We return to the previous 17- game, so Josh can try something different on move 25.
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25@14)23 14(26)24[17] 15(27)16 12(28)22 I
Sunday, June 20, 2010
Saturday, June 19, 2010
The 4th 17- of June, 2010 (Roman wins)
We return to move 25 of the previous 17- game, so Roman can try something different on move 26.
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 17(26)25[23] 6(27)19 6(28)6[5] I
Roman's precise tactics eradicate the ghosts from this part of the house.
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 17(26)25[23] 6(27)19 6(28)6[5] I
Roman's precise tactics eradicate the ghosts from this part of the house.
The 3rd 17- of June, 2010 (Josh wins)
We revisit the previous 17- game, so Josh can try something different on move 27.
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 8(26)8[9,10] 22(27)26
Now the fun begins!
2(28)19 17(29)25[23] II
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 8(26)8[9,10] 22(27)26
Now the fun begins!
2(28)19 17(29)25[23] II
The 2nd 17- of June, 2010 (Roman wins)
We go back to move 21 of the previous 17- game, so Roman can try something different on move 22. Will it help?
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 8(26)8[9,10] 2(27)2 14(28@23)24 I
Indeed it does help, but for how long? See the next 17- game, where Josh tries something different on move 27.
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[8-10] 13(23)13 14(24)14[15,16] 13(25)17 8(26)8[9,10] 2(27)2 14(28@23)24 I
Indeed it does help, but for how long? See the next 17- game, where Josh tries something different on move 27.
Thursday, June 17, 2010
The World Champion's thoughts on the recent series of games with Aunt Beast
Roman writes:
In April 2006, I wrote, "I don't believe an unassisted human will ever be able to compete with a computer program at sprouts." I'm finally beginning to see a small amount of evidence for this statement in "over-the-board play".
My fondest wish is that Roman will retire from sprouts, saying that the game is too hard for humans and should be left to computers. However, Russians never surrender, as the saying goes, and I wouldn't write him off just yet. With his tremendous tenacity and creativity, Roman has consistently dashed my hopes for computer superiority up to this point, and the safe money is that he will continue to do so into the future.
I would like to share with you the impressions I got after playing a series of games after the Axel Thue memorial tournament. I have no idea how Josh managed to make it, but I have witnessed how AB has turned from an old aunt's pocket monster into a sprouts devil! The new version of the program can turn a trivial position into every player's worst nightmare — you have my word on it. Every new game broadens my horizons of the misere game's world.
The games we play now are far ahead of all previous years' games; they are pure poetry... I wish that people could understand how unique every game is.
I used to think that misere was just a variation of the normal game, but now I tend to reckon that misere is totally different, a fully individual game with its own unique "ecosystem". Fighting against the new version of AB armed only with our old set of techniques will end in nothing. A whole new approach is required...
What approach? I have no idea!
I always thought that if you strictly followed a certain strategy AB wouldn't be able to create complex positions, i.e. if you walk down a good path in the forest, you wouldn't get lost... However, the new AB has learned how to trick you into losing your way completely and getting lost in dark woods.
To sum up it all - bravo, Josh!
In April 2006, I wrote, "I don't believe an unassisted human will ever be able to compete with a computer program at sprouts." I'm finally beginning to see a small amount of evidence for this statement in "over-the-board play".
My fondest wish is that Roman will retire from sprouts, saying that the game is too hard for humans and should be left to computers. However, Russians never surrender, as the saying goes, and I wouldn't write him off just yet. With his tremendous tenacity and creativity, Roman has consistently dashed my hopes for computer superiority up to this point, and the safe money is that he will continue to do so into the future.
Tuesday, June 15, 2010
The 4th 15- of June, 2010 (Josh wins)
15- (Jordan+Aunt Beast* - Khorkov) 1(16)1[2-7] 1(17)16[2] 8(18)9 8(19)9[10-12] 9(20)10 13(21)18 2(22)17 3(23)3[4,5] 23(24)3[4] 4(25)24 5(26)5 5(27)26 10(28)20[11-12] 6(29)7 13(30)14 I
The 1st 18- of June, 2010 (Roman wins)
18- (Khorkov - Jordan+Aunt Beast*) 1(19)1[2,3] 4(20)4[5-12] 19(21)4 1(22)2 2(23)2[3] 20(24)21[13-15]
5(25)5[6,7] 13(26)14 13(27)13[14,15] 5(28@8)25 26(29)27[15] 14(30)14 22(31)23 I
Roman's airtight tactics have quashed the game's last vestiges of complexity, and Josh resigns.
