Newsgroups: rec.games.go
Subject: More about go variants.
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: Sat, 26 Sep 1992 05:30:56 GMT
Organization: Department of Mathematics, University of Canterbury

Here's yet another article that doesn't really belong in this newsgroup !

For those go-only players who get tired of articles like these, about shogi
or go-moku or just games in general, remember to vote in favour of
          rec.games.abstract
          ~~~~~~~~~~~~~~~~~~
when it comes up in a week or two, and you won't have the newsgroup clogged
up with this sort of thing any more !

I am going to comment on two slightly unrelated topics.

(1) The first is the matter of the two variants
played on a hexagonal grid board; one played in the cells;
one played on the intersections.            "Tri-go" (3 liberties) has
been least regarded, being full of irritating (but fascinating) petty tactical
concerns.           "Hex go" (6 liberties) has had more coverage, and
Nicol N. Schraudolph, as well as going to the trouble of sending postscript
version of the boards, (thanks Nici !), has made a few comments on the
smallest-board versions of this game.

Nici says.....

>it looks like for board sizes up to 2, black can kill white completely.

This seems clear enough indeed. It's interesting to look at the "size 2"
board (i.e. 19 points) again though; and investigate the variant where
black is forbidden from playing the centre point on his first move (a kind
of komi). This is not nearly such an easy win for black ! At first I thought
it was a fairly simple-minded win for black, 10-9, (Chinese counting), but
then I noticed a clever variant play which leads to quite a different
result indeed (which I *think* is optimal). I will not give it here, as it is
rather fun to seek for yourself, and also I'd like "confirmation without
misinformation". So, all you small-board and variant investigators; have
a go at this one, and let me know your conclusions. (Incidentally, it never
fails to amaze me, how this type of 1st-move-restriction komi can make
such a large change in the length of analysis !)

Nici also mentions that

>On a size 3 board (37 intersections), black wins but white lives.

Yes, this seems clear too. I make it that the optimal result is a win
to black of 22-15. This is achieved, e.g. by the simple-minded play whereby
(black starting in the centre, and white attaching) both players make
a solid line across the board. Though variations are possible at different
stages, it doesn't seem as if either can improve on the 22-15 result.

It would be nice to have confirmation of this result !

Nici also says...

>I believe that this is also the case on the size 4 board, but would
>like to see others confirm or refute this, since it's a close call --
>it seems like white can *almost* invade successfully.

...but I'm not quite sure what this means. Surely if Black can win but white
can live on size 3, then both these will obtain on size 4 ? I would have
thought this was clear;   still, I have not investigated in detail what the
optimal result should be - it looks quite hard.


(2) My second lot of remarks follow up an interesting article by
Michael Chisnall about "save-go" and related topics.

The chief idea of the save-go game, was that one may either play one's move
normally, or save it up (and so on cumulatively), so as to play some larger
number of "simultaneous" moves later on, using part or all of one's "saved"
moves. Michael correctly points out that it is an advantage to save *some*
moves, but not indefinitely many. So somewhere in between there is a "best"
but changing optimum number of saved moves to keep, which will also depend
on the size of the board.

It should be noted, that in this game, and others mentioned below (where
more than one stone may be played at once), the multiple moves are not
really "simultaneous". The moves should be thought of as being played
CONSECUTIVELY, in that after each single play, a legal postion must
be left, even if more plays are about to be made. This is a vital
restriction in variants like "save-go" and the "progressive" types (below),
otherwise a game could never finish, as even very small eyses could be filled
up with sufficiently many moves.

So; in multi-move go variants, NO liberty-less groups may be left after any
of the separate moves. So two (small) eyes is always sufficient for life.

Also; regarding Ko-like situations, the logical alternative seems to me to
be that a seeming ko *can* be retaken on the first of a sequence of moves,
(allowing immediate retake-and-fill), provided, (as always), that the final
position you leave is *not* one you have left (as a final position) before.

In his article, Michael mentions various "CONSTRUCTORS", that make new
games out of old ones. I haven't heard this term before, but it is a nice
term for a widespread idea among game-variers, though perhaps "TRANSFORMER"
would be more accurate. I shall use this latter term. They apply to almost
any game; go, chess, and the rest.

