo "1782"]
[ECO "B07"]
[Opening "Pirc defense"]
[TimeControl "2700+45"]

1. e4 d6 2. d4 Nf6 3. Bd3 g6 4. Ne2 Bg7 5. c4 O-O
6. Nbc3 c6 7. Bf4 Nbd7 8. O-O e5 9. dxe5 dxe5 10. Be3 Qc7
11. b4 Nb6 12. c5 Nbd7 13. Qb3 b6 14. Na4 b5 15. Nac3 Bb7
16. Rad1 Rfd8 17. h3 a5 18. a3 a4 19. Qb2 Nf8 20. Bb1 Ne6
21. Ba2 Qe7 22. Rd2 Rxd2 23. Qxd2 Rd8 24. Qb2 Nd4 25. Rd1 Nxe2+
26. Qxe2 Rxd1+ 27. Qxd1 Qd7 28. Qxd7 Nxd7 29. Kf1 Kf8 30. Ke2 Ke7
31. g4 f6 32. f3 g5 33. Kd3 h6 34. Ne2 Nf8 35. Ng3 Bc8
1/2-1/2

Looks dead drawn to me. 1.e4 experiments bringing success?

edit: hmmm i guess Black could lose it after Nf5+ Bxf5 gxf5 if he somehow doesn't manage to rearrange to stop Kh5-Kg6. Doesn't seem very likely tho

I'm starting to enjoy it. It feels like I'm learning more "lines" and the games tend to be more dynamic. I'll still fall into the occasional Ruy Lopez trap and blow a game in the first 10 moves, but mostly it works well. I play Italian game more often anyway. I get to torment players just below my level with the the 4. Ng5 stuff that used to torment me.

This game just degenerated into a d4-style locked-pawn snoozer despite e4, though.

I'm sure it's been posted on here before, but it still boggles my mind every time I see it:



http://www.chessgames.com/perl/chessgame?gid=1143956
http://www.youtube.com/watch?v=VoPG4Vl__fs

Noob question, but "why" is castleing allowed? It always seemed totally arbitrary to me, does it make the game alot deeper... or is it a historical precedent? It always seemed weird that you could explain all the rules of chess really succinctly... but then after that you have to say, "oh yeah, there is this random thing where certain 2 pieces can move on the same turn if you do this...."

History of Castling in Chess:

Source: Wiki, http://en.wikipedia.org/wiki/Castling#History

yes it does, without castling every game would be a romantic slugfest, perhaps black would even be lost from the starting position. While flashy romantic attacks can be beautiful, it would become boring with time.

I'd argue that being able to move the pawn two squares -- and the resulting en passant capture rule -- is the most bizarre exceptional rule in chess.

You can en passant with pawns, but not with pieces.

I find that bizarre.

Place a White King on b7, Black pawn on a7. Now Black can play a7-a5 and the White King can't capture "en passant" and the Black pawn will promote.

Place a White pawn on b5, have Black play a7-a5 and now White can capture "en passant" as the Black pawn passes from a7-a6-a5.

How come the King can't capture the a7 pawn as it travels from a7-a6-a5 in one move?

This is something that has always puzzled me since when I realized it.

I guess you could say that "en passant" only deals with pawn moves, but still I find it kind of weird. The pawn still passes through a6, on its way to a5 (from a7), so why can't the b7-King take it?

En Passant is explainable through the history of the game ... originally pawns could only move one square at a time ... and games were slow & boring ... so to speed things up, pawns got the option to move two squares (or one) on their first move only ... but now a player could for example play c7-c5 when there was a white pawn on d5 & the pawn couldn't be taken ... but prior to the new rule the pawn had to go c7-c6-c5, meaning white COULD capture the pawn if they chose to ...
So to get around this problem, the en passant rule was created!

Think of it like the burn card in poker to get around cheating with marked cards ...

Yeah, I know that. It travels one square at a time for its first move but can go two spaces.

So why can't a King (or another piece) capture a pawn (on c6) when it travels c7-c6-c5?

I find this a bit peculiar.

How many times do you see a king (your example) trying to capture the a7 pawn from b7?
Not very often, because you rarely get such a situation.

Compare the situation with pawns ... not only are there so many more of them than any other piece ... but the situation where pawns are taken (or can be taken) by other pawns is so much more common ... hence the rule!

Also consider the name ... En Passant being French for 'in passing' (apparently anyway, my French isn't great) ... that's what the pawns are doing, unlike your Kb7/Pa7 example, when the pawn is hardly 'passing' the king at all.

Not sure if anyone's interested, but Hikaru Nakamura wrote on his blog today that he's not playing in the 2011 US Champs.

I dunno, WC? But props to him for thinking big. I would've thought that his "GM in residence" deal in St Louis would've sort of obliged him to play.

http://www.chess.com/news/le-quang-l...lot-again-6402

quite a huge achievement iyam, last year he held his own at Dortmund (Aeroflot victory = invitation to that super tourney) very well, lets see how he does this year.

Wow, ditto. Although is he actually a GM in residence there? I was under the impression that only Ben held that. Still surprising to me. Regardless, it definitely puts an asterisk by the 2011 champion imo.

Hmm. I don't recall ever hearing what his deal is in St Louis, but I just assumed that there is some kind of money support happening for which he's expected to do stuff just because (and this probably isn't very fair) why move from Seattle to St Louis?

Maybe there's a conflicting event somewhere else?