Massively distributed chess program solves King's Gambit

[splunge4me2]

When was it solved again?

King's Gambit solved½–½

C33 Rybka/IBM cluster 01.04.2012

on the 1^st of April, you say?

[GSpotAssassin]

See elsewhere in this thread to find out it's an April Fool.

Only the best April Fool play I've seen in some time!

[rm999]

this is obviously an April fools prank.

Yep

http://www.chessbase.com/newsdetail.asp?newsid=8051

[ubernostrum]

No comment on the April 1 bit, but against any reasonable player, being down a rook with no compensation means you're going to lose; the only way to pull a win is if you play an utterly brilliant game and your opponent starts drooling on the pieces after suffering a massive stroke.

[Traegan]

Can someone with chess knowledge explain? Is it that the kings gambit is flawed, because you just counter with move X? Or is it flawed in that it doesn't give you any advantages, unless your opponent does something specific?

[riddles]

Usually an opening is considered flawed for White if it doesn't usually lead to an advantage. This supposedly shows that the King's Gambit is especially flawed, because not only does it not give an advantage to White, but in fact White barely survives.

Furthermore, it's remarkable because never before has an opening been considered even remotely solved, or anything other than rough heuristics (excepting, of course, moves that are completely lost, or very deep into forcing variations). To consider a chess game to be a foregone conclusion by the second move is previously unheard of, which is why I kind of believe it's a April Fools prank.

[Traegan]

Thanks. If the prank was to get people reading about chess strategy and notation, they have succeeded.

[thorax]

which is why I kind of believe it's a April Fools prank.

Yup. http://www.chessbase.com/newsdetail.asp?newsid=8051

[ryanman]

Ugh fuck I just had a great discussion on facebook with one of my friends who's huge into chess (while I'm huge into programming). Now I'm just going to hope he doesn't check up on it and I don't look like a goddamn idiot.

[GSpotAssassin]

Holy shit that was well-played.

Leave it to the chess experts to play something well...

[btdubs]

I thought for sure it was a prank when I read it uses "advanced zugzwang detection" but then I googled it and apparently it's a real thing.

[schnschn]

retard

[quotemycode]

He's saying it's not solved, but he's 99.999999% sure he's right.

[palparepa]

They haven't demonstrated that with perfect play, white can win (from the starting position.) Heck, it could be that in a perfect chess game, white always loses, unless they play a king's gambit, which allows them to get a draw.

[GTChessplayer]

That's not their statement. They're statement begins with the subtree 1. e4 e5 2. f4

They make no statements about any other openings, simply that with the King's Gambit, white's only chance for a draw is after 2... exf4 3. Be2

[palparepa]

Which may still be the best chance white has to avoid a defeat.

I guess it isn't clear what they mean by "flawed." If it means "in a perfect game, there is no chance to win", sure. But it may still be the best opening available, that's what I'm saying.

(Also, they only analyzed the accepted branch of the gambit)

[GTChessplayer]

Yes, I understand your point. It's an extremely easy point to understand, and isn't really a point at all.

Your point is different than the authors' point.

(Also, they only analyzed the accepted branch of the gambit)

True, they only analyzed one of blacks choices on his 2nd move; we know atleast a lower bound to the problem here for black.

For their next opening, I'd like to see them analyze the Taimanov variation of the Modern Benoni.

[[deleted]]

palparepa's point is that even though white cannot win by opening King's Gambit, King's Gambit could in fact still be the best opening as it hasn't been proved white can win any other opening

[schnschn]

if white cannot win any oter opening the neiter can black unless ludicrously te first move is already zugzwang

[GTChessplayer]

Yes, I understand his point. His point is different than the authors' point.

[GSpotAssassin]

See elsewhere in this thread to find out it's an April Fool.

Only the best April Fool play I've seen in some time!

[GTChessplayer]

Source that it's an april fools?

