# 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.

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.

Number of different fuseki last edited by bugcat on February 25, 2018 - 23:44