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Chess

Timeline for Maximum number of pieces on board in dead position

Current License: CC BY-SA 4.0

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Dec 31, 2023 at 6:18 history edited Laska CC BY-SA 4.0
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add links to two more R(1,B)
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Dec 16, 2023 at 22:13 history edited Laska CC BY-SA 4.0
alert R(1,D)
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simplified the logic
Dec 15, 2023 at 9:23 history edited Laska CC BY-SA 4.0
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Dec 15, 2023 at 6:37 comment added Laska Let us continue this discussion in chat.
Dec 15, 2023 at 6:36 comment added Laska @supercat Two points (1) If BTM, White might have just moved e.g. Nh3-f2. But there was an alternative Bg1xc5. So the position is stalemate but reachable. (2) When a game ends, there is always still someone on move. FIDE Art 1.3 "A player is said to ‘have the move’ when his/her opponent’s move has been ‘made’."
Dec 15, 2023 at 6:36 comment added supercat @Laska: As a point of clarification, the reason your 32-piece diagrams would not be be solutions for R(1,A) with black to move is not that black would have no legal moves, but rather the position would be live after Black made the only legal move (capturing either a4 or c4 en passant).
Dec 15, 2023 at 6:21 comment added supercat ...solution you know of to R(1,A) since it has 30 pieces rather than 29.
Dec 15, 2023 at 6:20 comment added supercat @Laska: My definition for #1 was "the side on move has at least one legal move, but no sequence of moves will produce checkmate", and your definition for "A" was "Neither side in check; no additional information provided". It is possible to infer from my last diagram, without supplemental information, that it is not possible for Black to be on move. If White had moved last, the game would have ended and nobody would be on move. Thus, for anyone to be on move, White would have to have moved last. If the solution is valid, I would think it should be included in the answer as the best...
Dec 15, 2023 at 6:07 comment added Laska @supercat. Yes the chess works: nice idea. So this is WTM dead / BTM stalemate and in both cases the position is reachable. The issue is the interaction between the definition of Type A & the definition of Challenge 1. To resolve it, either BTM must be dead not stalemate (difficult, I think), or (better) you find some way of making BTM a zombie position.
Dec 15, 2023 at 5:25 comment added supercat @Laska: Oops. So I was missing something. Would the following be a valid 30-unit solution (White's g pawn captures black's f and g pawns and promotes to bishop)? bqn1KN2/rrk1pP2/nb1pP2p/p1pP3P/PpP5/1P6/B1B2N1R/5RBQ w - - 0 1?
Dec 15, 2023 at 5:00 history edited Laska CC BY-SA 4.0
continue to improve the text
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Dec 15, 2023 at 1:50 comment added Laska @supercat Thanks for this. (1) If WTM, it's living by 1.Ra3/Rc3: the last move was any of 5 Black pawn moves. (2) If BTM then as you say it's stalemate. Whatever White did could have been the living Ra3/Rc3 instead, so no problem reaching this position. But in neither case is the position dead.
Dec 14, 2023 at 18:19 comment added supercat @Laska: Try "bqn1KN1B/rrk1pBN1/nb1pPp1p/p1pP1PpP/PpP3P1/1P6/R1R3Q1/8 w - - 0 1" unless I'm missing something. I think that position would be reachable with either white on move, or as a stalemated position following a white move, but I don't think it can be a live position in any case.
Dec 14, 2023 at 18:09 comment added Laska @Supercat. Please propose specific FENs, and I will look at them. "Tweaks" are hard to interpret when there's so many diagrams. And it's time for bed here :)
Dec 14, 2023 at 17:51 comment added supercat @Laska: Upon further consideration, more tweaking would be required, but I think it's still doable. Move the bishop and knight that are on dark squares to h8 and g7, respectively, and change black's penultimate move to some other arbitrary pawn move.
Dec 14, 2023 at 17:44 comment added supercat @Laska: See my response to your comment to the question; unless I'm missing something, a tweak to the position for R(3,B) would satisfy R(3,A) on the presumption that if only one side has a legal move, that side must be the one on move.
Dec 14, 2023 at 15:48 vote accept supercat
Dec 14, 2023 at 13:44 history edited Laska CC BY-SA 4.0
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Feb 18, 2018 at 13:18 comment added Laska Realized oh so much later that I could find a place for wN in the 3rd position. Missing pieces count is exactly what's needed to explain the pawn captures: very lucky
Feb 18, 2018 at 13:14 history edited Laska CC BY-SA 3.0
pushed challenge 3, Type A from 28 to 29 units
