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Mar 6, 2011, 11:49:16 PM3/6/11

to sprouts-theory

(For diagrams, see http://www.files.takingthefun.com/sprouts/2011clashgame2/)

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

11(32)11[12] {7P1#1^1 + [0.0.1<AB>;0.0.1<AB>]#0^4}

Aunt Beast doesn't know who wins this position, but she can see that

Roman loses if he moves in the 0^4 component.

20(33)31[21,22] {7P1#1^1 + [0.0.1<CD>;0.0.AB;ABCD]#1^5} N

Roman moves in the 0^4 component, changing it to a 1^5. In a way,

Roman's hand is forced: he wants S(17) to have the nim-values 1^x, and

this is the only move that does that.

29(34)30[28] {7P1#1^1 + [0.0.1C;0.0.AB;A.B.D;C.D]#5^0} 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 misere sprouts. Understanding these positions will

require a fundamental breakthrough in the mathematical theory of

misere games.

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

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

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

11(32)11[12] {7P1#1^1 + [0.0.1<AB>;0.0.1<AB>]#0^4}

Aunt Beast doesn't know who wins this position, but she can see that

Roman loses if he moves in the 0^4 component.

20(33)31[21,22] {7P1#1^1 + [0.0.1<CD>;0.0.AB;ABCD]#1^5} N

Roman moves in the 0^4 component, changing it to a 1^5. In a way,

Roman's hand is forced: he wants S(17) to have the nim-values 1^x, and

this is the only move that does that.

29(34)30[28] {7P1#1^1 + [0.0.1C;0.0.AB;A.B.D;C.D]#5^0} 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 misere sprouts. Understanding these positions will

require a fundamental breakthrough in the mathematical theory of

misere games.

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

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

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