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Have anybody tried to verify retrograde analysis of a chess game in The Flanders Panel by Pérez-Reverte? So far I have found only reconstruction of the board in this post: http://bibliophilicnightowl.blogspot.ru/2011/02/on-chessboard-ii-flanders-panel-by.html

In hope one day to find myself time to analyse this game with Reverte's book in my hands, I wonder if anybody has already done so, and what are the findings? Does the description of the game in the book make sense?

[title "The position of the chess pieces as shown in the painting by Van Huys"]
[fen "1nb5/pp1p4/PRP5/pR6/k1K1P3/2P5/2qP1P2/1NrnQB2 w - - 0 1"]

* Update *

Analysis as described in Flanders Panel book:

"IT'S A REAL GAME," said Muñoz. "A bit strange, but perfectly logical. Black was the last to move." ... "The tricky question is: Who took the knight?" "You mean the white knight," said Muñoz. "There's only one left on the board." ... "Now, we've looked at the pieces actually on the board, but in order to analyse the game, it's essential to know which ones are off the board too, the pieces that have already been taken." He looked at the picture. "What's the player on the left called?" "Ferdinand of Ostenburg." "Well, Ferdinand of Ostenburg, who's playing Black, has taken the following white pieces."

"That is: a bishop, a knight and two pawns. For his part, Roger de Arras has taken the following pieces from his rival."

"That's four pawns, one rook and a bishop." Muñoz looked thoughtfully at the sketch. "When you look at the game from that point of view, White would seem to have an advantage over his opponent. But, if I've understood correctly, that's not the problem. The question is who took the white knight. Clearly it must have been one of the black pieces, which may seem to be stating the obvious, but we have to go step by step here, right from the beginning."

"This morning I reconstructed the two previous moves," he said, without a trace of boastfulness. "Then I ran into a problem. Something to do with the unusual position of the pawns." He pointed to the chess pieces in the picture. "We're not dealing with a conventional game here."

"According to the way the pieces are distributed," Muñoz went on, "and bearing in mind that Black has just moved, the first thing to find out is which of the black pieces made that last move."

"The easiest way to do that is to discount the black pieces that could not have been moved because they're blocked or because of the particular position they're in. It's clear that none of the three black pawns, on a7, b7 or d7 could have moved, because they're all in the position they occupied at the start of the game. The fourth and last pawn, on a5, couldn't have moved either, because it's between a white pawn and its own black king. We can also discount the black bishop on c8, still in its initial position, because the bishop moves diagonally and both of his two possible diagonal paths are blocked by the black pawns that have not as yet been moved. As for the black knight on b8, that wasn't moved either, because it could only have got there from a6, c6 or d7 and those three squares are already occupied by other pieces. Do you understand?"

"Perfectly," said Julia, who was leaning over the board following his explanation. "That means that six out of the ten pieces could not have moved." "More than six. The black rook on cl couldn't move, since it only moves in a straight line and its three surrounding squares are all blocked. So none of those seven black pieces could have made the last move. And we can also discount the black knight on dl." "Why?" asked César. "It could have come from squares b2 or e3." "No, it couldn't. On either of those squares, that knight would have had the white king on c4 in check; in retrograde chess that's what we might call an imaginary check. And no knight, or any other chess piece for that matter, with a king in check is going to abandon that position voluntarily; that's simply impossible. Instead of withdrawing, it would capture the enemy king, thus ending the game. Since such a situation is impossible, we can deduce that the knight on dl could not have moved either." "That," said Julia, who had kept her eyes glued to the board, "reduces the possibilities to two pieces then, doesn't it?" She put a finger on each of them. "The king and the queen." "Right. That last move could have been made only by the king or the queen." Muñoz studied the board and gestured in the direction of the black king, without actually touching it. "First, let's analyse the position of the king, which can move one square in any direction. That means he could have arrived at his present position on a4 from b4, b3 or a3 ... in theory." "Even I can see what you mean about b4 and b3," remarked César. "No king can be on a square next to another king. Isn't that right?" "Right. On b4 the black king would have been in check to the white rook, king and pawn. And on b3, he'd have been in check to rook and king. Both of which are impossible positions." "Couldn't he have come from below, from a3?" "No, never. It would then be in check to the white knight on bl, which, given its position, is clearly not a recent arrival, but must have got there several moves ago." Muñoz looked at them both. "So it's another case of imaginary check showing us that it wasn't the king that moved." "Therefore the last move," said Julia, "was made by the black queen."

