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Infinitesimals Discussion
Path: CGTPath · Prev: IntroductionToInfinitesimals · Next: Infinitesimals
Keywords: EndGame
Here are some infinitesimals in chilled go.
Can you tell what they are? What is this position worth? (Answers in Infinitesimals, further discussion here. :-)) Holigor: The upper one is 2 points for Black if Black moves first and 0 points if White moves first. So, it is a one-point move, value one point. The second is 3 (Black)/reduces to the first one (White). As we know that the first was one point then the score is 2 points, and a move is worth one point. The third is 4 points (Black)/reduces to previous (White). The previous was two points. Thus the score is three points, a move value is one point. Bill: Yes, indeed. :-) JanDeWit: Let's see if I have been paying attention :-) Top position is {2 | 0}, mast value 1, temperature 1, and chills to * (star), I think. Bill: Right. :-) Second one is { 2 , 3 | {4 | 0} , {2 | 0} } which is equal to {3 | {2 | 0}} (both first options are dominated by the second). Left stop is 3 with Right to play; right stop is 2 with Right to play. Cooling by one gives {2| 1+*}, so I think the mast value is 5/2 and temperature is 1/2. Bill: Chilling gives {2 | 2*}. Remember to include the effect of a white play to 1*. Bottom position is (crunch crunch) { {3|1}, 3 , 5 | {4,5|{6|0},{4|0}} , { {4|2},5 | {6|0},{2|0} } , {2,3 | {4|0} ,{2|0}} } which simplifies to { 5 | {5|{4|0}} , { 5 | {2|0}} , {3 | {2 | 0}} which in turn simplifies to { 5 | { 3 | { 2 | 0 }}}. (Modulo the early-morning fudge factor of course!) Bill: A little too early! ;-) The game simplifies to { 4 ||| 3 || 2 | 0 } which chills to { 3 | 3^} = 3^^* Jan: Indeed! Memo to self : 3 + 1 captured stone is not equal to 5; I think I counted the captured stone three times. The rest is wrong as well now... :-( Path: CGTPath · Prev: IntroductionToInfinitesimals · Next: Infinitesimals This is a copy of the living page "Infinitesimals Discussion" at Sensei's Library. ![]() |