TalkChess.com

[H.G.Muller]

I found a few other interesting Spartan end-games: Q vs 2 light pieces. In Chess this would be KQKBB, KQKBN and KQKNN. The Spartan equivalents are KQKCC, KQKLC, and KQKLL. Now the statistics of such end-games suggest they are won by the Queen, but this is mostly because the overwhelming majority of positions will have at least one of the light pieces unprotected, after which it will be an easy prey for the Queen through checks. So almost all wins in end-games like this are fast tactics. This eclipses what happens in the small but important minority of positions were all pieces are protected.

In KQKBN, for instance, there is a fortress draw, based on the position

[d]8/8/8/8/K2n4/7Q/1b6/1k6 w - - 0 1

This fortress is impenetrable, as the defending King can safely step between b3-a3-a2-b1-c1-c2, keeping the Bishop defended, while the the minors lockout the attacking King at a safe distance. It does not even crumble when the attacker has an Amazon (= QN compound) in stead of a Queen.

In Spartan Chess there are such fortresses too; with the usual substitutions L=B and R=C:

[d]8/8/8/8/4K3/3c1c2/7Q/4k3 w - - 0 1
[d]8/8/8/8/4K3/3r1r2/7Q/4k3 w - - 0 1

and

[d]K6Q/8/8/8/8/3l4/3c4/3k4 w - - 0 1
[d]K6Q/8/8/8/8/3b4/3r4/3k4 w - - 0 1

Another gend-game is 2 light pieces vs Rook. In Chess this is usually trivially drawn, because all you have to do is sac the Rook for oneof the minors, and the remaining minor will not have mating potential. In Spartan Chess both Captain and an extra King do have mating potential. When one of the light pieces is Lieutenant, which does not have mating potential, the Rook can succesfully employ the same strategy, and harrass eithe King or the light piece with mating potential. But when both the light pieces do have mating potential, it gets tricky. Every Rook sac is now fatal, and the attacking side can afford to ignore attacks on its light pieces, so you can only harass the King, which will be hiding behind its pieces.

Turns out that KRKCC is still draw, but KRKKC is a win for the Spartans. (KRKKK would also be a loss for the Rook, but in Spartan Chess you cannot have more than two Kings.) Even with predesignated royal and non-royal Kings it would be a win for the Spartans, but the possibility toexpose either of them to check when you still have two makes live of course a lot easier. Now the extra K is worth nearly a Rook even in the middle game, because of the 'delocalized royalty' it offers (the tactical middle-game value of a non-royal King would only be ~250cP). So it seems this high value, making it significantly better than other light pieces, is retained all the way to the end-game. (Remember KQKK is also draw, while KQKL and KQKC are easy wins.)