@AyrtonTwigg , @Sarg0n , at first I also thought that solving this challenge is impossible - I even started to sketch a proof on a game theory basis - but then I realised that there could actually be a (hopelessly complicated and controversial) way. In retrograde chess problems, it is generally accepted that castling is legal unless proven otherwise, whereas en passant is illegal unless proven otherwise. It is feasible to construct a position where legality of castling implies legality of en passant, so that you can capture en passant, but then, some moves later, you have to back it up by castling. If you are not able to do it, you lose the game, because it turns out that you made an illegal move (as I mentioned, en passant is illegal unless proven otherwise). It means that you can forfeit the game by checkmating without castling! Therefore, one theoretically could construct a problem in which White could win only by beginning with en passant capture and backing it up two moves later by promoting to the rook, because the queen would checkmate, causing forfeit. It seems to me that the most probable construction would consist of White long castling and Black light-coloured bishop, which is able to block the castling, but not to disrupt it actively. Creating such a position most probably lies well outside my capabilities, but I see no reason for it to be impossible. It is also still regular chess, or at least pretty close (as far as I know, these rules may be applied in a tournament game if the notation sheet was lost and cannot be reconstructed).
@classicalMpk
You're right, although it does involve a stalemate, but where the object is to PRODUCE a stalemate instead of avoiding one. So the extra power of a queen would give White a further move, which it doesn't want.
I should have written in 2.... if the extra power does not cause a stalemate, and where it is not advantageous to cause a stalemate.
But you're absolutely right: your example of the special case where getting a stalemate is optimal is not barred by the OP's challenge, so your example meets his requirements. If he had banned that case THEN it would be impossible.
Incidentally, regarding your example, I'm not sure if underpromotion to a knight (barred in his challenge) won't also lead to a draw, although in a few moves.
Also, as you noted, the challenge stipulated "regular chess", implying that all positions could have been arrived at legally. It's an interesting question if yours could have been arrived at legally. The h7 pawn would have had to take pieces diagonally while black's g6 pawn was still on g7, to get in behind the black h6 pawn. Black has all his pieces, so black would have had to promote pawns to get pieces to lose. Maybe...
You're right, although it does involve a stalemate, but where the object is to PRODUCE a stalemate instead of avoiding one. So the extra power of a queen would give White a further move, which it doesn't want.
I should have written in 2.... if the extra power does not cause a stalemate, and where it is not advantageous to cause a stalemate.
But you're absolutely right: your example of the special case where getting a stalemate is optimal is not barred by the OP's challenge, so your example meets his requirements. If he had banned that case THEN it would be impossible.
Incidentally, regarding your example, I'm not sure if underpromotion to a knight (barred in his challenge) won't also lead to a draw, although in a few moves.
Also, as you noted, the challenge stipulated "regular chess", implying that all positions could have been arrived at legally. It's an interesting question if yours could have been arrived at legally. The h7 pawn would have had to take pieces diagonally while black's g6 pawn was still on g7, to get in behind the black h6 pawn. Black has all his pieces, so black would have had to promote pawns to get pieces to lose. Maybe...
The chapter 4 is regular chess I think.
@nayf
I think the problem with your proof is that, strictly speaking, it is not a proof at all, since you need also proof that your points 2 and 3 are true:
"2. No advantage obtained by a weaker piece could not be obtained by substituting a stronger piece for the weaker piece in the same position, if the stronger piece includes all the powers of the weaker piece, and if the extra power does not cause a stalemate. (Tautology).*
3. No advantage using a rook or bishop cannot be obtained by substituting a queen for the weaker piece if the extra power does not cause a stalemate (From 1, 2, and 3)."
