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Infinitesimals

 

Infinitesimals Discussion
Path: CGTPath   · Prev: PlayingInfinitesimals   · Next: AmbiguousPositionDiscussion
    Keywords: EndGame

Here are some infinitesimals in chilled go.

[Diagram]
Diag.: Infinitesimals

Can you tell what they are? What is this position worth?

(Answers in Infinitesimals, further discussion here. :-))

--BillSpight



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... :-(




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