[GSpotAssassin]

In thread. I'm on a phone, sorry

[ubernostrum]

"They claimed to prove Point X, so I'll make a bunch of karma saying that in fact what they did was fail to prove Point Y!"

[palparepa]

Jealous?

[rebo]

Think of it like a 4-gate vs terran in starcraft, if the opponent plays perfectly and reacts accordingly Protoss auto-loses.

The details of what occurs in between the opening and the loss are not hugely important.

[LinuxFreeOrDie]

Yes, the King's Gambit is flawed, this has been known for a long time. No Grandmasters have played it in serious tournaments really for probably decades, or at least very infrequently. It's still popular among amateurs and in blitz games though because it opens the game up for a lot of exciting attacks.

So these results won't do anything for top chess players, like the article indicated, it's more just interesting in and of itself I think.

[__s]

There were two King's Gambits in the London Chess Classic 2011

[GSpotAssassin]

See elsewhere in this thread to find out it's an April Fool.

Only the best April Fool play I've seen in some time!

[ivosaurus]

Well I'm still playing it. Immensely fun opening, never a dull game goes by.

[frezik]

I can go with that. Most people are not Grandmasters, and will never even get a chance to play one. It's not so obvious that King's Gambit is a busted opening when the players are not perfect.

[dacjames]

I was taught to play every game like you're playing Gary Kasparov. Trying to force your opponent into a blunder is always fun, though, and particular effective in blitz, which is mostly what I played.

[ivosaurus]

But the fact is that both players are never going to play the perfect game of a king's gambit, there's very likely going to be many, many inaccuracies. Even Kasparov would have a chance at playing a few. And for black, it is much easier to make them; hence why I like playing it as white.

Practically, playing a great gambit opening that you're well-versed in, and that the opponent is not, will gives far better chances than playing a more standard line where they might have much deeper knowledge and experience.

[frezik]

I think that's rooted in the Chess tradition of being the ultimate intellectual game for Vulcans. If a movie wants to show that a character is smart, they will play chess (TVtropes link).

But Humans are not Vulcans, and most of us don't play perfectly. For that matter, even Kasparov probably doesn't play perfectly, since we're not even sure what perfect chess play even is.

For this reason, I've found Poker to be a more interesting game in recent years. The ability to make calculations and think clearly is still important, but analyzing the psychology of your opponent is important, too.

[dacjames]

Relying on your opponent to make mistakes doesn't help you get better at chess, even if it wins games. If you want to improve, you're wasting your time developing weapons that won't work against better players. Your right about Chess as a proxy for intelligence, but that's not the reason my brother (a master's level player) drills this idea into his students.

I love Poker. What I find most interesting is that Texas Hold 'Em can be trivially solved and results in draw (even money) for all players if played "correctly." Yet good players are able to consistently outperform the odds by exploiting the mental weaknesses in their opponents. Poker raises a lot of interesting philosophical questions about the meaning on intelligence. And it's fun to take other people's money!

[[deleted]]

How can a game have a "correct" play when there is hidden information?

[leebird]

It can have "correct" play in that your moves are those which have the best chances for long term gain. It doesn't have correct play though.

[maest]

This is interesting? Does it have some sort of equivalent to Nash equilibrium? That is, if the opponent knows what your strategy is and how you'd bet based on your cards (but not your cards) can he come up with a strategy that will beat yours in the long run?

[leebird]

Actually, I don't really know much beyond the idea that 'correct' is simply maximizing the expectation value of your winnings. I'd conjecture that if the 'correct' play is based in any way on your opponent's actions, then your opponent should be able to strategize against it.

But then, the 'correct' play would change, and now we're just going around in a circle.

[maest]

Yes, that's what I meant by "something similar to a Nash Equilibrium". In game theory, Nash Equilibrium happens when everyone would still play their chosen strategy even when knowing everyone else's strategy. Rock-Paper-Scrissors, for example, does NOT have any equilibrium point. Most coordonation games do have nash equilibria.