One could even say that the position from #12 already refutes this:
<iframe width=600 height=371 src="lichess.org/study/embed/LAmzUlfT/IrmXVVQP" frameborder=0></iframe>
Here, promotion to a queen does not immediately cause stalemate - black has still a rook free to roam after the promotion and can give perpetual check, ending the game in a 3-fold repetition. Only if white takes the rook, then it's stalemate. Ok, agreed, in the end of the causal chain there's still a stalemate hanging over the sky. But hypothetically one could imagine some other forced sequence of moves that is caused by the queen, but not by rook or bishop. No one seems to know how to construct such a position, and I do suspect it's impossible. But I also don't know how you would formally refute the possibility.
On the other hand, one single example of a meaningful, not stalemate-related underpromotion to R or B would settle the issue forever. (;
I think the problem with your proof is that, strictly speaking, it is not a proof at all, since you need also proof that your points 2 and 3 are true:
"2. No advantage obtained by a weaker piece could not be obtained by substituting a stronger piece for the weaker piece in the same position, if the stronger piece includes all the powers of the weaker piece, and if the extra power does not cause a stalemate. (Tautology).*
3. No advantage using a rook or bishop cannot be obtained by substituting a queen for the weaker piece if the extra power does not cause a stalemate (From 1, 2, and 3)."
One could even say that the position from #12 already refutes this:
<iframe width=600 height=371 src="lichess.org/study/embed/LAmzUlfT/IrmXVVQP" frameborder=0></iframe>
Here, promotion to a queen does not immediately cause stalemate - black has still a rook free to roam after the promotion and can give perpetual check, ending the game in a 3-fold repetition. Only if white takes the rook, then it's stalemate. Ok, agreed, in the end of the causal chain there's still a stalemate hanging over the sky. But hypothetically one could imagine some other forced sequence of moves that is caused by the queen, but not by rook or bishop. No one seems to know how to construct such a position, and I do suspect it's impossible. But I also don't know how you would formally refute the possibility.
On the other hand, one single example of a meaningful, not stalemate-related underpromotion to R or B would settle the issue forever. (;
@Panagrellus
Thank you for your comment. I took line 2. in my proof to be intuitively knowable, but maybe I should have broken it down further. The basic tautology is that: more power in a piece is always at least as advantageous as less power of the same kind, except when the extra power is disadvantageous. So that should read as an obvious tautology not requiring proof, like p=p. The next step is an assertion that extra power in a piece can be disadvantageous only in cases of stalemate. That seems to me obvious, but I guess it's not a tautology, but a deduction from the rules of chess. However, you are right that it may require proof if it is a deduction.
In your example, I'm not sure if a8 (immediate promotion) is the right move at all. Why not Rb7, then Re7. If he tries to lose his rook, take it! He can always move his bishop, and then mate.
Thank you for your comment. I took line 2. in my proof to be intuitively knowable, but maybe I should have broken it down further. The basic tautology is that: more power in a piece is always at least as advantageous as less power of the same kind, except when the extra power is disadvantageous. So that should read as an obvious tautology not requiring proof, like p=p. The next step is an assertion that extra power in a piece can be disadvantageous only in cases of stalemate. That seems to me obvious, but I guess it's not a tautology, but a deduction from the rules of chess. However, you are right that it may require proof if it is a deduction.
In your example, I'm not sure if a8 (immediate promotion) is the right move at all. Why not Rb7, then Re7. If he tries to lose his rook, take it! He can always move his bishop, and then mate.
If Rb7, Rc8 and black will move his bishop all the time for blocking the b-pawn.
@ayan2007
@AyrtonTwigg
@Bishop1964
@classicalMpk
@dboing
@Demonolith
@KingPuzzles
@MoistChess
@Panagrellus
@Sarg0n
@nayf
@clousems
My own posting # 27 inspired me to make a new, a little bit more elaborate, study about this underpromotion theme.
🎭Romeo and Julia - A Chess love story🎭
I hope you like it.
Wilhelm "Bishop1964" Shakespeare
@AyrtonTwigg
@Bishop1964
@classicalMpk
@dboing
@Demonolith
@KingPuzzles
@MoistChess
@Panagrellus
@Sarg0n
@nayf
@clousems
My own posting # 27 inspired me to make a new, a little bit more elaborate, study about this underpromotion theme.
