The Chess Variant Pages

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H. G. Muller wrote on 2020-05-27 UTC


I converted my 4-men EGT generator to doing the Omega Chess board. (I mapped the board into an 11x12, and then it effectively only needs 122 elements, as neighboring boards can be partly interleaved.)

Oddly enough this confirms the numbers you gave for Bishop+Knight and Wizard+Knight!

What I had not realized is that these end-games are not generally won at all, but are mosty fortress draws: you can only deliver mate in the corner of the Bishop's/Wizard's shade, as you need to cover both the corner and the Wizard square, or the King will simply escape to the latter. And if the bare King takes shelter in the other corner there is no way to smoke him out of the Wizard square there. So you have to go through excessive trouble to prevent the bare King fleeing into that corner, which apparently causes an enormous slowdown. On a normal board it is easy to drive the King along the edge from one corner to the other, so trying to reach whatever corner is not a good defensive strategy there.

As a consequence, only 38.3% of the KBNK positions are won (22.3% lost), and 33.7% of the KWNK positions (17.9% lost). Against 99.8%won / 81% lost on regular 10x10.

Your 3-men generator seems buggy, though; as the checkmating applet here shows, WD is a quite easy win on 8x8.

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