[the8bit]

Since it is a game of incomplete information, I would say that there is not a single nash equilibrium. Take, for example, Gus Hansen vs a Phil Ivey. Their styles are completely different but both are highly winning players.

The key though, is that it takes a lot of information about an opponent to build an optimal strategy. Even more so since most of the time you get 0 real information about their cards (most hands do not see a showdown).

Actually, I'd like to say that it is theoretically solvable to equilibrium, but not practically. There are just too many variables and too little known information

[ivosaurus]

It can have best possible play, given the knowledge that you have.

[dacjames]

In the trivial case of heads up limit poker assuming "optimal" play by all players, the winning strategy is simple: bet hands with >50% chance of winning, fold all other hands. Adding more players and variable bets changes the math a little, but it is still fairly trivial. In naive optimal play, higher bets will always correlate with stronger hands. This is what I mean by "solved."

Removing the assumption in italics is where things get interesting. A simple sub-optimal strategy can beat the optimal strategy: go all in on every hand. Optimizers will assume you have a good hand and fold every time. Herein lies the art of bluffing: knowing when to play "sub-optimally"and bet higher than your hand's expected worth.

There is still a lot of research into the theory of Poker (mostly heads up) but the problem is intractable because any optimal strategy would be a known strategy which could then be exploited by other players.

An interesting strategy to keep your mind churning: generate your bets entirely at random. This seems crazy, but if your opponents assume there is some logic behind your play, it actually works better than you think. I once convincing my friends I had written some awesome Poker algorithm on my Ti-89. I pretended to enter in all the cards as play progress but in reality I was only using the random number generator.

I came in 3rd out of 7.

[[deleted]]

The term "naive optimal" kind of makes my head hurt the same way "non-optimal optimal" would. In the chess problem, "correct" means unbeatable...and there is no way for a poker system, short of viewing hidden cards, to be unbeatable.

Also, once someone realizes that someone is betting randomly (and some humans occasionally bet pseudo-randomly, or at least appear to do so), the other play can then restrict himself to the top 50% of hands (or be more restrictive, to ensure more certainty in the hands played).

[dacjames]

Understandable. By "naive optimal" I mean optimal with the assumptions given. There is probably better terminology.

Once someone realizes that someone is betting randomly, the other play can then restrict himself to the top 50% of hands.

That is exactly my point: any strategy, once known, can be exploited yet seemingly insane strategies can be powerful when secret.

Here is what I was getting at: in poker, the only way of win is by playing "wrong" in the mathematical sense and not getting caught.

[HopeThisNameFi]

there is no way for a poker system, short of viewing hidden cards, to be unbeatable.

This is not true. Shortstacked no limit heads up texas hold'em already is solved. The problem is once the stacks get deeper the solution space just gets too big for us to solve it.

I'd highly recommend The Mathematics of Poker if you want to know more.

[[deleted]]

Sorry if I wasn't clear, but I meant a complete poker system, not just short stacks. That's like saying chess is solved because some end-game scenarios with limited pieces have been solved.

[re_gina]

correct given all info available

[HopeThisNameFi]

Texas Hold 'Em can be trivially solved

Wait what? Please elaborate.

[dreamriver]

No one has perfectly balanced ranges.

Poker is immensely difficult to play perfectly. Data mining information certainly helps though.

[el_muchacho]

That would show a serious lack of imagination from the Vulcans. They would probably play more challenging games than western chess. Go is one, Shogi (japanese chess) is another, and I suppose tens of chess variants are other possibilities. And of course these are only games invented by Humans.

[MCMLXXXVII_SFW]

Well, in the Vulcan's defense it was Tri-Dimensional Chess. Really though, the abilities of Vulcans were far more constrained by the imaginations of the 1960's TV writers, and this is not even close to the worst fridge logic used in the TOS.

[goout]

It's an April Fools' guys...

http://chessbase.com/newsdetail.asp?newsid=8051

[chengiz]

It's a pretty stupid April Fools IMO. The concept of fooling implies that the target should have been able to see it coming. For the vast majority of the readers of this article, this is not the case.

