Number of different fuseki

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.

bugcat: If you're talking about professionally then the Waltheri database (~70,000 games) has no record of Black playing two parallel 3-3s against White playing a 3-3 and any other stone (and that's the first opening I checked.) So we can say that not all of these openings have been played professionally, as far as the Waltheri database can elucidate us.