  • 1
    What is the question? – ferit Mar 15 '16 at 17:09
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    If the question is 'can this position be achieved?' then the answer is 'yes, and without much difficulty' - from a retro perspective there's nothing locked in this position. The Black pawn on a5 has made two captures to get there, but white is short a knight and bishop (and of course could have promoted their g- or h-pawns) so there's plenty of material available for it to capture; the 'cage' that the B king is in unlocks easily after e.g. retracting White's rooks while Black shuffles around his Q or N. – Steven Stadnicki Mar 15 '16 at 19:15
  • Perhaps the position is missing a white pawn on b2? That looks like it would leave a much more challenging 'cage' to unlock; now Black has no legal unmoves (my previous comment about black shuffling their N was incorrect, it has no unmoves that wouldn't check the White king) and White has four pawn captures spoken for, leaving only two 'free' captures on that side (while all of Black's captures are spoken for - two by the pawn on b6 and a5, and the WBc1 captured at home). Things still look like they would unlock relatively straightforwardly, but there's at least a chance for analysis then. – Steven Stadnicki Mar 15 '16 at 19:42
  • Reverte in his book gives an interesting analysis of this game. – zork Mar 15 '16 at 22:18
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    IIRC, the analysis in the book goes much further. But it assumes different arguments than classical chess retrograde analysis, like "this didn't happen because White rather have mated in one / We can exlcude this possibility because Black would rather have taken the queen", etc. – Evargalo May 2 '18 at 8:28
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Unfortunately, I can't really speak to making 'chess sense' of the game — the position is sufficiently artificial that it's implausible for it to have arosen out of a sensible game (for instance, whatever White's move before Black's most recent Qb2-c2, they could simply have captured the Black queen instead). Instead, I'll speak to the game from a retrograde analysis perspective, and particularly the question of 'what can we necessarily say about the capture of the White Knight?'. As it turns out, the answer is 'next to nothing without any further information.' To see this, let's try and get from the position we're given to a position that's more amenable to direct analysis. First, let’s get the White pieces towards home and untangle some of the Black pieces in the process: retract Qb2-c2 (the only Black move, as noted), then WKd3-c4, BNe3-d1, WKe2-d3, BNf5-e3, WPc2-c3, BQg7-b2, WNa3-b1, BNe7-f5, WRh5-b5, BRb1-c1, WRh1-h5, BRb5-b1, WQd1-e1, BRh5-b5, WKe1-e2, BRh8-h5, WRb1-b6, BKb4-a4 (note that by Black unmoving ‘into’ check, he’s actually moving out of it!), WRa1-b1 (White is now ‘forced’ to undo the check), BKc5-b4, Wnb1-a3, BKd6-c5, WPe3-e4, BNg8-e7, WPe2-e3, BKe7-d6. This leaves us with this position:

[FEN "1nb3nr/pp1pk1q1/P1P5/p7/8/8/2PPPP2/RN1QKB1R w - - 0 1"]

From here, there are a few salient features of the position to notice:

  1. White is missing two pieces (the knight of mystery and their black-squared bishop) and two pawns; Black is missing two pieces (their black-squared bishop and a rook) and four pawns.
  2. Two of White’s missing units were captured by the pawn presently on a5, with the captures happening on b6 and a5. (It would appear that either these were the bishop and knight or that one of the pawns must have promoted, but this isn’t necessarily so: Black could have captured White’s b-pawn on b6, and the White pawn currently on c6 could have been the e-pawn, with the White pawn at e4 in the original position coming from g2 — it would take some effort but I think such a game could be constructed)
  3. Black’s queen’s rook couldn’t have gotten out past the bishop on c8; it was captured either on a8 or b8.

Beyond these constraints, though, there’s very little restriction on the game; it’s straightforward to get to the intermediate position shown above with the missing white knight having been captured by the Black pawn on either b6 or a5, or by any of the other Black pieces (except of course the bishop on c8), including even a capture by the missing rook on either a8 or b8 — it’s even possible that both of the ‘original’ White Knights were captured and that the knight on the board is a promoted Knight! As an example, here’s a game leading to the intermediate position above with the White Knight having been captured by the missing Black rook:

[Title "Proof game"]
[fen "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1.Nf3 Na6 2.Nd4 h5 3.Nc6 h4 4.Nb8 Rxb8 5.g3 g5 6.gxh4 Bh6 7.hxg5 f6 8.gxf6 Be3 9.fxe7 Bc5 10.b4 Kf7 11.bxc5 Qf8 12.e8=N Qg7 13.Nf6 Ra8 14.Nd5 Rb8 15.Nb6 cxb6 16.Bb2 Nb4 17.Be5 Nd5 18.Bxb8 Ndf6 19.Be5 Ne7 20.Bc3 Nc6 21.a3 Rxh2 22.a4 Rh8 23.a5 Nb8 24.a6 Ng8 25.c6 Nh6 26.Ba5 bxa5 27.Rh5 Ke7 28.Rh3 Ng8 29.Rh1
  • It is not quite clear how you get white pieces bsck home. For example in WKd3-c4 how you got d3? Why could not it be e3-d4-c4 or something else? – dokondr Mar 17 '16 at 21:25
  • @dokondr It could easily have been (and that's part of the point) - I chose a particular path that got the pieces into a position that makes it obvious what freedoms there are, but that path was essentially arbitrary; the final position isn't at all locked. – Steven Stadnicki Mar 17 '16 at 21:35
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And we can also discount the black knight on dl." "Why?" asked César. "It could have come from squares b2 or e3." "No, it couldn't. On either of those squares, that knight would have had the white king on c4 in check; in retrograde chess that's what we might call an imaginary check. And no knight, or any other chess piece for that matter, with a king in check is going to abandon that position voluntarily; that's simply impossible. Instead of withdrawing, it would capture the enemy king, thus ending the game. Since such a situation is impossible, we can deduce that the knight on dl could not have moved either."

They neglect to consider the possibility that the knight came from e2, and was a pawn last move! White has 4 pieces off the board (a bishop, a knight, and two pawns.) Two captures were made by the a5 pawn, leaving the possibility of fxe2 (or fxe3) and exd1=N. White's h and g pawns could have promoted to anything and gone to those squares.

If further analysis of the position makes it necessary for Black to not use all his captures on this, there's also the possibility that White's d4 pawn was originally a b-pawn, and the d1 knight was Black's e-pawn instead of the f-pawn. This lets Black use one capture elsewhere.

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