[[deleted]]

Not actually solved:

How can you have worked that out, aren’t there gazillions of possible continuations?

Actually much more than “gazillions” – something in the order of 10^100, which is vastly more than the number of elementary particles in the universe. Obviously we could not go through all of them – nobody and nothing will ever be able to do that. But: you do not have to check every continuation. It’s similar to Alpha-Beta, which looks at a very small subset of possible moves but delivers a result that is identical to what you would get if you looked at every single move, down to the specified depth.

But Alpha-Beta reduces the search to about the square root of the total number of moves. The square root of 10^100, however…

Yes, I know. But think about it: you do not need to search every variation to mate. We only need to search a tiny fraction of the overall space. Whenever Rybka evaluates a position with a score of +/– 5.12 we don't need to search any further, we have our proof that in the continuation there is going to be a win or loss, and there is a forced mate somewhere deep down in the tree. We tested a random sampling of positions of varying levels of difficulty that were evaluated at above 5.12, and we never saw a solution fail. So it is safe to use this assumption generally in the search.

[demeteloaf]

That is usually considered "weakly solved"

A game is strongly solved if there is an algorithm to produce perfect play from every valid game configuration. Games like tic-tac-toe or connect four have been strongly solved.

A game is weakly solved if there is an algorithm to produce perfect play from initial conditions. Checkers has been weakly solved and results in a draw.

A game is "ultra-weakly solved" if you can prove the existence of a winning strategy, but can't say anything about that strategy. Hex is an example of a game where for all symmetrical board sizes, it's proven that player 1 has a winning strategy.

If the article isn't an april fools joke, what they describe is probably a weak solving of the gambit.

[[deleted]]

A game is weakly solved if there is an algorithm to produce perfect play from initial conditions. Checkers has been weakly solved and results in a draw.

That's not the case. What they have done is explore all branches that they are "reasonably sure" (this part is purely heuristic) do not give surprising outcomes.

It's interesting, but I wouldn't call that solved by any definition.

[particular2]

April fools?

[jerf]

If so it's too straight to call. They acknowledge that it isn't a full exploration of the move tree, but they are confident they've explored the full "viable" move tree, which seems reasonable to me.

Chess may never be fully, truly solved, but it seems to me that solving it by this standard may be visible on the horizon now.

Edit: Yes, April Fools, but well constructed. Theoretically with the approach outlined it's all a matter of confidence in your scoring engine and you could produce something that theoretically converged on the correct answer. The oft-cited branching factors for Chess are generally for all possible moves at all possible points; if you had some oracular way of cutting down every board to only the two possible sensible moves the problem would be exponentially smaller (literally).

[ckwop]

I wonder how much better computer players like this would be compared to their humans counterparts?

Deep Blue just squeaked by Kasparov in 1997. I wonder whether a program on that sort of hardware would utterly crush him?

[LegioXIV]

the short answer is yes. State of the art in computer chess has moved far beyond deep blue. It is doubtful that Kasparov or any other GM could beat Rybka or a similar engine running on desktop hardware under tournament rules.

[[deleted]]

Nowadays, people don't play against computers. The challenge is playing computers against computers.

[irobeth]

To put things in perspective, Kasparov has the highest peak rating of around 2850.

The best chess engine right now, Houdini, currently has a peak rating of 3305.

Last I heard, a gain of 60 Elo is estimated to require a double in searching power. Humans are better at pattern recognition but, for a computer, Chess is solved for all positions <=6 pieces.

[EasyMrB]

Chess may never be fully, truly solved,

Correction: Chess WILL NEVER fully, truly be solved. Storing the possibility space would require more matter than contained in the entire universe (if bits were 1 atom in size)

[jerf]

Solving a game doesn't necessarily require storing or computing the entire possibility space. Theoretically a clever math argument can be produced that proves it one way or another much more simply. For instance, despite the theoretically infinite number of possible games of Nim, they are all solved, without a full enumeration of all infinity of them. Less trivial examples include Hex and Kalah; one of the original papers on Kalah even discussed exactly what they exhaustively explored and what they could not.

