Approaching a Definition of Ko
Robert Jasiek
general definition of kos consisting of any number of intersections so
that not(!) all strings in all positions are ko strings. For the
moment, I don't bother you with the details of precise definitions yet
but outline my current approach. Kos consist of intersections - the ko
intersections. My trick is to treat empty and occupied intersections
equally. This has turned out to be easier because a cycle uses both
kinds of intersections anyway.
As you might recall, Ing's naive description a la "can be captured in
a cycle" did not work: I proved that then all strings in all positions
would be ko strings since the players' cooperation and single passes
let it be straightforward to construct trivial cycles.
What then distinguishes ko strings from non-ko strings? The basic idea
is surprisingly simple: Additional criteria are required! Needless to
say, there are also complications: Different types of ko intersections
deserve closer study. So far I think to have identified these types:
1) Each play of a cycle destroys or creates a player's area on all the
cycle's intersections.
2) A player moving first forces a cycle while the opponent moving
second prevents the player's uncapturable life on the intersection.
3) A player moving first forces a cycle (incl. the intersection) while
the opponent moving second prevents the player's score-improvement.
Have I overlooked any further type? What do you think of these types?
My definition approach is generous so that I will be able to identify,
e.g., dead big kos, too. So far I have not seen unexpected ko
intersections (bad counter-examples) yet.
An intersection can be of more than one type. A ko can consist of
intersections of different types.
Type (1) means a) single stone suicide, b) basic ko, c)
capture-2-return-1. I hope that these are all type (1) shapes. One
should try to prove it.
Type (2) occurs in various basic kos or big kos but not for all
intersections of all big kos.
Although it occurs also in other shapes, type (3) is especially
important for explaining triple ko stones or quadruple ko stones with
forced cycles. (Matti, do you agree? :) )
As you might guess, being able to define big kos is a requirement for
a study of big ko types to be classified later.
Robert Maas, http://tinyurl.com/uh3t
> It has turned out to be yet tougher than expected to find a useful
> general definition of kos consisting of any number of intersections so
> that not(!) all strings in all positions are ko strings.
For what purpose would anybody ever need to make such a definition?
No such definition is needed to specify the rules of the game,
nor to introduce one of the most interesting/complicated aspects of
tactics and strategy. For either, all you need is:
- Introduce the basic rules of play, not including any ko rule.
- Show a situation where under *those* rules only, the game would
degenerate into each player un-doing the other's previous move
by back-and-forth one-stone capture, the only way for either
player to save a large group from immediate capture:
| X X X O O |
| - X X O O |
| X X O - O | (X to play next)
| X X X O O |
| X X X O - |
- Mention how in Chess this type of situation-loop issue is
resolved by declaring the game to be a draw. Say that since
draws are quite common and accepted in Chess, this resolution is
fine, but in Go games are *never* desired to be drawn (hence the
half point komi!!), so some *other* means to resolve situation
loops is needed.
- Propose forbidding any two-step situation-loop, i.e. you aren't
allowed to re-take so as to effectively UNDO the opponent's
just-previous play.
- Describe "ko threats", how they affect tactics, for example:
| - X 1 X O 4 O | (O plays at 1; X has threat at 2, O replies at 3,
| X X X O O O O | X can now re-take to right of 1, O has no threat,
| X O O X X X X | X can now play 4 to capture O's group)
| O O - X O O O |
| - O - X O - 2 |
| O O - X - O 3 |
| - O - X - O - |
- Show a more complicated situation where under *those* rules, a
multi-step (2*N plays where N>1) situation-loop will follow as
best (mixmax) sequence of moves for each player.
- Present various ideas how to deal with the situation and sequence:
- Allow draw if neither player is willing to avoid the situation-loop.
- SuperKo rule (placing stone to achieve exact repeat of earlier
position with same person to play next is FORBIDDEN;
PASS that results in exact repeat is *always* allowed)
- Horrible mess of inscutable special cases defined by Ing.
- Recommend SuperKo as the least-bad of the available options.
- Warn that referees for a game, including computer software such
as IGS, may need o(2**N) storage to keep track of which
positions have occurred already with N simultaneous
back-and-forth captures on a large board, which *must* be
available in order to have a SuperKo-conformant referee. The
so-called "database-ko rule" (forbidden for either player to
exceed the capacity of the storage available to the referee) is
*not* a reasonable alternative solution!
P.S. The Ing rule that neither player may place more than 180
stones during the *entire* course of a 19*19 game is IMO even more
stupid than the database-ko rule (for all reasonable database
sizes, such as several gigabytes).
Robert Jasiek
(Robert Maas, http://tinyurl.com/uh3t) wrote:
>For what purpose would anybody ever need to make such a definition?
1) To contribute to a solution of the game of Go. Although there are
also alternative ways to solve Go, it might turn out that a definition
of ko eases later progress in finding a solution. In fact, it becomes
possible to define and then study the behaviour of more sophisticated
objects (example: types of big kos).
2) To classify big kos. Then it will be easier to study their
different behaviours.
3) To study and make propositions about more advanced objects and
tactics and strategy related to them.
4) To find more kinds of ko shapes.
5) To understand common characteristics of (certain kinds of) kos.
6) To better understand in general when fighting or not fighting kos
is correct strategy.
7) As study on its own purpose.
Etc.
>No such definition is needed to specify the rules of the game,
Yes. (It becomes possible though to improve understanding of those
rulesets that do attempt to use general definitions of ko. In
particular, the Ing 1986, 1991 or 1997 Rules.)
>nor to introduce one of the most interesting/complicated aspects of
>tactics and strategy.
Yes. Teaching complete understanding of all kos is not needed when
introducing ko to beginners:)
>For either, all you need is:
Wrong. For a complete understanding of the intention behind Ing ko
rules, one does need a complete understanding of kos. For Korean or
Chinese ko rules, I do not know yet if it will be necessary. For
superko as a rule it is not and for Japanese ko rules it was not
necessary indeed.
>- Show a situation where under *those* rules only,
It is possible to have applications where it suffices to refer to
exactly one ruleset. For other applications (e.g., study of different
ko behaviours under different rulesets), a generic methodology is
appropriate or at the very least very helpful, as could be seen, e.g.,
in the Types of Basic Ko study.
>- Describe "ko threats", how they affect tactics, for example:
For the purpose of teaching beginners, one can come up with peaceful
enough examples of ko threats. Ko threat in general in contrast to
what is not a ko threat will require research yet more difficult than
understanding what a ko is versus what is not.
> - SuperKo rule
> - Horrible mess of inscutable special cases defined by Ing.
There are more ko rulesets. If you want to explain a few, you do not
need to include Ing ko rules. You can choose easier ko rulesets.
>- Recommend SuperKo as the least-bad of the available options.
There are aims so that superko is the best option (e.g., the smallest
number of complete rules). There are other aims so that another ko
ruleset is the best option (e.g., complete rules so that long cycle
strategy is the easiest suggests usage of the Basic-Fixed-Ko-Rules).
alex
http://tinyurl.com/uh3t) wrote:
> P.S. The Ing rule that neither player may place more than 180
> stones during the *entire* course of a 19*19 game is IMO even more
> stupid than the database-ko rule (for all reasonable database
> sizes, such as several gigabytes).
Just FYI - have a look at the page's [1] keywords... before this gets
totally out of hand.
-alex-
Robert Jasiek
<alexander.d...@gmail.com> wrote:
>Just FYI - have a look at the page's [1] keywords... before this gets
>totally out of hand.
What do you mean those keywords to suggest us?