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Fuseki

 

Number of different fuseki
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    Keywords: Opening

Out of curiosity, I recently figured out how many different fuseki there are under a few simplifying assumptions:

  1. Only the first four moves in an even game are considered.
  2. Those first four moves are in a different corner each (so no Shusaku fuseki)
  3. The order of the first moves is not important; neither is the orientation of the board.

Under these assumptions only two types of fuseki can occur: the parallel fuseki and the diagonal fuseki.

Naturally the number of fuseki varies along with the number of possible moves in each corner:

  • If we only look at plays at the 3-4 point and the 4-4 point (sensible beginner's moves, perhaps?) the number of different parallel fuseki is already 45 and the number of different diagonal fuseki is 24, for a total of 69.
  • When we also take the 3-3 point into account the numbers grow to 136 for parallel and 72 for diagonal (208 in total).
  • Finally, if we add the 3-5 point and 4-5 point, so that we have the normal moves, the number of different parallel openings is 2080 and the number of diagonal openings is 1048 (if I didn't mess up my back-of-the-envelope math :-) A grand total of 3128!

(Actually, the numbers for the diagonal openings go up slower because asymmetric parallel plays come in twos, while asymmetric diagonal openings come in fours.)

I wonder whether each of these openings has been played seriously... Probably not, since an opening where one player plays san san twice while the other takes the two remaining hoshi points seems a bit silly, even to me!

SAS: Actually, this isn't particularly uncommon, especially Black nirensei versus two 3-3 points.

Jan



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This is a copy of the living page "Number of different fuseki" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.