🎭Romeo and Julia - A Chess love story🎭
I hope you like it.
Wilhelm "Bishop1964" Shakespeare
@nayf
True, whether immediate promotion is the best idea in this position is yet another question. But if the pawn is promoted immediately, promotion to a Bishop is winning (but not all that easy), promotion to a Queen is a draw by either stalemate or perpetual checks from the rook.
The example is from Tim Krabbe's blog, who shows some possible continuations (scroll way down, it's the very last example on the page).
timkr.home.xs4all.nl/chess2/minor.htm
True, whether immediate promotion is the best idea in this position is yet another question. But if the pawn is promoted immediately, promotion to a Bishop is winning (but not all that easy), promotion to a Queen is a draw by either stalemate or perpetual checks from the rook.
The example is from Tim Krabbe's blog, who shows some possible continuations (scroll way down, it's the very last example on the page).
timkr.home.xs4all.nl/chess2/minor.htm
Yes, my statement "to avoid stalemate" used the wrong word choice. I missed that little detail. It should have said "where the purpose of the underpromotion does not involve stalemating".
I actually created a position that satisfied my requirements on March 12 2019 at 2:20 AM while taking a dump.
The position is quite nice and it takes a second to see why the Q promotion is not good.
lichess.org/analysis/nK1k4/PPp5/bpp5/n7/8/8/8/8_w_-_-_0_1
I actually created a position that satisfied my requirements on March 12 2019 at 2:20 AM while taking a dump.
The position is quite nice and it takes a second to see why the Q promotion is not good.
lichess.org/analysis/nK1k4/PPp5/bpp5/n7/8/8/8/8_w_-_-_0_1
And then there is this 2013 blog post from Johan Wästlund:
http://wastlund.blogspot.com/2013/06/a-remarkable-pawn-promotion.html
... reporting a hilarious underpomotion to a rook that was meant as a joke, but actually won the game because Black's time ran out with white keeping sufficient material for a checkmate (with some added hilarity as the rook was placed upside-down on the board at the end of the game).
"lichess.org/study/embed/EUWkTUDh/GSECrknJ"
edit: in the game, black's time run out right after he played Kd8. I got the above study wrong first, I hope it's correct now.
With a new queen on b8 , a forced sequence of moves would have led to an inevitable stalemate - 1/2:1/2 despite time running out. No legal sequence of moves could lead to a win for white (edit : after black's last move Kd8).
But with the rook, it's a different story. There now is sufficient material on the board to continue the game, provided black's King decided for whatever reason escape to d7. As there is sufficient material for white to checkmate, Black lost on time.
"...and ladies, this moment goes to history. For centuries, problemists and study composers have thought that the only motives for promotion to rook or bishop are forcing or avoiding stalemate. But tonight our friend B has demonstrated, with his extraordinary 66:th move, that there is another motive: retaining sufficient material."
http://wastlund.blogspot.com/2013/06/a-remarkable-pawn-promotion.html
... reporting a hilarious underpomotion to a rook that was meant as a joke, but actually won the game because Black's time ran out with white keeping sufficient material for a checkmate (with some added hilarity as the rook was placed upside-down on the board at the end of the game).
"lichess.org/study/embed/EUWkTUDh/GSECrknJ"
edit: in the game, black's time run out right after he played Kd8. I got the above study wrong first, I hope it's correct now.
With a new queen on b8 , a forced sequence of moves would have led to an inevitable stalemate - 1/2:1/2 despite time running out. No legal sequence of moves could lead to a win for white (edit : after black's last move Kd8).
But with the rook, it's a different story. There now is sufficient material on the board to continue the game, provided black's King decided for whatever reason escape to d7. As there is sufficient material for white to checkmate, Black lost on time.
"...and ladies, this moment goes to history. For centuries, problemists and study composers have thought that the only motives for promotion to rook or bishop are forcing or avoiding stalemate. But tonight our friend B has demonstrated, with his extraordinary 66:th move, that there is another motive: retaining sufficient material."
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