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5x5 Board
    Keywords: Equipment

[Diagram]
5x5 board

Capture Go is commonly taught initially on this size board. Even this tiny board can be amazingly instructive.



The book [ext] How to Improve on a 5x5 board contains problems ranging from low kyu to high dan. It's by Fukui Masaaki.

Erik van der Werf's MIGOS program has [ext] solved 5x5 Go for optimal play. It's very interesting to see optimal play against non-center openings.

Bill: All I saw was the first move. :-(

AshleyF: Hummm... yes, they're animated GIFs. I'll post below for reference.

Bill: Thanks, Ashley. :-)


Taken from Erik van der Werf's page (with his permission) claiming that [ext] 5x5 Go is solved:

Optimal Play For Opening At 2-2

[Diagram]
Optimal Play For Opening At 2-2 (1-10)

[Diagram]
Optimal Play For Opening At 2-2 (11-20)



Why not B5 here in the second diagram at W6? Doesnt this kill the white group? Or am I being silly? - NoFairyLiquid?

Erik?: No, B5 at W6 leads to a white win by 4 points.

[Diagram]
Optimal Play For Opening At 2-2 (21-23)

[Diagram]
Optimal Play For Opening At 2-2 (Final Position)


Optimal Play For Opening At 3-2

[Diagram]
Optimal Play For Opening At 3-2 (1-10)

[Diagram]
Optimal Play For Opening At 3-2 (11-19)

[Diagram]
Optimal Play For Opening At 3-2 (Final Position)


Cho Chikun's Play At White 6 (Mistake?)

[Diagram]
Cho Chikun's Play At 6 In Opening At 3-2 (1-10)

[Diagram]
Cho Chikun's Play At 6 In Opening At 3-2 (11-20)

[Diagram]
Cho Chikun's Play At 6 In Opening At 3-2 (21-22)

[Diagram]
Cho Chikun's Play At 6 In Opening At 3-2 (Final Position)


Uno I'd like to defend Cho Chikun.

It seems to me that the result was 0-0, and hence better for White.

(Territory inside seki groups does not score under Japanese rules).

Bill: Don't forget the captured stones. The result is B +1, one point better for White than the main line.

Uno Thanks for the correction, Bill, but still seems that Cho's sequence is correct and best under Japanese rules. :)


AshleyF Very true! The [ext] Japanese Rules (Article 8) explicitly count territory as: "Eye points surrounded by stones that are alive but not in seki..." Erik says in his paper, "In all experiments reported in this article area scoring is used and points surrounded by a single player in seki count as territory." Cho and the computer are playing different games. :-)

Erik?: I'm not so sure about that. The analysis published in AGJ (V28:2, 1994) was based on AGA rules. Cho's mistake was reported in AGJ (V29:3, 1995), which explicitly states "Cho confessed that he had completely overlooked this move".


The program solves for other openings as well but not nearly as interesting. Center opening results in Black taking the entire board. First play on the edge results in White taking the entire board.


[Diagram]
White to play

Is the analysis given on that webpage complete? There could be a poorly-placed handicap.



AshleyF I don't know if this has been analyzed. Not everything has. Erik states, "We further solved all other opening moves on the empty board." I don't think that they've gone as far as handicap openings or other random positions. Even on this tiny board there are several hundred-billion unique legal positions!

Erik says, 'On my page web-page I only discussed opening moves for the empty board. We did however also test other positions, such as the "Hop" "Step" and "Jump" (from the Super Book of 5x5 Go you referenced). "Jump" is the hardest, our current version of MIGOS requires about 7 seconds to solve it. Unfortunately I don't have the book itself so I only tested these three problems from their webpage. I also tested some poorly-placed handicap openings, such as your two opposite corners, as far as I remember most were lost by black. However, as you say there's a huge number of such positions.'


anonymous What about 6x6? Shouldn't that be technically feasible now?

Erik? The empty 6x6 board is not yet feasible. However, Migos can solve some positions with 8 (or more) stones on the board (an example is shown in the ICGA article).



This is a copy of the living page "5x5 Board" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.