5(25)5[6,7] 13(26)14 13(27)13[14,15] 5(28@8)25 26(29)27[15] 14(30)14 22(31)23 I
Roman's airtight tactics have quashed the game's last vestiges of complexity, and Josh resigns.
Monday, June 14, 2010
The 9th 21- of June, 2010 (Josh wins)
After losing the previous 21- game "in haste", Roman tries something different on move 36.
21- (Khorkov* - Jordan+Aunt Beast) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12] 13(31)13[14-17] 18(32)18[19,20] 13(33)31[14] 21(34)21[18] 19(35)20 11(36)12 7(37)8 II
21- (Khorkov* - Jordan+Aunt Beast) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12] 13(31)13[14-17] 18(32)18[19,20] 13(33)31[14] 21(34)21[18] 19(35)20 11(36)12 7(37)8 II
The 1st 17- of June, 2010 (Josh wins)
17- (Khorkov - Jordan+Aunt Beast*) 1(18)1[2-6] 1(19)18[2-3] 7(20)7[8-12] 8(21)9 7(22)20[15] 19(23)4
This is 2 + PP3 + A5 + 4P1, an absurd position which no unassisted human can hope to play correctly, given the current state of Sprouts theory.
The game continues with 2(24)3 13(25)14, resulting in A2+PP3+A5+A4P1, an unusual position with three anagos. At this point Roman resigns, saying it was a "bad game" and calling his defeat "silly". The story continues in the next 17- game, in which Roman tries something different on move 22.
This is 2 + PP3 + A5 + 4P1, an absurd position which no unassisted human can hope to play correctly, given the current state of Sprouts theory.
The game continues with 2(24)3 13(25)14, resulting in A2+PP3+A5+A4P1, an unusual position with three anagos. At this point Roman resigns, saying it was a "bad game" and calling his defeat "silly". The story continues in the next 17- game, in which Roman tries something different on move 22.
The 1st 16- of June, 2010 (Josh wins)
16- (Khorkov - Jordan+Aunt Beast*) 1(17)1[2-4] 1(18@2)17 (Roman: This is the simplest of games.) 2(19)18 5(20)5 2(21)19 6(22)6
5(23)20[6] 7(24)8 2(25)21 7(26)7[9-11,23]
22(27)23 12(28)24
12(29)8[13-15] 8(30)13 II
5(23)20[6] 7(24)8 2(25)21 7(26)7[9-11,23]
22(27)23 12(28)24
12(29)8[13-15] 8(30)13 II
The 8th 21- of June, 2010 (won by Josh)
We revisit Roman's challenge, going back to move 30 of the previous game, so Josh can try something different on move 31.
21- (Khorkov* - Jordan+Aunt Beast) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12] 13(31)13[14-17] 18(32)18[19,20] 13(33)31[14] 21(34)21[18] 19(35)20 18(36@19)32 5(37)6 5(38)6[7] 14(39)14 33(40)39 10(41@21)30 II
Roman writes: "Ha-ha-ha! Great! I didn't see this move (haste). You win."
21- (Khorkov* - Jordan+Aunt Beast) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12] 13(31)13[14-17] 18(32)18[19,20] 13(33)31[14] 21(34)21[18] 19(35)20 18(36@19)32 5(37)6 5(38)6[7] 14(39)14 33(40)39 10(41@21)30 II
Roman writes: "Ha-ha-ha! Great! I didn't see this move (haste). You win."
Sunday, June 13, 2010
The 7th 21- of June, 2010 (Roman wins)
Roman posed the following challenge:
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12]
This is *1+4+9L2. I accept.
11(31)12 11(32)12
This is *1+4+9L0BL0. The position grows steadily more complex.
10(33@13)30 13(34)13[14-15] 14(35)15
Will the mounting pressure of complexity finally cause a fracture in Roman's titanium defenses? This is *1+4+A2L6P0, or, in other words:
14(36)35[15] 16(37)17
No obvious fractures yet, but sometimes these things don't become apparent until the whole structure suddenly collapses.
And sometimes the structure doesn't collapse. Roman writes, "We will finish this farce. You lose."
13(38@14)34 I
And indeed I do. The way Roman correctly replies to three anagos (move 31, 35, and 37) in three different ways is one of the marks of a true sprouts master.
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 10(30)10[11-12]
This is *1+4+9L2. I accept.
11(31)12 11(32)12
This is *1+4+9L0BL0. The position grows steadily more complex.
10(33@13)30 13(34)13[14-15] 14(35)15
Will the mounting pressure of complexity finally cause a fracture in Roman's titanium defenses? This is *1+4+A2L6P0, or, in other words:
14(36)35[15] 16(37)17
No obvious fractures yet, but sometimes these things don't become apparent until the whole structure suddenly collapses.
