[Note: all problems were original to this article, which appeared in pages 140-141 of The Problemist, July 2001. In that issue, problem {A1} was attributed to another magazine, but this has since been happily corrected. This is Ronald's text (with his own cute draft diagrams) edited by John Rice for The Problemist, and as typeset by me for this site. Thanks to Ronald for permission to reproduce his work here. The compositions alone can be found here. My annotations are in square brackets. AB]

Dead Reckoning: a new discovery in problem chess

by Ronald Turnbull

Andrew Buchanan of Edinburgh and the USA has made a new discovery in problem chess. Consider the simple diagram {A1}. This position emerged during a game played strictly in accordance with the FIDE Rules of Chess. Who just moved? This can clearly not be determined. Except that it can!

{A1}: A.G.Buchanan
The Problemist,
July 2001
Who just moved?

The relevant Rule of [the 1997 Laws of] Chess is Article 1.3 (Dead Game): "If the position is such that neither player can possibly checkmate, the game is drawn." Article 9.6 adds: "This immediately ends the game." The diagram shows a game thus drawn (Dead Game). The last move to the diagram must have been a capture of Q or R, else the game was dead before that move. Now suppose Black has just captured Q or R, from a7 say (see {A2} here). Black's only move to escape check is Kxa8, with a drawn game to follow. Accordingly, no checkmate is possible from this position: Article 1.3 applies and the move Kxa8 does not take place. So Black didn't just move, and White did. [Note: in the current 2005 version of the Laws of Chess, 5.2b is the relevant article.]

Article 1.3 presumably exists so that if some player suffers flag fall in a dead position, the game is drawn not lost. (I'm a problemist: don't cite me if you're a player who has accidentally resigned in a dead position.) But it has striking problem consequences. In Diagram {B}, with White to play, Andrew asks: which (if any) is the original White Queen's Rook?

{B}: A.G.Buchanan
The Problemist, July 2001
White to move: where is White's original Queen's Rook?

Here it appears that White cannot avoid giving stalemate. However, Black's last move to the diagram was Kh2-g1 - possibly with capture of some white unit. Black King was here escaping check from the white Rook, which had just made some capture on h3.

That move was Black's only legal one. Accordingly, if position {B} is dead then so was the position before that black move. That black move took place, so position {B} is still alive.

We now notice that there is just one way that White can avoid giving stalemate - and that is by giving checkmate! This he can do in just one way: by castling. The position before Black's last move was still alive only if this castling option is available to White. And so we have a position, never before seen in orthodox chess play, where we can say with certainty that White has not lost the right to castle. The history of the Queen's Rook is that it has no history: it has remained where it started, on a1.

Reasoning from Article 1.3 will destroy certain existing problems - for instance, any selfstalemate. Accordingly, we label a problem as Dead Reckoning (DR) in cases where Article 1.3 is to be applied. [This practice is not followed on this site.] And we shall say White/Black to move even in positions (such as Diagram {E}) where the side that has the move may not exercise that right as the game has just died.

{C}: R.Turnbull
The Problemist, July 2001

The point of {C} becomes apparent when we realize that, far from anyone achieving mate in 3, Black is about to get stalemated.

So what was Black's last move to the diagram? If it was Kg8-h8 (or with capture) that move was forced and led to a dead position: so was itself a dead move. If it was Pa6-a5, then Black did have a choice. He could instead have played Pa6xb5+. However, this is followed by wKa5 or wKxb5, both stalemate. And so the position with bP on a6 is also dead. Accordingly, Black just played Pa7-a5, and White may play 1.bxa6e.p. bxa6 2.b7 a5 3.b8R/Q#.

{D}: R.Turnbull
The Problemist, July 2001

Not every Dead Reckoning problem involves retroanalysis. Diagram {D} seems rather easy. White starts, and with Black's help stalemates him on the 7th move. Provided Black plays b7-b5, stalemate of Black in 7 moves seems inevitable. Indeed, it is inevitable... and 2.b5 is Dead Game with no further play. So Black must advance more slowly, and White must play so as to allow still-alive game ... by checkmate to White! 1... Kg7 2.b6 Kf6 3.b5 Ke5 4.b4 Kd4 5.b3 Kc3 6.a4 Kb2 7.a3+. Now the game is still alive as 7...Kxa1 8.b2#. Accordingly, White may play 7...Kxb3=. Note that 2.a4? turns out not to work - wK can't get through to b2.

The two final diagrams are offered for solving.

turnbull/DeathE.jpg turnbull/DeathF.jpg  
{E}: A.G.Buchanan
The Problemist, July 2001
White to move:
How many moves by bK?

{F}: R.Turnbull, A.G.Buchanan,

The Problemist, July 2001
3 solutions

Almost 100 DR positions, mostly with retro stipulations, are to be seen on Andrew's website anselan.com/chess.html. Dead Reckoning gets dead complicated, and prospective composers of retros would be well advised take a look at this material.

Extracts from the FIDE Laws of Chess (Jan-Feb 1997):
A1.3: If the position is such that neither player can possibly checkmate, the game is drawn.
A9.6: The game is drawn when a position is reached from which a checkmate cannot occur by any possible series of legal moves, even with the most unskilled play. This immediately ends the game.

See the problems by themselves here.

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