[Retros] The generic understanding of Retro-Strategy

Rol, Guus G.A.Rol at umcutrecht.nl
Tue May 29 13:59:13 EDT 2007

Dear retro-friends,

At this point in time nothing is to be found in the FIDE Laws or Codex conventions about retro-strategy (or retro-synthesis). One might therefore be tempted to believe nu such thing as retro-strategy exists. There are a few conventions about e.p. and castling(s) and 50 moves and repetitons which stand in their own rights and do not seem to point at anything of the generic quality one would associate with a broad concept like "retro-strategy". But, when looking further, it becomes clear that there is a lot more in the rules than just a few scattered case-laws. First of all, there is the "footprint definition" of retro-strategy in the Codex. It does not define what retro-strategy is, but it defines what it is not! See:

article 16 .... Other conventions (which also affect other rights to move) should be expressly stipulated, for example: .... (b) If several possibilities that result in several solutions are to be distinguished in the retro play, i. e. in the proof game or in some parts of it, then these possibilities are called retro-variants (for example RV).

The immensely important statement made here is that the default conventions do not contain retro-variants as the latter require expressed stipulations. In a generic translation it means that every non-RV retro-problem must have a synthesized (forward) solution. That of course implies the assumption that there are rules to decide every contest between uncertain game state variables - such as the one between mutually exclusive castlings. As my composition Probleemblad R309 below demonstrates, this is not the case. There is nothing in the Codex to arbitrate between castling right and repetition. Is this a problem? No, it is not. Driven by necessity we apply every available cellular state convention in the only mode available to us which is "first come, first served". How else could we abide by the rules if retro-variants are unavailable? In R309 the first game state to be resolved is "repetition draw?". Answer: No draw, because this is not the preferred value for this game-state variable; the repetition draw must be 100% certain. The second issue arises a full move later after the first one has been decided. Black can no longer castle and must accept defeat because of the unavoidable earlier choice.

Where does this lead us? Most certainly in the direction of a concept driven by generic principles. We need the idea of "preference" in game state conditions and we need the idea of "time-order" to resolve yet uncharted territories. What we don't need is "the mutually exclusive castling rule" (also in article 16) since it is already contained by the forementioned principles! By the way "first come, first served" is often referred to as "Leap before you Look" or LbyL. Note that I did not define retro-strategy from LbyL but I found LbyL by outlining retro-strategy from its complementary approach, retro-variants. Of course, RV is a valid subject in itself and arguably more akin to the scientific method. I do not extend such compliments to AP but that is a subject for another day.

The most important reason for discussing retro-strategy is the bearing it has on fairy chess variants, like "fuddled men", in fact on any variant with "lagging" game state conditions. Generically understood retro-strategy is quite powerful enough to resolve the "stipulation crisis" in Ronald Turnbull's otherwise very enjoyable article on the subject. For another post.

PB R309 Rol

Diagram: r3kn1R/p2p1ppB/P1pP2pb/4p1Pr/2Q4p/1P5K/7P/8 Stipulation: #7

Solution: (composer comments) The solution shows the battle between castling right and the strategic threat of an automatic repetition draw. 1.Bg8 Ne6 2.Bh7+! Nf8 3.Bg8! Ne6 At this point black has lost the right to castle as a retro-strategic consequence of the single white repetition plus the retro-analysis of the diagram position. If black still had castling rights, then the last two moves could only have been Ne6-f8 and Bg8-h7+!, or in other words, the position after move 3 would be drawn. However, no position may be considered drawn unless double repetition is absolutely certain. Such not being the case, we are forced to play on at the expense of the black castling right. 4.Qf1! Another way to look at it is by considering the black defense 0-0-0 at this point. Analysis shows that any proof game must contain a "premature" double repetition and is therefore an illegal game. Hence, 0-0-0 is illegal. 4... Nxg5+ 5.Kg2 Ph3+ 6.Kh1 Nf3(Ne6) 7.Bh7(Bxf7)#.

An additional question arises if we attempt the dual solution: 4.Bh7+ Nf8 5.Bxg6 Pxg6 6.Qg8/Qf1 en 7.Qxf8#! It is apparently dismissed by observing that after 4.... Nf8 an actual repetition draw did occur during the solution phase. But some might debate that on the basis of "un-identical positions by the loss of castling right during play". IMHO this viewpoint cannot be upheld against Retro Article 18 "Repetition of Position - A position is considered as a draw if it can be proved that an identical position [with same rights and same choices] has occured three times in the proof game combined with the solution.". You will find it impossible to construct a single legal proof game in which the diagram + the moves "1.Bg8 Ne6 2.Bh7+ Nf8 3.Bg8 Ne6 4.Bh7+ Nf8" occurred, and in which black still possessed castling right in the diagram position. This secures a draw in the dual-try.

Due to its theoretical retro-strategic implications (awaiting a more elaborate exposé) I decided to dedicate this composition to game-theorists Robert J. Aumann en Thomas C. Schelling, who received a Nobel prize in Economy during the time that I was slaving on this material. Not that they will come to know about it.....

Guus Rol.

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