And sometimes the structure doesn't collapse. Roman writes, "We will finish this farce. You lose."
13(38@14)34 I
And indeed I do. The way Roman correctly replies to three anagos (move 31, 35, and 37) in three different ways is one of the marks of a true sprouts master.
The 3rd 15- of June, 2010 (Roman wins)
15- (Jordan+Aunt Beast* - Khorkov) 1(16)1[2-5] 1(17)16[6-10] 6(18)7 6(19)6[7,8] II
Finally this part of the forest is safe for humans again.
Finally this part of the forest is safe for humans again.
The 2nd 15- of June (Josh wins)
We go back to move 24 of the previous game, so Roman can try something different on move 25.
15- (Jordan+Aunt Beast* - Khorkov) 1(16)1[2-5] 1(17)16[6-10] 6(18)7 6(19)6[9-10] 2(20)3 2(21)2[3-4] 9(22)10 7(23)19 11(24)11 12(25)12[13-14]
Roman writes, "The previous game - mere chance because of carelessness. The forest is on fire." He even included an image:
How would you respond if the world champion sent you such a message? It would be natural to run away and hide under the bed. However, even if you can't win, you should at least try to fight.
9(26)9
Also, a little psychological warfare never hurts.
A few hours later, with a shout heard round the world, Roman resigns.
I
Roman: aaaaaaaaaaaaaaaaaaa!!!!!!!!!!!!
15- (Jordan+Aunt Beast* - Khorkov) 1(16)1[2-5] 1(17)16[6-10] 6(18)7 6(19)6[9-10] 2(20)3 2(21)2[3-4] 9(22)10 7(23)19 11(24)11 12(25)12[13-14]
Roman writes, "The previous game - mere chance because of carelessness. The forest is on fire." He even included an image:
How would you respond if the world champion sent you such a message? It would be natural to run away and hide under the bed. However, even if you can't win, you should at least try to fight.
9(26)9
Also, a little psychological warfare never hurts.
A few hours later, with a shout heard round the world, Roman resigns.
I
Roman: aaaaaaaaaaaaaaaaaaa!!!!!!!!!!!!
Saturday, June 12, 2010
The 1st 15- of June (Josh wins)
15- (Jordan+Aunt Beast* - Khorkov) 1(16)1[2-5] 1(17)16[6-10] 6(18)7 6(19)6[9-10] 2(20)3 2(21)2[3-4] 9(22)10 7(23)19 11(24)11 9(25)9 12(26)13 7(27@8)23 11(28)24 ...
At this point, I notified Roman that "The Russian Army has posted a warning: Due to severe danger including loss of human life, all soldiers are henceforth ordered to stay away from the forest 15- until further notice!" In response, Roman requested a picture. Of course, I was happy to oblige:
Roman: I wanted to see the picture of the game... I didn't want a tiger. You got me wrong.
Josh: No one who enters a forest wants a tiger!
12(29)12[14-15] 14(30)15 I
Here Roman resigned, stating that the loss was "mere chance because of carelessness."
At this point, I notified Roman that "The Russian Army has posted a warning: Due to severe danger including loss of human life, all soldiers are henceforth ordered to stay away from the forest 15- until further notice!" In response, Roman requested a picture. Of course, I was happy to oblige:
Roman: I wanted to see the picture of the game... I didn't want a tiger. You got me wrong.
Josh: No one who enters a forest wants a tiger!
12(29)12[14-15] 14(30)15 I
Here Roman resigned, stating that the loss was "mere chance because of carelessness."
Friday, June 11, 2010
The 6th 21- of June
In which Roman decides to try something different on move 35 of the previous game, splitting the game into three components.
21- (Jordan+Aunt Beast* - Khorkov) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-14] 5(26)6 5(27)5[7-14] 7(28)8 2(29)2 15(30)16 15(31)15[16] 17(32)18 17(33)17[18-19] 7(34)8[9-12] 25(35)27 20(36)20 20(37)36[21] 9(38)10 9(39)9[10-11] II
Roman writes, "Aunt Beast destroyed."
21- (Jordan+Aunt Beast* - Khorkov) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-14] 5(26)6 5(27)5[7-14] 7(28)8 2(29)2 15(30)16 15(31)15[16] 17(32)18 17(33)17[18-19] 7(34)8[9-12] 25(35)27 20(36)20 20(37)36[21] 9(38)10 9(39)9[10-11] II
Roman writes, "Aunt Beast destroyed."
Friday, June 4, 2010
The 5th 21- of June
The World Champion returns Aunt Beast's serve with a vengeance, playing an opening novelty on move 25 of the theoretically winning side of 21-. Aunt Beast will have to think about this for a while. The position is *3 + 10P7.
