Not every software, of course not. But a complex enough, that can search through the space of all possibilities fast enough to find a hole, if there is one.
Nobody thought, that in a chess a king with two knights is doomed against a king with two bishops. The most brilliant human minds have never suspected that. Then a simple software program found this hole in the FIDE’s rules of “50 moves without check”. The million or so best human minds haven’t. People are able to explore only a small part of the solutions space.
Nobody thought, that in a chess a king with two knights is doomed against a king with two bishops. The most brilliant human minds have never suspected that.
I’m trying to find a reference for that but I can’t find any mention of that endgame. Do you have a reference or maybe another detail which could narrow the google search down?
Then a simple software program found this hole in the FIDE’s rules of “50 moves without check”.
Isn’t the 50 move rule “50 moves without a pawn moved or a piece captured”? Just requiring a check wouldn’t (always) prevent the problem the rule is trying to prevent.
There are some long general theoretical wins with only a two- or three-point material advantage but the fifty-move rule usually comes into play because of the number of moves required: two bishops versus a knight (66 moves); a queen and bishop versus two rooks (two-point material advantage, can require 84 moves); a rook and bishop versus a bishop on the opposite color and a knight (a two-point material advantage, requires up to 98 moves); and a rook and bishop versus two knights (two-point material advantage, but it requires up to 222 moves) (Müller & Lamprecht 2001:400–6) (Nunn 2002a:325–29).
It is almost all I find online. But I will keep try.
Who do you think proved this? A human? Do you have a supporting link?
If there was such a proof it would have been found by a computer.
Do you think it isn’t proven?
I initially just believed you and wanted to find out more. But it turns out there isn’t any mention of it in the places where I expected it to be mentioned. A winning endgame between a combination so similar in material would almost certainly be mentioned if it existed. Absence of evidence (that should exist) is evidence of absence! Perhaps there was another similar result in the magazine?
The most interesting endgame I found in my searching was two knights vs king and pawn, which is (depending on the pawn) a win. This is in contrast to the knights vs the lone king which is an easy draw. On a related (better to be worse) note there was a high ranked game in which a player underpromoted (pawns to knights) twice in one game and in each case the underpromotion was the unambiguous correct play.
Somebody recalls a slightly different version than I.
FSR: Incidentally, knights really suck on b7, e.g., Soltis vs A J Goldsby, 1981, so driving your opponent's knight there tends to be a good thing. If you're defending the endgame of two bishops versus knight, disregard the above advice, since there the various "N2" squares (b7, g7, b2, and g2) are the key squares the knight should occupy. See P Popovic vs Korchnoi, 1984. (Computers proved 20 years ago that that ending is a theoretical win - though it's very difficult, see Timman vs Speelman, 1992.)
I second wedrifid’s request, please provide a link to the two knights against two bishops problem. It sounds interesting. Also, it’s indeed not “50 moves without check” but rather “50 moves without a capture or a pawn move”.
Sure. Machines are good at systematically checking cases and at combinatorial optimization, once the state space is set up properly. But this isn’t a good model for general-purpose intelligence. In fact, this sort of systematic checking is precisely why I think we can build correct hardware.
The way systematic verification works is that designers write a specification and then run moderately-complex programs to check that the design meets the spec. Model-checking software or hardware doesn’t require a general-purpose intelligence. It requires good algorithms and plenty of horsepower, but nothing remotely self-modifying or even particularly adaptive.
Not every software, of course not. But a complex enough, that can search through the space of all possibilities fast enough to find a hole, if there is one.
Nobody thought, that in a chess a king with two knights is doomed against a king with two bishops. The most brilliant human minds have never suspected that. Then a simple software program found this hole in the FIDE’s rules of “50 moves without check”. The million or so best human minds haven’t. People are able to explore only a small part of the solutions space.
I’m trying to find a reference for that but I can’t find any mention of that endgame. Do you have a reference or maybe another detail which could narrow the google search down?
Isn’t the 50 move rule “50 moves without a pawn moved or a piece captured”? Just requiring a check wouldn’t (always) prevent the problem the rule is trying to prevent.
here
Quote:
It is almost all I find online. But I will keep try.
The “50 rule” changed several times.
This doesn’t seem to mention two knights vs two bishops. Is that specifically something you recall seeing elsewhere?
I’ve read this about 25 years ago in a magazine.
But do try this:
and this
Google? Yes, I tried that. I found no confirmation. I still haven’t found said confirmation. I now doubt the claim.
Who do you think proved this? A human? Do you have a supporting link?
Do you think it isn’t proven?
If there was such a proof it would have been found by a computer.
I initially just believed you and wanted to find out more. But it turns out there isn’t any mention of it in the places where I expected it to be mentioned. A winning endgame between a combination so similar in material would almost certainly be mentioned if it existed. Absence of evidence (that should exist) is evidence of absence! Perhaps there was another similar result in the magazine?
The most interesting endgame I found in my searching was two knights vs king and pawn, which is (depending on the pawn) a win. This is in contrast to the knights vs the lone king which is an easy draw. On a related (better to be worse) note there was a high ranked game in which a player underpromoted (pawns to knights) twice in one game and in each case the underpromotion was the unambiguous correct play.
Here
Somebody recalls a slightly different version than I.
I second wedrifid’s request, please provide a link to the two knights against two bishops problem. It sounds interesting. Also, it’s indeed not “50 moves without check” but rather “50 moves without a capture or a pawn move”.
Sure. Machines are good at systematically checking cases and at combinatorial optimization, once the state space is set up properly. But this isn’t a good model for general-purpose intelligence. In fact, this sort of systematic checking is precisely why I think we can build correct hardware.
The way systematic verification works is that designers write a specification and then run moderately-complex programs to check that the design meets the spec. Model-checking software or hardware doesn’t require a general-purpose intelligence. It requires good algorithms and plenty of horsepower, but nothing remotely self-modifying or even particularly adaptive.