Ordinary chess forbids moving into check (and hence from moving into checkmate), which means you automatically lose if there's no way to avoid moving into check. Is there a variant of chess in which you're not allowed to make a move that would cause you to lose 2 moves in the future? (Replacing 2 by larger integers, we get a game in which the legality of a move can become rather murky!) Jim
On Fri, Nov 13, 2020 at 2:10 PM James Propp <jamespropp@gmail.com> wrote:
Ordinary chess forbids moving into check (and hence from moving into checkmate), which means you automatically lose if there's no way to avoid moving into check.
Those aren't the rules of chess. If you have no legal move (and a move which would put your own king in check is illegal), then you do not lose; the game is a draw. This is called "stalemate". This rule leads to different outcomes in some important endgames, especially K + P vs. P, where some games that would be winnable if a player with no legal moves lost, and would also be winnable if moving into check was legal and the game ended when the king was captured, are actually draws. Assuming all players are good enough to detect positions where the king could be captured, if no legal moves was a loss, then the outcome of any game under "capture the king wins", and "exposing your king to capture" would always be exactly the same. You'd just be stopping games one move earlier whenever the outcome is inevitable. You can perform this operation on any game where not being able to move is a loss, making all moves which lead to an immediate loss illegal. Conway has some name for this operation in Winning Ways, because while it doesn't effect the outcome of a game, it may affect the outcome of certain kinds of sums of games where this game is a component. Similarly, if we take chess with the modification that no legal moves is a loss rather than a draw, then prohibiting any move which leads to a forced capture of the king in two moves has no effect on the game as long as all players are good enough to see all mate-in-1 positions (and if they are not, they cannot determine the legality of moves in this version of the game); this is just performing this operation, which doesn't change the outcome of a game, twice, which still leaves the outcome unchanged. If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced capture of the king in two moves (or equivalently, allows a mate in 1) leads to a game that is an easy draw for minimally competent players. Here's the simple drawing strategy. If all moves lead to mate in 1, the game is a stalemate draw, by the new rule. If there is at least one move that does *not* lead to a mate in 1, make any such move. This strategy cannot be defeated, so the game is a draw unless someone blunders by allowing a mate in 1 where a different move would avoid it. Andy
Is there a variant of chess in which you're not allowed to make a move that would cause you to lose 2 moves in the future?
(Replacing 2 by larger integers, we get a game in which the legality of a move can become rather murky!)
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
On 13/11/2020 20:01, Andy Latto wrote:
If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced capture of the king in two moves (or equivalently, allows a mate in 1) leads to a game that is an easy draw for minimally competent players. Here's the simple drawing strategy. If all moves lead to mate in 1, the game is a stalemate draw, by the new rule. If there is at least one move that does *not* lead to a mate in 1, make any such move. This strategy cannot be defeated, so the game is a draw unless someone blunders by allowing a mate in 1 where a different move would avoid it.
I don't think that's quite the right generalization of the rules of ordinary chess. If you compare ordinary chess with "take-the-king chess", the right way to describe what changed is that if every (otherwise) legal move leads to immediate loss then you (1) lose if a null-move also leads to immediate loss, and (2) draw if not. So for the iterated version, the correct rule would be: if every (otherwise) legal move gives the opponent a mate in 1, then you (1) lose if a null-move also gives the opponent a checkmate, and (2) draw if not. I believe this version is neither exactly equivalent to ordinary chess, nor trivially a draw. (By a "null-move" I mean simply doing nothing, which of course is not actually a legal move in chess.) -- g
On Fri, Nov 13, 2020 at 4:54 PM Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 13/11/2020 20:01, Andy Latto wrote:
If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced
I don't think that's quite the right generalization of the rules of ordinary chess. If you compare ordinary chess with "take-the-king chess", the right way to describe what changed is that if every (otherwise) legal move leads to immediate loss then you (1) lose if a null-move also leads to immediate loss, and (2) draw if not.
So for the iterated version, the correct rule would be: if every (otherwise) legal move gives the opponent a mate in 1, then you (1) lose if a null-move also gives the opponent a checkmate, and (2) draw if not.