21- (Jordan+Aunt Beast* - Khorkov) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-14] ...
Trying turn the game into a sum of several complicated components, Josh plays three anagos in a row: 5(26)6 5(27)5[7-14] 7(28)8 2(29)2 15(30)16
Rather than responding to the anago 7(28)8 with an enclosing Q as per his typical strategy, Roman instead replies in a different component entirely, reducing the *3 to *0. Having an anago hanging around tends to make the game more complex, and this position, A8Q1PA7, is no exception.
The game continues with 15(31)15[16] 17(32)18 17(33)17[18-19] 7(34)8[9-12] 8(35)34[13-14] 13(36)35.
Josh's strategy of repeatedly nudging the game in a more complex direction is succeeding: this is *3 + X, where X is a rather complicated position that cannot be completely described in chained pivot/loop notation, due to the fact that spots 24 and 25 are on the same boundary. As Josh warned Roman, "A person could easily lose their way in a forest such as this." Can Roman find his way? Is there even a way for him to find?
Update: Roman resigned a few days later.
21- (Jordan+Aunt Beast* - Khorkov) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-14] ...
Trying turn the game into a sum of several complicated components, Josh plays three anagos in a row: 5(26)6 5(27)5[7-14] 7(28)8 2(29)2 15(30)16
Rather than responding to the anago 7(28)8 with an enclosing Q as per his typical strategy, Roman instead replies in a different component entirely, reducing the *3 to *0. Having an anago hanging around tends to make the game more complex, and this position, A8Q1PA7, is no exception.
The game continues with 15(31)15[16] 17(32)18 17(33)17[18-19] 7(34)8[9-12] 8(35)34[13-14] 13(36)35.
Josh's strategy of repeatedly nudging the game in a more complex direction is succeeding: this is *3 + X, where X is a rather complicated position that cannot be completely described in chained pivot/loop notation, due to the fact that spots 24 and 25 are on the same boundary. As Josh warned Roman, "A person could easily lose their way in a forest such as this." Can Roman find his way? Is there even a way for him to find?
Update: Roman resigned a few days later.
Thursday, June 3, 2010
The 4th 21- of June
Now it's Aunt Beast's turn to try something different, and we return to move 38 of the previous game.
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] 12(34)12[10] 13(35)13 12(36)13 34(37)36[14-16] 35(38)37[17] 18(39)18[19-20]
The position is A2 + 3 + 2L1P1 + [0.1AB;0.AB].
It's not all Grundy numbers and Genus sequences, though — there has been an unusual amount of trash talking on both sides. A recurring theme of mine is is that Roman has wandered too far into a metaphorical forest of complexities, and he should stick to simpler positions that he can actually analyze. A recurring theme of Roman's is that he will vanquish any and all complexities with his superior mental artillery.
Here's a sample of the back-and-forth.
Josh: This forest is very dangerous.
Roman: It's not a forest — it's weeds.
Josh: Those weeds have grown very high all of a sudden. They almost look like trees.
Roman: 14(40)15 you lose
Roman: [1 minute later] Ah no... thinking
Roman: 5(40@7)33 weeds
Roman: [2 minutes later] stop...thinking
Josh: I hope you have a lawnmower powerful enough to mow these weeds, colleague.
Roman: The gas mixture will be better.
In response, I sent Roman this image:
He sent back these two images:
I'm not sure why Aunt Beast gets stereotyped as weeds or a gnome while Roman's avatar is always a brave soldier, but such is life. If you see Roman, tell him it's his move!
Update: Roman finally moved to 5(40)33[6], saying, "It's time to see who's the master of this garden." Aunt Beast replied with 19(41)20.
This is A2 + 3 + A2L1P1 + [0.A;1A]. With a one-word reply, Roman reaffirms that the positions is "weeds".
10(42)11 18(43)41 ...
Now we have 0BL0 + 3 + [0.A;0.A.B;11<B>] + [0.A;1A], and the wind seems to have shifted.
19(44)20 20(45@39)44 II
Two words from Roman: "you win", and finally the long fight is over. Garden Gnome: 1, Gardener: 0.
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] 12(34)12[10] 13(35)13 12(36)13 34(37)36[14-16] 35(38)37[17] 18(39)18[19-20]
The position is A2 + 3 + 2L1P1 + [0.1AB;0.AB].
It's not all Grundy numbers and Genus sequences, though — there has been an unusual amount of trash talking on both sides. A recurring theme of mine is is that Roman has wandered too far into a metaphorical forest of complexities, and he should stick to simpler positions that he can actually analyze. A recurring theme of Roman's is that he will vanquish any and all complexities with his superior mental artillery.