Oct 12, 2017 at 6:55 history edited Laska CC BY-SA 3.0
edit text now there is more info in titles
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Oct 11, 2017 at 23:37 comment added Laska I wanted to see if I could get at least 2 more units by moving to Type C. I have just found such a position with 30 units, where 3 forced captures take place at the beginning. For the first time, I am not confident that this can be improved.
Oct 11, 2017 at 23:32 history edited Laska CC BY-SA 3.0
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Oct 11, 2017 at 9:31 comment added Evargalo +1 for th beautiful 28-men dead draw. That will even be 29 if you force the move for black and add a wQb2...
Oct 11, 2017 at 8:00 history edited Laska CC BY-SA 3.0
very minor text edits
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Oct 11, 2017 at 3:12 comment added Laska I agree. It replaced and generalized the old "draw by insufficient material" FIDE rule. I don't know why they felt this was necessary, but it was a gift to retro composers. It does make sense that no claim is needed. 50 moves & 3 rep are complicated and require arbiter verification. But deadness is usually simple to see. I have also heard that "no claim" simplifies the online world, where a game just ends immediately when e.g. KNvK is reached.
Oct 10, 2017 at 14:35 comment added supercat If a position is dead, then by definition pretty much nothing the players could do would affect the outcome whether or not the game was recognized as "dead". The only situation I can think of where there could be an issue would be if someone resigned a dead position and later realize it was dead, and could plausibly claim the resignation was not deliberate bad sportsmanship (since bad sportsmanship might justify a forfeit even if the game would otherwise have been drawn). Otherwise, I would think that the official scores for games would include all the moves that were played.
Oct 10, 2017 at 7:00 history edited Laska CC BY-SA 3.0
correct the 2nd diagram
Oct 10, 2017 at 6:37 comment added Laska Thanks very much! Actually the laws of chess do say that a dead position game ends immediately. It's as sudden as checkmate or stalemate. Francois Labelle on his website wismuth.com has a list of games where players carried on going for a couple of turns before they realized! (Nit: he incorrectly terms such impossible moves "illegal".) But for formal chess problems, a recent 2015 convention says dead position, like 50 moves, only applies by default to retros (to protect e.g. self-stalemates). Most dead position problems are retro, so it's no issue. In others, as here, the condition is implied.
Oct 10, 2017 at 5:58 comment added supercat I hadn't been asking for that retrograde wrinkle, but I must say it's quite cute if one adds the wrinkle that the position must have been rendered dead by the last move. I don't think the laws of chess require that play stop as soon as a dead position is reached, or would require that an arbiter recognize whether a position is dead except in cases where the game is over for other reasons (e.g. because a player's flag has fallen) and the question is whether to score a full or half point. Still, definite +1 for the retro puzzle and the 32-piece version.
Oct 10, 2017 at 1:46 history edited Laska CC BY-SA 3.0
have added 32 unit record
Oct 9, 2017 at 23:42 history edited Laska CC BY-SA 3.0
recognition that upvoting mechanism does not encourage puzzle, so have simply explained how the position was reached
Oct 9, 2017 at 23:14 history edited Laska CC BY-SA 3.0
Fixed restatement of problem cases. Gave hint to bonus question.
Oct 9, 2017 at 22:57 comment added Laska Thanks supercat for clarification on 1,2,3 I will edit the post - I knew I was missing something. There are apparently three possibilities for last move (b3,f4,h3). (d6 had impossible prior check on wK). But the fact that we are in dead position.has retro implications. The answer is a bit sneaky.
Oct 9, 2017 at 20:27 comment added supercat Looking at the diagram, I can see five potential last moves for Black (b3, d6, f4, h3). I don't see any particular reason Black couldn't have had a pawn on b4, d7, f5, or h4 prior to the last move. If the f8 knight were on g6 and the f7 bishop on g8, Black could temporize indefinitely with Ke8/Kd8 and White with Ra1/Rf1 with pawns in any of the aforementioned positions.
Oct 9, 2017 at 20:13 comment added supercat The difference between #2 and #3 is that a game of #3 could not end except by draw-by-repetition, draw-by-N-moves, or other such rule that is not based purely upon the position of pieces on the board, side on move, etc.. By contrast, #2 would allow for the possibility that players could end the game with a stalemated position.
Oct 9, 2017 at 16:39 history answered Laska CC BY-SA 3.0
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