5x5 Board

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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:

Opening At Centre (3-3)

When Black opens at centre (3-3), and plays correctly, then White cannot live anywhere.

Opening At 3-3 (1-10)  
Opening At 3-3 (11-17) (16 at 13)  
Opening At 3-3 (18-22)  
Opening At 3-3 (final move)  

At this point Black is PassAlive and White is PassDead.

fool (2023-03-05): I took this line from the GIF on EvdW's page. Maybe this is supposed to be the line where White delays becoming PassDead as long as possible. But I'm not sure. What 'optimal' means for White is not clear, since White is dead from the start.

Optimal Play For Opening At 2-2

Optimal Play For Opening At 2-2 (1-10)  
Optimal Play For Opening At 2-2 (11-20)  
Optimal Play For Opening At 2-2 (21-23)  
Optimal Play For Opening At 2-2 (Final Position)  

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.

The Count: The point is that although B5 at W6 would deprive White of two eyes, Black doesn't have them yet either and so Black might lose a capturing race.

Dave: Can someone provide a sequence? I have B dead after B5 at W6.

Does anyone know if these moves are presented as the unique best ones? What if White plays hane with W4 at B9 in the first diagram? I can't see a good continuation which isn't the same (by symmetry) after W6.

Dave: W4 at B9 is the same. But I have B11 at W16 for the same (non-unique) result.

Optimal Play For Opening At 3-2

Optimal Play For Opening At 3-2 (1-10)  
Optimal Play For Opening At 3-2 (11-19)  
Optimal Play For Opening At 3-2 (Final Position)  

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

Cho Chikun's Play At 6 In Opening At 3-2 (1-10)  
Cho Chikun's Play At 6 In Opening At 3-2 (11-20)  
Cho Chikun's Play At 6 In Opening At 3-2 (21-22)  
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.

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).

Erik?'s paper quotes James Davies as saying, "If you doubt that 5x5 Go is worthy of attention, you may be interested to know that Cho Chikun devoted over 200 diagrams to the subject in a five-month series of articles in the Japanese Go Weekly"

Does anybody happen to have copies of those Go Weekly issues?

5x5 Board last edited by fool on March 5, 2023 - 19:34
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