I agree that this is both a more consistent way to generalize, and a more interesting one. I don't know of any positions likely to occur in actual play that would be different in this version, but it is a common theme in chess problems. It's common in mate in two problems for the solution to be a move that does not threaten mate in 1, but allows white to mate after any black move. Take for example the position in https://www.youtube.com/watch?v=GaBw9RmUoNM This is mate in 2 problem, and the solution in conventional chess is for white to play Qa8. But in twice-forshortened chess, the resulting position is a draw, rather than a win for white; white is not threatening mate but has a mate after any black move, so in the variant, black has no legal moves, so this is a stalemate. Taking the limit as we perform this foreshortening operation infinitely often, we get the chess variant that is like normal chess, except it allows a pass as a legal move. This affects many endgames: I strongly suspect that K + B + N vs K is a draw, for example. In fact, I'm not even sure that K + R vs K is a win if the K is allowed to pass. Unfortunately, I think the effect of any of these changes is primarily to change wins into draws, which is not what chess needs to make it more interesting. Andy Andy
I believe this version is neither exactly equivalent to ordinary chess, nor trivially a draw.
(By a "null-move" I mean simply doing nothing, which of course is not actually a legal move in chess.)
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
At the risk of a thread hijack, chess fans who have Netflix should watch "The Queen's Gambit," a seven-part miniseries starring Anya Taylor-Joy as a blossoming chess prodigy. It's a 60's period-piece, based on a 1984 novel by Walter Tevis. On Fri, Nov 13, 2020 at 6:00 PM Andy Latto <andy.latto@pobox.com> wrote:
On Fri, Nov 13, 2020 at 4:54 PM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
On 13/11/2020 20:01, Andy Latto wrote:
If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced
I don't think that's quite the right generalization of the rules of ordinary chess. If you compare ordinary chess with "take-the-king chess", the right way to describe what changed is that if every (otherwise) legal move leads to immediate loss then you (1) lose if a null-move also leads to immediate loss, and (2) draw if not.
So for the iterated version, the correct rule would be: if every (otherwise) legal move gives the opponent a mate in 1, then you (1) lose if a null-move also gives the opponent a checkmate, and (2) draw if not.
I agree that this is both a more consistent way to generalize, and a more interesting one.
I don't know of any positions likely to occur in actual play that would be different in this version, but it is a common theme in chess problems. It's common in mate in two problems for the solution to be a move that does not threaten mate in 1, but allows white to mate after any black move. Take for example the position in https://www.youtube.com/watch?v=GaBw9RmUoNM This is mate in 2 problem, and the solution in conventional chess is for white to play Qa8. But in twice-forshortened chess, the resulting position is a draw, rather than a win for white; white is not threatening mate but has a mate after any black move, so in the variant, black has no legal moves, so this is a stalemate.
Taking the limit as we perform this foreshortening operation infinitely often, we get the chess variant that is like normal chess, except it allows a pass as a legal move. This affects many endgames: I strongly suspect that K + B + N vs K is a draw, for example. In fact, I'm not even sure that K + R vs K is a win if the K is allowed to pass.
Unfortunately, I think the effect of any of these changes is primarily to change wins into draws, which is not what chess needs to make it more interesting.
Andy
Andy
I believe this version is neither exactly equivalent to ordinary chess, nor trivially a draw.
(By a "null-move" I mean simply doing nothing, which of course is not actually a legal move in chess.)
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
And I was pleasantly surprised to find that the audiobook is available free to Audible members. On Fri, Nov 13, 2020 at 3:14 PM Allan Wechsler <acwacw@gmail.com> wrote:
At the risk of a thread hijack, chess fans who have Netflix should watch "The Queen's Gambit," a seven-part miniseries starring Anya Taylor-Joy as a blossoming chess prodigy. It's a 60's period-piece, based on a 1984 novel by Walter Tevis.
On Fri, Nov 13, 2020 at 6:00 PM Andy Latto <andy.latto@pobox.com> wrote:
On Fri, Nov 13, 2020 at 4:54 PM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
On 13/11/2020 20:01, Andy Latto wrote:
If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced
I don't think that's quite the right generalization of the rules of ordinary chess. If you compare ordinary chess with "take-the-king chess", the right way to describe what changed is that if every (otherwise) legal move leads to immediate loss then you (1) lose if a null-move also leads to immediate loss, and (2) draw if not.
So for the iterated version, the correct rule would be: if every (otherwise) legal move gives the opponent a mate in 1, then you (1) lose if a null-move also gives the opponent a checkmate, and (2) draw if not.
I agree that this is both a more consistent way to generalize, and a more interesting one.
I don't know of any positions likely to occur in actual play that would be different in this version, but it is a common theme in chess problems. It's common in mate in two problems for the solution to be a move that does not threaten mate in 1, but allows white to mate after any black move. Take for example the position in https://www.youtube.com/watch?v=GaBw9RmUoNM This is mate in 2 problem, and the solution in conventional chess is for white to play Qa8. But in twice-forshortened chess, the resulting position is a draw, rather than a win for white; white is not threatening mate but has a mate after any black move, so in the variant, black has no legal moves, so this is a stalemate.