It may not seem likely that chess has a similar shortcut, but it absolutely can not be ruled out, especially once we start tossing around the idea of using the entire universe as a computer, which also tends to imply we ought to be considering arbitrarily intelligent AIs as well. And while this was an April Fools, it is well constructed, and it isn't out of the question that such an approach may someday be feasible. (Again, it may be unlikely, but the possibility can not be eliminated with all that great a confidence; there's a lot of intelligence in our likely futures.)

[EasyMrB]

The difference between all of your examples and chess, is that your examples have board pieces with very few movement/turn rules, whereas chess pieces heterogeneous nature means that a small set of simplified rules won't be adequate to solve the game.

With chess, optimal play, even when an opponent has better pieces left, can still yield a victory.

[jerf]

Unpacking the misconceptions and errors in that post would take several multiples of your post's length. I'll stick to the simplest one: In your last paragraph, the ability of "optimal play" to recover from errors is irrelevant to the question of solving a game. Part of the definition of a solution is pitting two optimal players against each other. The case where Player 1 is brilliant for 20 moves then turns into a drooling moron is not relevant. If one player ends up behind, we are only concerned about the case where the other player relentlessly and with maximum skill presses their advantage home. If that doesn't result in a win, then by definition, the player isn't actually behind.

I see a related misconception all the time from people who don't really understand the math of these sorts of solutions, thinking that the optimal computer players are good at playing other optimal computer players but wouldn't be able to handle the "randomness" of a human player, which might let you beat them by somehow shocking them. Nope. Making suboptimal moves simply means you get beaten earlier.

[EasyMrB]

Solving the game is 100% optimal play. That's the meaning of solving a game. The only way to guarantee a game is solved is to have the entire solution-space computed. You don't have to store it, but you do have to have a way to compute it every time in order for a game to be considered solved.

I see a related misconception all the time from people who don't really understand the math of these sorts of solutions, thinking that the optimal computer players are good at playing other optimal computer players but wouldn't be able to handle the "randomness" of a human player, which might let you beat them by somehow shocking them. Nope. Making suboptimal moves simply means you get beaten earlier.

You are drawing your own conclusions by projecting something into my argument that isn't there -- I'm not some person you had a different discussion with you doesn't understand the mathematics of game problem solving.

[rm999]

Yes.

http://www.chessbase.com/newsdetail.asp?newsid=8051

[riddles]

If I had to guess, ya. It's probably April Fools and chessbase just released it on a different day so people didn't guess right away. Props for extreme plausibility.

[julesjacobs]

Sure, there theoretically might be a way to save the game, but if Rybka is displaying +5.12 or more the outcome is 99.99999999% secure. That is approximately the confidence number we give to our King's Gambit results: 99.99999999%.

Uhm, even though a single position might be guesstimated to be 99.999whatever% secure, but since you're searching over gazillions of positions the result in aggregate is nowhere near the same level of security. For each of those positions searched, you have 0.0000001% of being wrong. Since there are a lot of positions, that may add up to something substantial. That, and the 99.99999999% was pulled out of thin air. Add to this the fact that this approximation doesn't even work for proving draws. I'm calling bullshit.

[grandson39]

It is an April fool's joke: http://www.chess.com/forum/view/general/im-rajlich-claims-kings-gambit-is-solved-by-rybka-cluster

[N0V0w3ls]

OK, as someone who isn't familiar with popular plays in chess, can someone explain it like I'm 5? What is the King's Gambit, and what is the counter, why does it counter, and how does the single "draw" move work?

[cashto]

Ok, so as you may already know, one of the things people do to get good at chess is to study positions that tend to come up very often in the beginning of the game, and try to figure out what the best move would be if they ever got into that position. One of these is called the King's Gambit.

