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Playing Infinitesimals
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Keywords: EndGame
The play in infinitesimals is all about getting tedomari. Chilling produces infinitesimals from go positions that have miai values of 1. Both {0 |tiny-1} (the lower corridor) and ^ (Up, the upper corridor) have atomic weights of 1. Which should White choose to play in?
Should White play at a or b? The difference game provides the answer. Let's have White play at a in this position and Black play at b in the negative position.
(Note on the diagrams. The stones that frame the positions are, by convention, alive.)
Does either player have an advantage?
After The difference game favors Black, so White should play in {0|tiny-1} rather than ^. In fact, White should prefer to play in any corridor ending in a tiny before one ending in *. That seems reasonable, because White's eventual threat is larger in {0|tiny-1}. Both 0(2)tiny-1 (upper corridor) and 0(2)tiny-2 (lower corridor) have atomic weights of 2. Which should White choose to play in?
Should White play at a or b? Of course, we do the difference game. White plays at a, Black at b.
If
After
Black interposes
White gets tedomari when she plays first, too. Since White gets tedomari, regardless of who has sente, the difference game favors White. That means that White should play at a, the corridor with the smaller sente at the end. Now that's a surprise, isn't it? The key, it seems, is to save the hotter sente for later. Much like saving a big ko threat. :-) This is not a case where the opponent's play is my play. Black prefers b, removing the larger threat. Black can block White at a or b. Here a is sente, with an atomic weight of 0, b has an atomic weight of 1. Which does Black prefer?[1]
Again, we play the difference game. Let Black play at a and White at b.
Black plays sente and then takes tedomari.
Here, too, Black plays sente and then gets tedomari. Note that the choice depends on the size of Black's threat versus the size of White's threat by playing at 4. Also see -- BillSpight [1] Assuming Black is independently alive. --dnerra I thought that was covered by assumptions of yose problems; but looking at that page, it could be made (more) explicit. -- Charles Bill: I thought I covered that with the "note on the diagrams" above that said that the stones framing the diagrams were alive by convention. Path: CGTPath · Prev: MoreInfinitesimals · Next: Komaster Path: Endgame · Prev: GoInfinitesimals · Next: BasicEndgameTheory This is a copy of the living page "Playing Infinitesimals" at Sensei's Library. ![]() |