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George Duke wrote on Sun, Jan 15, 2017 09:57 PM UTC:

Using CENTAUR as widely as possible can only further popularize.

BLUE CENTAUR is on e4 to start. It is owned by both sides, cannot be captured, and does figure in capturing and checkmate normally. Player may move immortal BLUE CENTAUR up to five times in place of regular move.  No moving Blue Centaur until Move 11, but of course it blocks off the e4 square as expected the first ten moves too. This problemists' piece as uncapturable BLUE QUEEN could readily be used, but the following score describes BLUE CENTAUR on e4.

1 d4 d5 /Since e-file gets blocked, d-file is important. 2 e3 a5 / Positioning for Rook egress.  3 N-a3 b6. 4 c3 Ra8-a6 /Black Rook safe distance from Blue Centaur. 5 B-d2 B-g4 /Black wants to draw the Queen into harm's way near the Blue. 6 Qxg4 e7-e6 /White Queen cannot resist the bait taking Bishop. 7 0-0-0 h6. 8 Q-h4 Q-d7 / Both Queens jockeying away as Blue Centaur phase nears. 9 K-b1 Q-a4. 10 K-a1 K-d8.   Upcoming move 11 Blue Centaur can be moved, and six pieces are in the a-file away from e-file, achieving some safety from the Immortalist. No diagonal from e4 reaches a-file after all. Likely over 1/3 the remaining moves will be Blue Centaur, and games run fewer than 30 Moves, but it's anybody's guess. At first Blue Centaur, whichever side uses him first can only capture Pawn, since pieces have stayed clear of the reaches. White's King is particularly well-disposed on a1, which from e4 is quite a slog.

Play would be different with Blue Queen instead of Blue Centaur, to avoid Blue Queen lines of attack differently.