Clash of the Titans, Game 2

Analysis by Josh Jordan

For background, see my analysis of game 1.

22- (Khorkov - Jordan+Aunt Beast*) 1(23)1[2-10] 1(24)23[11-14] 11(25)24 2(26)2 2(27)26[3] 15(28)16 15(29)16[17-19] 15(30)17 16(31)20


Aunt Beast doesn't know who wins this position, but she can see that Roman loses if he moves in the 04 component.

20(33)31[21,22] N

Roman moves in the 04 component, changing it to a 15. In a way, Roman's hand is forced: he wants S(17) to have the nim-values 1x, and this is the only move that does that.

29(34)30[28] P

Move 34 and every subsequent even-numbered move is P. Based on its nim-values, this seems to be another one of those moves which magically win, seemingly at random. As John Conway wrote in Winning Ways, "You mustn't expect any magic formula for dealing with such positions."

Situations like this demonstrate just how inadequate nim values can be in the analysis of misère sprouts. Understanding these positions will require a fundamental breakthrough in the mathematical theory of misère games.

17(35)17[18,19] 21(36)22 18(37)19 18(38)19 19(39@35)38 20(40)36

After move 40, S(3) still has nim-values 11 (the sphere hasn't changed since move 27), but S(40) has evolved into a component with nim-values 55 — and the result is still a misère P-position! We've truly crossed over into the Twilight Zone.

18(41)37[39] 4(42)4[5-8] 4(43)42[5] 3(44)3 3(45)27 9(46)9 9(47@10)46 21(48)22 21(49@33)48 40(50)49[22] II

After a long endgame, Roman concedes.