Michael mentions the well-known  "misere transformer", much handled by
Conway Guy & Berkelamp in "Winning ways", (but not really sensible in go);
and also the "-spiel transformer", where the players play blind to their
opponent's moves, a referee being needed to keep track of legalities.
(One might also mention the "stake-doubling" transformer of backgammon, though
this really only applies to money games; but could be used in long go matches!).
Then there is Michael's "save" transformer, which has great possibilities.

Another class of transformers are the "multi-move" transformers, and it is
these I want to mainly talk about.     ~~~~~~~~~~

The simplest is the 1-2-2-2-.. transformer.
That is, black starts with one move, then each has two consecutive moves
from them on. I have seen a chess game recorded between Alekhine and Euwe
of this type; and have played 6-in-a-row this way (5 is too easy), and
also small-board go.  9x9 go in this style is quite fun; the tendency is
for the two moves to be played in a little line of two, but not always.
There are still hanes, and some fascinating timing problems arise when
there are two active areas. Give it a try some time.

The main idea of the 1-2-2-2-... transformer is to eliminate 1st-move
advantage, and it seems to achieve this very well; as an analysis of very
small boards indicates, and play on 9x9 seems to confirm. For those who
like mathematical over-exactitude though, it may be argued that it doesn't
*quite* achieve this, in that *first* black is a move up, *then* white is
a move up, *then* black is,  *then* white,  and so on.  But of course,
black is still the *first* to be up; so if the game were interrupted "at
random", black would be *slightly* more likely to be a move ahead (though
nowhere near so overwhelmingly as in standard play).
                                                       To cancel this tiny
effect, a 1-3-4-4-4-4-4-.... multi-move transformer is suggested. This has
the effect of having black lead first by one move, then white by 2, black
by 2, white by 2, and so on; and now seems exactly fair, (though keen
mathematical bush-lawyers might want to iterate this procedure indefinitely!)

I have never played 1-3-4-4-4-4-.... at go, but have analysed some small
board versions; it seems quite fun, but not greatly more different than
the simpler 1-2-2-2-2-... type, and so hardly worth bothering with.

Another variant along these lines is the "PROGRESSIVE" transformer.
This is multi-move 1-2-3-4-5-...., where each player has one more move in
his series than his opponent just had. This is quite popular among chess
variant players, (where, unlike most variants, the concept of "check" must
be retained rather than just "king-capture"; otherwise it is trivial).

Progressive go does not seem to get so much attention; but (of course!) I
have played it from time to time in after-tournament sessions, and it
really is quite fascinating and well worth a look. It should not be attempted
on a 19x19 board (!!), I strongly suspect. I have played it mainly on 9x9, and
once on 13x13 which is also quite fun. As the number of moves per turn mounts
up, all but completely invulnerable groups come under threat; some amazing
effects become possible, and it becomes vital to have a good understanding of
the concept of "hypercontrol", that appeared in this newsgroup for some time,
a while ago (also available at Milton).
Hypercontrol and progressive go are true bedfellows !

As a final little topic, I will mention still another multi-move transformer
which I think has some merit, especially for go (rather than say, chess).
Just as considerations of "who has played more moves than the other", led
to the introduction of the 1-3-4-4-4- over the 1-2-2-2-2- transformer, the
same ideas applied to the "progressive" concept lead to the intoduction
of the "ODD-PROGRESSIVE" transformer. This is progressive go where each
player has an increasing number of ODD moves; that is 1-3-5-7-9-11-...
multi-move go.  The advantage of this over progressive, is that each
player is an increasing number of "moves-ahead" at the end of his turn,
namely 1,2,3,4,...; (rather than 1,1,2,2,3,3,.. as at ordinary progressive,
which clearly still favours black slightly). I have *not* played this
variant, (nor do I ever expect to really!), but again, I *have* analysed small
board examples, and it seems a quite worthwhile fun variant.


Well, that's all for now folks; *do* try some of these with a friend, and
remember to vote in favlur of  rec.games.abstract  when the time comes !!  ;-)
                               ~~~~~~~~~~~~~~~~~~
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              Bill Taylor              wft@math.canterbury.ac.nz
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