How many corner sequences (not counting combinations of all 4 corners in one game) exist in Go?

In josekipedia, the number is so high the count rollsover into the negatives.

The 3-4 stone gives me 113,050 moves
4-4 gives 65,979
5-3 gives 25,769

I doubt there is any work which completely lists them all so there probably is no exact count available. Also, any number given will be out of date as soon as it is written because new ones are continually being created.

The best solution is not to ever play a joseki. Do what the pros do: work out the best move for the situation and don't worry if it is considered joseki or not.

_________________
Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

If only we all had that ability.


"The best solution is to always play the best move."

Thanks.

Taking as the starting point a set of sequences that a large team of top professionals, not specially constrained by time or money, thought had to be listed comprehensively as sequences that were joseki or closely related - and which they had all clearly not just seen but had considered in some detail and wrote about - you get the 20,000 sequences in The Great Joseki Dictionary (in Japanese; see The Go Companion for more details).

To these have to be added newly introduced ideas and some obsolete sequences (which they would also have known, of course), so as a plausible figure to indicate how many corner sequences you need to consider in some detail to match a top pro, we can say perhaps a minimum of 30,000. Roughly ten a day for ten years, starting NOW

I suggest that would also be a reasonable estimate of the number of tsumego problems you need to do, too.

Under the assumption the OP means sequences of standard good play for both sides* John's answer in the tens of thousands seems sensible. But how about standard "after joseki" sequences? How many of these are included in that 20,000 figure for The Great Joseki Dictionary. For example after this common joseki:

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

Here is a continuation for white:

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . |
$$ . . . . . . 5 . . . |
$$ . . . . . 3 . . . . |
$$ . . . . 4 2 1 O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

Black could also tenuki instead of . Does that count as a difference sequence? And another choice for white:

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . 5 3 . . . . |
$$ . . . . 4 2 1 O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

And black could now hane or extend (or even cut perhaps). Another idea for white:

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . |
$$ . . . . . . . O . . |
$$ . . . . 1 . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

And for black:

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . 1 . . . . |
$$ . . . . . . . O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

or

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . |
$$ . . . . . . 1 O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

or

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . |
$$ . . . . . . 3 1 . . |
$$ . . . . . . . 2 . . |
$$ . . . . . . . O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

or

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . |
$$ . . . . . . 6 1 . . |
$$ . . . . . 4 . . . . |
$$ . . . . 5 3 2 O . . |
$$ . . . . . . X . . . |
$$ , . . . . . X O . . |
$$ . . X . O X X O . . |
$$ . . . . . X O O . . |
$$ . . . . . . . . . . |
$$ --------------------+[/go]

And so on and so on. I could easily make a tree of common continuations after this joseki with several dozen leaf nodes. Now this joseki is perhaps particularly rich in the breadth and depth of standard continuations (though of course me being ignorant of standard continuations in other josekis, or other continuations in this one, doesn't mean pros/other players don't know them!) but it wouldn't surprise me if including these 'after joseki' standard sequences could bring the total of "corner sequences" up to 50,000.

*rather than just some combinatorics of possible number of legal moves which would be utterly huge: as a first approximation we could say a corner is 9x9 and 81! is 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000