## Solutions for Drawn Proof Games
The general approach for most of these problems is: (1) Find the unique draw cycle (from diagram position to diagram
position), usually in 2.0 moves. This "flipping" will repeat twice.
Article 18 of the Chess Problem Codex: A position is considered as a draw if it can be proved that an identical position [i.e. the same kinds of pieces on the same squares with the same move rights] has occurred three times in the proof game combined with the solution. There are two self-consistent opinions on this. (1) The first approach would rely on an over-arching principle, one that says that the compositions try to remove all human decision-making. Just as players in chess problems don't resign, and just as we codify the meaning of "direct play" and "help play", so we should not be trying to reason whether a player claimed a draw they were entitled to. We should simply specify that when a trigger happens, the draw will be claimed. This approach is basically simpler than any other, particularly in cases where we know a position did repeat 3 times historically, by one of many different ways. Or do we look at different points in history and alternative paths at each point? Moreover, some retro compositions from the past depend upon the pre-eminence of Article 18, and it would be churlish to render those problems cooked after the fact. (2) The second approach would apply a different over-arching principle: that conventions should apply only where there is otherwise irresolvable uncertainty about the solution. They should never reverse a logical implication from the diagram and stipulation. The e.p. & castling conventions are well-behaved from this point of view. Now apply this principle to draw by repetition. If a game is known to have lasted past the third repetition (because we are told that the game was e.g. a Draw at SPG 14.0, and there is no other route to the final position), then the logical conclusion is that no player chose to claim a draw through repetition. This is simple retro reasoning, and no recourse to any convention is necessary. If there are two possible histories on the other hand, and exactly one would have traveled via a third repetition, then Article 18 would apply to ensure that the solution is unique. See the solution to {J} below.
The Black QR was captured in cage, and bishop & knight by pawns.
Black captured one unit on b file, but two other captures unclear. Last
move 23...Kh6×Mg6 Prior 23 Rg5-h5+. So M=0 and 22...Kg6×M'h6 Prior 22
Rh5-g5+ So M'=0 again. Same for previous series, since the only escape
from retrogression is b4, not available until 19. Note the bonus switchback in Black's 15/16 moves.
In fact some of the earlier problems could also be retracted by half a move, and given a similar stipulation to {P}. For example in {K} if 8. Nc6-b8 is retracted, then that nevertheless is the unique continuation which could lead to the draw by repetition. On the other hand, {L} does not admit such a step: retracting 12. Ra1-b1 would allow the alternative 12. Rh1-g1. The diagram for {I} is very clean, and in fact inspired Nicolas Dupont to turn to the "homebase" theme, with which we have both since had some success. Just fifteen years after this problem was composed, I have finally managed to generate a fully-homebase version, which has been entered for a competition so I am not free yet to publish it.
(1) Design a "Drawn. Proof game n" problem in which there are
(2) Design a "Drawn. Proof game n" problem with Ceriani-Frolkin, but where the whole game is determined, including the repetition. (C.f. composition {I}.] [1] Article 9.2 of FIDE Laws of Chess
[2] In the stipulation for problems {G} &
{I}, I discuss claiming a draw "with" the next move. This choice
of preposition is intended to glide over an issue with clause a in Article
9.2. Namely: if the draw comes |