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Here are some notes that I got from from Matthew Macfadyen on 26-JAN-1996.
The position called "molasses ko" in the recent American Go Journal was actually described by Mark Hall in a BGJ a few years ago. It looks like this:
Black is to play, and throws in to the 2-point eye. White had better take the ko (atari), Black takes two stones (atari), White takes the second ko, and then Black can play one move elsewhere. If this is not a huge ko threat White will throw in to the 2-point eye and the position continues. The point about molasses is that something like a normal game can proceed at 20% of the usual pace on the rest of the board.
But the real fun begins if this position arises in a game played under a superko rule (no repetition of the whole board after any number of plays). Because, in this case, it is fatal to use your free move as a pass, and you suddenly find that the game has reverted to the primitive form of go in which passing constitutes a loss. The concept of territory is still there, but it can be worth quite a few points to play loose stones inside your opponent's territory. This is sometimes referred to as 'Conway Go' after J.H.Conway's work on games in which the loser is the first player unable to find a legal move.
Incidentally the bestiary should include this group
which is dead in Conway go (else Black gets to play an infinite number of moves here), but also annoys various rule sets:
- With Chinese counting and a 'two passes ends the game' rule, and if the ko rule is worded carelessly, it is possible for Black to play repeatedly in this area without losing points, thus winning on time or by waiting for the opponent to go to sleep.
- With a superko rule which does not regard passing as significant, and if the whole of the rest of the board consists of groups with exactly two eyes except that Black has one ko threat; Black can play the 1-3 point, White captures, Black makes the ko threat, White answers, Black retakes one stone, White has to pass (there's no other option by hypothesis). Now when Black plays 1-3 again White can't capture because that would repeat the position.
And here's another beast which should be there:
Things look good for White. In Japanese rules it's easy- Black is dead and you can't fight ko in the analysis phase of the game. But such a position is likely to last all game- Black will be trying to create a ko threat big enough to make the 1-1 point worthwhile, but White may well prevent this.
However, if White should actually try to take Black off, he'd better start by adding a 5th stone to the nakade, Black will capture and White will play at the centre. But now Black has a nice ko threat to make two eyes.
I believe this position to be a seki if left to the end on most Chinese type rule sets, but to be a win for White in Japanese.
I also got another note from Matthew Macfadyen on 27-JAN-1996
Here's another beast (top left is a corner):
Black has two interesting moves- the 1-1 point, which makes seki, and the 2-1 which makes ko (requiring Black to find the first ko threat). But if Black is behind on ko threats and fears that White will start the ko he had better play 1-1 to cool things down.
And having done that Black still has the option to play 2-1 later, sacrificing 3 stones, and then start the ko.
Which brings up the topic of nonremovable ko threats. The obvious one is a seki, where your ko threat is self atari (which might be expensive) but do you know about this one? (the top left is a corner again):
This is a seki, albeit not a very plausible shape, and Black has a ko threat which costs nothing and is not removable.
I got this from mmueller@ICSI.Berkeley.EDU -- (Martin Mueller)
Here is another non point-losing irremovable Ko threat for you:
Top left corner of the board. White can capture two stones as a threat. Matthew's example is a bit nicer though, because in my example W eventually has to capture the stones.
I have slightly cleaned up the following message, which I have
re-labelled, and which came from Nick@maproom.demon.co.uk
Subject: position for bestiary
on 22-APR-1996 10:29:45.97
Harry, Frank Janssen showed me this position yesterday:
This is the whole of a 9*6 board. It is Black's move. The superko rule is in use.
Common sense, and all other rulesets, suggest that White's upper group is alive. However under the superko rule Black can kill it:
Black plays 'b' and says atari.
White plays 'a', capturing two stones.
Black plays 'd' in the lower left corner, as a ko threat.
White answers at 'c'.
Black makes a record of the position (with Black to play); and plays 2-1 in the upper right corner, capturing one stone (the one at 'a').
White cannot play with putting himself in atari, and so passes.
Black plays 'b' and says atari. He reminds White that a play at 'a' will repeat a previous position.
In the position shown above, you may ask why White has not already played at 'c' (to remove the ko threat, before it can be used). Obviously White may not have had a chance to do so yet! Another possibility is that the scoring is only of empty points and prisoners (rather than of both stones and territory), and that if White played there (given the particular number of prisoners, and the size of `komi') they would lose anyway.
It is possible to construct a more 'credible'/general problem with a slightly bigger board. One could make a ko-threat (against White) which could not be extinguished --- you can simply have a 'seki' which Black would deliberately throw away, gaining the White group in the top right as compensation.
Last Updated 2000/03/13
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