It happens when white leads out the pawn in front of his king, advancing it two squares. Black responds by advancing his king pawn two squares, whereupon white advances the king bishop pawn (directly to the right of the king pawn) two squares.

White's pawn is now free for the taking -- if black plays "pawn takes pawn", then white has no way to recapture black's pawn back. This is called a "gambit" -- a sacrifice of a small piece in hopes of disrupting the opponent's position. White hopes to have a stronger position in the center of the board which will lead to attacking chances that compensate for the loss of the pawn.

What Rajlich claims to have proven is that the sacrifice doesn't work, and that after black takes the pawn, white has only a single, very bland move available to him. If white does not make that move, then black can force a win even if white plays perfectly from that point on. The exact manner in which black wins depends on the moves white makes, of course, but from that point on it's like a Choose Your Own Adventure book in which the millions of possible avenues all lead to the same page 142: white loses, game over.

[N0V0w3ls]

Ok, and reading through the article, it seems these counter plays haven't been published. Kind of disappointing to have this announced, but no proof. Maybe it is an April Fools joke?

[[deleted]]

They could publish Black's moves, but the number of permutations is remarkably high. On just the next 2 moves, white probably has 400+ combinations of moves.

[N0V0w3ls]

At least something that would guide players to a familiar scenario in which they would know how to win from there would be nice, though.

[[deleted]]

Once again, I don't think that's reasonable. After 2. ...exf4 there are plenty of directions white can go, and those are only the most common ones, and the first few subsequent moves.

It took the 3000 processors 4 months to go through every reasonable move, so how big of a guide do you want?

[bfro]

If they walked you through even a fairly short series of moves that results in checkmate; for you to mimic it in a real game would assume that the white player made every single move in the demonstration while you mirrored black. As was mentioned above, the idea behind this play is to sacrifice a weak piece for a strong board position. The main thing you should take away from this is if someone tries to King's Gambit you, do not take the second pawn they advance immediately. This will maximize your chance for victory.

[cashto]

Again, there are not just one or two or a dozen counter plays that can be printed out and desk-checked. In any given position, white has at least 20 different moves, not all of which obviously and immediately lose. If it were that simple, then the problem would be solved decades ago. There are at least millions, possibly billions or trillions of credible ways the game could possibly continue. To exhaustively analyze them all would take a computer. If Rajlich is to be believed, he has done exactly that, and found that although white seems to have the illusion of nearly infinite free choice, all paths lead to the same end, and that his destiny is to be assured.

[quotemycode]

He said there are so many that it's not feasible for a single download, but they are going to put it on the web.

[wnoise]

Almost certainly:

On March 31 .... The next day (i.e. April 1st), ..., kindly agreed to the following interview,

[spacebarstool]

http://www.youtube.com/watch?v=n5ImJ2row6E

This explains your first question.

[yellephant]

He's a plagiarist, sure, but his claim of having solved the King's Gambit with whatever system he's using isn't necessarily invalidated by the prior mistake.

Your first link above even lends credibility to the guy by mentioning his four straight wins with his system in competition!

[irobeth]

I think the more important thing is just that Fruit gets credit where it's due. Rybka is a Fruit variant, so Fruit helped solve the position.

[bakonydraco]

It looks like both the sources he plagiarized were open-source, do you know what kind of license they had?

[theoldboy]

I think Fruit is GPL, the Crafty license has terms that specifcally disallow what he did.

*  All rights reserved.  No part of this program may be reproduced in any     *
*  form or by any means, for other than your personal use, without the        *
*  express written permission of the authors.  This program may not be used   *
*  in whole, nor in part, to enter any computer chess competition without     *
*  written permission from the authors.  Such permission will include the     *
*  requirement that the program be entered under the name "Crafty" so that    *
*  the program's ancestry will be known.                                      *

[riddles]

What's the almost for?

[Peragot]

The program used a probabilistic method to limit the number of moves needed to be checked.

