Short game


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In CGT, a short game is an abstract game with only finitely many positions, while a long game has infinitely many.

Note that this is not equivalent to the requirement that play cannot continue indefinitely, which is usually stipulated in CGT (unless we are treating loopy games with cycles such as ko). Of course all small games terminate after a finite number of moves[1] but, for example, the game ``omega={0,1,2,3,cdots|}`` is not small, even though all Left’s options move to positions which are small.

The restriction to short games is necessary for various parts of the theory, in particular as it is applied to go. Go is of course a very short game, since the board permits a mere ``3^(19*19)=``
``17","408","965","065","903","192","790","718","823","807","056","436","794","660","272","495","026","354","119","482","811","870","680","105","167","618","464","984","116","279","288","988","714","938","612","096","988","816","320","780","613","754","987","181","355","093","129","514","803","369","660","572","893","075","468","180","597","603`` positions, of which only ``208","168","199","381","979","984","699","478","633","344","862","770","286","522","453","884","530","548","425","639","456","820","927","419","612","738","015","378","525","648","451","698","519","643","907","259","916","015","628","128","546","089","888","314","427","129","715","319","317","557","736","620","397","247","064","840","935`` are legal positions.

See also

  • Small game — a game small in comparison to all numbers, i.e. small by comparison rather than in structure.


[1] This follows from the inductive construction of games, which means that a game cannot be a proper position of itself and hence that cycles are excluded. With a different definition of ‘game’ – e.g. to handle sums of loopy games – this might not be the case.

Short game last edited by PJTraill on February 9, 2019 - 00:37
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