|(1) Posted by Joaquim Crusats [Saturday, Oct 31, 2020 12:08]|
A game-like proposition that you cannot lose.
Consider the following proposition. There are four half boards on the table, two of them with white units (ranks 1st to 4th) and two of them with black units (ranks 5th to 8th). Reassemble a full board, White is on the move, then play!
Since you feel generous, you can let your opponent be the first one to choose any of the four half-boards that he prefers (the strongest one?).
However, the half-boards are composed so that they have the following property:
White-1 / Black-1 White wins
White-1 / Black-2 Black wins
White-2 / Black-1 Black wins
White-2 / Black-2 White wins
He who has the second choice can always win the game!
|(2) Posted by Joost de Heer [Saturday, Oct 31, 2020 13:47]|
A (= 0+4 )
B (= 0+4 )
C (= 2+0 )
D (= 2+0 )
A+C: White wins
A+D: Black wins
B+C: Black wins
B+D: White wins
|(3) Posted by Juraj Lörinc [Saturday, Oct 31, 2020 15:27]|
The word "generous" can be perfectly misleading. :)
In this case it is a matter of making choice with more information.
Well done, Joost.
|(4) Posted by Hauke Reddmann [Saturday, Oct 31, 2020 17:35]|
With smaller boards, less material is possible:
|(5) Posted by Andrew Buchanan [Saturday, Oct 31, 2020 18:23]|
Got to have a pawn to win. But is anything more than that necessary?
(= 4+2 )
White to move. Diagram shows one Bl constellation and the two Wh constellations (a-file and h-file). To see the other Bl position, just flip left-right
|(6) Posted by Joaquim Crusats [Saturday, Oct 31, 2020 18:36]|
Nice proofs of concept!
This situation may be the case for certain Chess960 positions.
It would be nice to have four orthodox homebase positions, not symmetry related, showing this behavior with subtle winning lines. That perhaps would be worth showing in your local club.
|(7) Posted by Andrew Buchanan [Saturday, Oct 31, 2020 18:49]|
(= 3+7 )
WTM. Each constellation contains king and the Kside or Qside units of that colour. Sorry that it’s still trivial and symmetric Joaquim. But at least it’s a miniature homebase :) castling doesn’t help anyone btw
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