Here's a sample of the back-and-forth.
Josh: This forest is very dangerous.
Roman: It's not a forest — it's weeds.
Josh: Those weeds have grown very high all of a sudden. They almost look like trees.
Roman: 14(40)15 you lose
Roman: [1 minute later] Ah no... thinking
Roman: 5(40@7)33 weeds
Roman: [2 minutes later] stop...thinking
Josh: I hope you have a lawnmower powerful enough to mow these weeds, colleague.
Roman: The gas mixture will be better.
In response, I sent Roman this image:
He sent back these two images:
I'm not sure why Aunt Beast gets stereotyped as weeds or a gnome while Roman's avatar is always a brave soldier, but such is life. If you see Roman, tell him it's his move!
Update: Roman finally moved to 5(40)33[6], saying, "It's time to see who's the master of this garden." Aunt Beast replied with 19(41)20.
This is A2 + 3 + A2L1P1 + [0.A;1A]. With a one-word reply, Roman reaffirms that the positions is "weeds".
10(42)11 18(43)41 ...
Now we have 0BL0 + 3 + [0.A;0.A.B;11<B>] + [0.A;1A], and the wind seems to have shifted.
19(44)20 20(45@39)44 II
Two words from Roman: "you win", and finally the long fight is over. Garden Gnome: 1, Gardener: 0.
The 3rd 21- of June
Roman wanted to redo move 40 of the last game.
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03#1) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] 12(34)12[10] 13(35)13 12(36)13 34(37)36[14-16] 35(38)37[17] 18(39)19 5(40@7)33 38(41)39 18(42)41[20] I
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-03#1) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] 12(34)12[10] 13(35)13 12(36)13 34(37)36[14-16] 35(38)37[17] 18(39)19 5(40@7)33 38(41)39 18(42)41[20] I
The 2nd 21- of June
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-02) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] 12(34)12[10] 13(35)13 12(36)13 34(37)36[14-16] 35(38)37[17] 18(39)19 ...
Roman decided to revisit move 36 of the previous game.
The position is [0.1AB;0.AB] + A2 + 3 + A4P1, which simplifies, with a little Sprouts algebra, to *3 + *2 + A4P1. By examining LV6, we can simplify the last component, and the game becomes X + *3 + *2, where X is restive with G+(R) = 1 and G-(R) = 2. From ONAG, p 146, we know the following:
Roman decided to revisit move 36 of the previous game.
The position is [0.1AB;0.AB] + A2 + 3 + A4P1, which simplifies, with a little Sprouts algebra, to *3 + *2 + A4P1. By examining LV6, we can simplify the last component, and the game becomes X + *3 + *2, where X is restive with G+(R) = 1 and G-(R) = 2. From ONAG, p 146, we know the following:
If R is Restive, thenNow {1, 1 ⊕ 1, 2, 2 ⊕ 1} = {0,1,2,3}, and clearly {3,2} ⊆ {0,1,2,3}, thus we have o-(X + *3 + *2) = o+(*2 + *3 + *2). This is a next-player-winning position, so Aunt Beast has made a mistake here. Can Roman capitalize on it? The game continues with 20(40)21 33(41)5[6].o-(R + *m + *n + ...) = o+(*r + *m + *n + ...)
where r = { G-(R), if {m, n...} ⊆ {0, 1, G-(R), G-(R) ⊕ 1},
G+(R) otherwise.
This is A2 + 3 + [1<1>.1<1>.A;0.A]. From LV6 we see that the latter is just *3, so the position is *2 + *1 + *3.
After 10(42)10 21(43)20:
Usually when a game gets this far into the endgame, one party or the other will realize that they have lost and resign, but for some reason that hasn't happened here.
39(44)40 18(45)43[20] 18(46@19)45 19(47)21[46] II
This time it is Roman who realizes he has lost. And so it ends, not with a bang, but with a whimper.
Tuesday, June 1, 2010
The First 21- of June
21- (Khorkov* - Jordan+Aunt Beast, 2010-06-01) 1(22)2 1(23)1[2,3] 4(24)23 4(25)4[5-8] 2(26)2 24(27)25 9(28)9[10-21] 9(29@27)28 27(30)29 10(31)11 5(32)6 5(33)32[7] ...
12(34)12[10] 13(35)13 ...
12(36)34[35] 13(37)35 ...
21(38)21[20] 33(39@7)5 II
12(34)12[10] 13(35)13 ...
12(36)34[35] 13(37)35 ...
21(38)21[20] 33(39@7)5 II
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