Number of different fuseki

    Keywords: Opening, Theory

This page attempts to figure out how many different fuseki there are under a few simplifying assumptions:

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.

Calculations

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 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

A grand total of 3128!

Notes

  • Actually, the numbers for the diagonal openings go up slower because asymmetric parallel plays come in twos, while asymmetric diagonal openings come in fours.
  • It remains to be verified if each of these openings has been played seriously.

This is a copy of the living page "Number of different fuseki" at Sensei's Library.
(OC) 2012 the Authors, published under the OpenContent License V1.0.
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