Taking the limit as we perform this foreshortening operation infinitely often, we get the chess variant that is like normal chess, except it allows a pass as a legal move. This affects many endgames: I strongly suspect that K + B + N vs K is a draw, for example. In fact, I'm not even sure that K
R vs K is a win if the K is allowed to pass.
Unfortunately, I think the effect of any of these changes is primarily to change wins into draws, which is not what chess needs to make it more interesting.
Andy
Andy
I believe this version is neither exactly equivalent to ordinary chess, nor trivially a draw.
(By a "null-move" I mean simply doing nothing, which of course is not actually a legal move in chess.)
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- - https://cube20.org/ <http://cube20.org/> - https://golly.sf.net/ <http://golly.sf.net/> - https://experiments.cubing.net/ -
Can't resist mentioning: I've been wondering about a variant where pawns must promote to bishops only. It would subtly diverge from normal chess, increasingly differing towards endgame, but only sometimes.
K+B+N vs K is not a draw: https://en.m.wikipedia.org/wiki/Bishop_and_knight_checkmate Best, É. Catapulté de mon aPhone
Le 14 nov. 2020 à 00:41, Marc LeBrun <mlb@well.com> a écrit :
Can't resist mentioning: I've been wondering about a variant where pawns must promote to bishops only. It would subtly diverge from normal chess, increasingly differing towards endgame, but only sometimes.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Fri, Nov 13, 2020 at 7:19 PM Éric Angelini <eric.angelini@skynet.be> wrote:
K+B+N vs K is not a draw:
Yes, I understand that in standard chess, K + B + N vs King is a win. I was speculating as to whether, in a hypothetical version of chess in which pass was a legal move, this would still be a win; I suspect that it would be a draw under these rules. Andy https://en.m.wikipedia.org/wiki/Bishop_and_knight_checkmate
Best, É. Catapulté de mon aPhone
Le 14 nov. 2020 à 00:41, Marc LeBrun <mlb@well.com> a écrit :
Can't resist mentioning: I've been wondering about a variant where pawns must promote to bishops only. It would subtly diverge from normal chess, increasingly differing towards endgame, but only sometimes.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
Ok, yes, sorry Andy. à+ É. Catapulté de mon aPhone
Le 14 nov. 2020 à 03:35, Andy Latto <andy.latto@pobox.com> a écrit :
On Fri, Nov 13, 2020 at 7:19 PM Éric Angelini <eric.angelini@skynet.be> wrote:
K+B+N vs K is not a draw:
Yes, I understand that in standard chess, K + B + N vs King is a win. I was speculating as to whether, in a hypothetical version of chess in which pass was a legal move, this would still be a win; I suspect that it would be a draw under these rules.
Andy
https://en.m.wikipedia.org/wiki/Bishop_and_knight_checkmate
Best, É. Catapulté de mon aPhone
Le 14 nov. 2020 à 00:41, Marc LeBrun <mlb@well.com> a écrit :
Can't resist mentioning: I've been wondering about a variant where pawns must promote to bishops only. It would subtly diverge from normal chess, increasingly differing towards endgame, but only sometimes.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hi, On 11/13/20 11:09, James Propp wrote:
Ordinary chess forbids moving into check (and hence from moving into checkmate), which means you automatically lose if there's no way to avoid moving into check.
Agreed, provided the king was in check in the first place (i.e. if the king is in check and cannot escape check by any moves, that side loses).
Is there a variant of chess in which you're not allowed to make a move that would cause you to lose 2 moves in the future?
Hmm. It seems the endgame of that (excuse the pun) is increasingly deep table bases. These are used in computer chess all the time, they improve play by sparing the computer program from having to calculate the correct outcome of e.g. two rooks vs queen and pawn. Did you look at e.g. the Syzygy and Lomonosov 7-man table bases? Andres.
No, Andres, do not agree with a false statement. —Dan
On Nov 13, 2020, at 1:10 PM, Andres Valloud <ten@smallinteger.com> wrote:
On 11/13/20 11:09, James Propp wrote:
Ordinary chess forbids moving into check (and hence from moving into checkmate), which means you automatically lose if there's no way to avoid moving into check.
Agreed, provided the king was in check in the first place (i.e. if the king is in check and cannot escape check by any moves, that side loses).
participants (9)
-
Allan Wechsler -
Andres Valloud -
Andy Latto -
Dan Asimov -
Gareth McCaughan -
James Propp -
Marc LeBrun -
Tomas Rokicki -
Éric Angelini