Anti Atari Go

Anti-Atari Go^[2] is a variant of go that is basically the opposite of Atari Go. Play follows the normal rules of go. However, the first to capture any stone loses the game. No passes are allowed.

Warning: do not try this on a large board. You will have a long game with hundreds of meaningless moves. The game plays much like the game of dots and boxes. It's surprisingly interesting on small boards.

Bill: How about these rules?

1) No pass allowed.
2) No capture allowed.
3) No suicide allowed.
4) If you have no move, you lose.

Here is the reason for rule 4.

No move  

After Black has no move.

You need a rule to cover such positions. Let the player with no move lose.

impu1se: Nice and simple rules. Having the last to move win seems to fit in nicely with game theory ideas.

Black to Win  

unkx80: I presume suicide is not allowed?

Black to Win  

is not suicide, Black wins  

Tderz]: B wins

Black wins  

Tderz]: I thought of the equivalent.

Black wins  

Tderz]: also equivalent, funny game, resembles Nim.

impu1se: Yes, very good. I guess that wasn't really a great example since 3 out of 5 possible moves work.^[1] So here's a harder one (only one correct move).

White to Win  

Bill: How about this?

White to Win  

Possible sequence  

impu1se: Correct! Here's some analysis of why this works to make a start at understanding some principles to this game. I'll leave the failed white attempts for someone else.

Black Failure 1  

Now if black tries d3 or e3 white can play c2 leaving black no moves. If black plays c2 or a3 white plays d3 to protect the e3 point.

Black Failure 2  

Now if black plays c2 or d3 white can respond at a4 to create three groups in atari covering all remaining points.

Black Failure 3  

Black at any of the circled points and White a makes one extra move for white at c1.

Black Failure 4  

Now white gets the extra move at e3. If b-d4, w-a3. If b-a4, w-d4.

White Failure  

Bill: looks reasonable, but plays to zero and wins.

White Failure (i)  

In this variation after White has no play and loses.

White Failure (ii)  

White fails in this variation, too. makes White damezumari.

impu1se: I hacked together a quick program to solve simpler boards. Of course black wins on 2x2. Black also wins on 3x3, regardless of the starting position. 4x4 is a white win. It appears that mirror moves are the simplest way to win - up to a certain point. 5x5 appears to be another win for black. It seems likely that black will win on the odd sized boards.

Mirror Go Failure  

White can't let two opposing groups form with only shared liberties.

Mirror Success  

and are the only winning moves.

[edit]

Problems

Gone Problem 2

Gone Problem 3

See also Numbers in Gone and Infinitesimals in Gone.

[1]

Black to Lose  

Bill: In fact, I think that this is Black's only losing move. Now, how does White win?

Anonymous: white moves at the marked square

Black to Lose  

[2]

DrStraw: Anti-Atari Go seems like a huge misnomer. The examples below are full of ataris. Anti-capture Go seems more appropriate.

Bill: Well, Atari Go is a misnomer, too. ;-)

Anyway, I have suggested the snappier name of Gone.

impu1se: The anti-atari name was originally tongue-in-cheek and I'm not that fond of it anymore. Lately I just call it no-capture go since this almost completely sums up the rules for any go player. Btw, love your problem examples Bill.

Bill: Thanks, impu1se. I'm still trying to get a handle on this game. ;-)

BobHearn: This game was independently discovered at Dalhousie, and named "NoGo" (which, confusingly, also seems to refer to Forced Takeback Go on Sensei's). It was studied under that name at the 2011 BIRS Combinatorial Game Theory workshop; there was a human tournament (6x7 board) and a computer tournament (9x9 board).

SiouxDenim The latest version of CGSuite contains a NoGo evaluation tool.