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Atomic Weight
Path: CGTPath · Prev: Orthodox · Next: Reversal
Keywords: EndGame
Each infinitesimal is approximately equal to some number of ^s (UPs). This number is called its uppitiness or atomic weight (Winning Ways, by Berlekamp, Conway, and Guy). Atomic weight is similar to the external liberty count in a semeai. If the atomic weight of an infinitesimal game is >= 2, Black can win; if it is <= -2, White can win. An atomic weight of 1 may not be enough for Black to win. For example, with sente White can win ^* (UP STAR). For more on the application of atomic weight to go, see Go infinitesimals, Corridor infinitesimals, and Playing infinitesimals. Bill Spight, moved by Charles Matthews The notations of * (star) and ^ (up) are introduced in Chilling. Modern chemistry refers to atomic mass rather than atomic weight. Charles The definition in Winning Ways is quite subtle (and impressive); so the rather clumsy name is a bit disappointing. How to explain this area to Go players? Firstly the class of games for which atomic weight is defined is called 'all small' in Winning Ways. For a Go player these all look like dame-filling, that is, no territory involved. But the simple dame in Go are all copies of *: taking n copies of * in a sum reduces to 0 if n is even, and to * if n is odd. That's not so interesting, just something familiar for the comparison between area scoring and territory scoring. These games are all in a sense contests for final play (tedomari to go players) - and that's all. They include all impartial games, certainly; but those don't provide interesting examples, because the atomic weight in those is always 0. What is wanted is to define a notion of 'lead' in a game considered as a race for final play. The definition relies on a normal case ('neck-and-neck') modelled on temperature as opportunity cost: in a level race, the difference one play makes is between 'one ahead' and 'one behind' (cf. capturing races) so is taken to be play at temperature 2. Only in a situation which you could call 'clear-cut' is the atomic weight defined by reference to the opponent's options in playing first, plus two. The definition of clear-cut for a game G has two parts:
Obviously this sort of definition can only be justified by the work one can get out of it. Not easily assimilated. Path: CGTPath · Prev: Orthodox · Next: Reversal This is a copy of the living page "Atomic Weight" at Sensei's Library. ![]() |