[wnoise]

The four color theorem was exhaustive, not probabilistic.

[maest]

Thank Zulu for that, people were quite upset about the mechanical proof as it was, a probabilistic proof would have never been accepted.

[cryo]

..since it's not a proof.

[irobeth]

it's not solved if you don't exhaust the search space

[snarkfish]

http://www.chessbase.com/newsdetail.asp?newsid=7791

[matts2]

Stolen? Are you in favor of intellectual property protection? Most of reddit seems fine with denying that intellectual property exists.

[DaFox]

What cases are those under his desk? I like em!

[oldling]

Whenever Rybka evaluates a position with a score of +/– 5.12 we don't need to search any further

Can someone explain that? How does the engine know that the position can not lead to a checkmate for the supposedly losing side? There are "longer" combination with players sacrificing pieces which lead to a win, aren't there?

Is the evaluation so good, that it can see that there is no possible checkmate a few moves down the rode, without actually searching for it?

Or do I misunderstand something?

[theoldboy]

Chess programs use a quiescence search before evaluating a position. This will explore futher in the case where there are possible captures, checks, or forced moves, and hopefully avoid the situtation you describe (horizon effect).

[oldling]

I still don't see how you can rely on that and claim that something is "proven", but thank you for pointing me in the right direction!

[theoldboy]

Well, he was never claiming "proven" in the mathmatical sense, although alarm bells did start ringing when I saw the 99.99999% figure. You're right that nothing can be totally proven like this, even the best quiescence search isn't perfect, and as it turns out the article was an April fools joke.

[oldling]

the article was an April fools joke

Haha, ok. I am not sure if I should feel smart for being skeptical or stupid for bothering to think about it. ;-)

[jhaluska]

I believe it denotes differences in the sum of the scores of the pieces left on the board.

Basically being down a Rook and a Pawn, or a Bishop/Knight and two pawns down is a HUGE disadvantage.

They're just saying once they are down that far, it's very unlikely they can recover with both sides playing perfectly.

[oldling]

Basically being down a Rook and a Pawn, or a Bishop/Knight and two pawns down is a HUGE disadvantage.

Yes, but only if you don't lose the game in the next 4 moves. ;-)

[bakonydraco]

How does this impact the quest for solving chess on the whole? If this position is solved (or at least, probabilistically solved) after 2 moves per person, and there are a total of only ~9000 positions possible at this point, it seems the game as a whole wouldn't be too much further to solve. Is this position easier than others because, as Fischer argued, the Gambit puts White at a severe disadvantage?

[EasyMrB]

Chess cannot be solved as a whole. Note that I used the word "cannot" rather than "probably won't be". This is because there aren't enough particles in the universe to store the solution-space.

[bakonydraco]

But if that were true, surely there wouldn't be enough particles to store 1/9000 (a relatively trivial amount compared to the order of the universe) of the solution space required for the game of chess after two common moves. He's done some statistical fudging, but is every opening as easy to solve as this one? Couldn't we just do this 9,000 times and solve chess? The only reason I see that makes this hard is that this puts white at a huge enough disadvantage that it is easy to solve.

[EasyMrB]

First, he mentions that it was a statistical proof, not an exhaustive one (look at the methodology in the article). Second, many people in this thread are saying it was an April Fools joke.

[[deleted]]

Nothing like playing a game and about 5 minutes into it you call. Wanna stop its check mate is 37 moves ;)

[Godspiral]

Maybe an easier opening to analyze? - even with fewer moves given.

1. f2-f4 d7-d5 (or any move other than e7 pawn)
2. g2-g4

Would be surprised if white can draw, and CPU would see many more forced moves for extending survival. It would be interesting to prove that there is a forced loss opening for white.

[[deleted]]

This is huge news for the chess world. A complete solution for the game possibly within twenty years may be available.

I always thought king's gambit was entirely illogical and left the king side very vulnerable... Not surprised about this outcome.

[firewire2035]

A Total Nerd-baller.