What is the longest Go problem?
Ralf Gering
(1)
The longest Tsume Shogi is said to be "Microcosmos". The solution requires
1525 plies (moves) according to:
http://www.cs.inf.shizuoka.ac.jp/~iida/GPW/program.html
(2)
A very long F.I.D.E.-Chess mating problem has been reported in "Games
of No Chance" by Lewis Stiller (Editor: R.J. Nowakoswki, 1996) which
requires 485 plies (page 178-79).
(3)
I have composed the following ladder problem in Go, in c.1983 which is
probably the longest Go problem without a Ko fight:
. . . . . . . . . . . . . . . . # # .
# . . . . . . . . . . . . . . . . . .
# . . # # . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . # . .
. . . . . # # . . # # . . . . . # . .
. . . . . . . . . . . . . . # . . . .
. . . . . . . . . . . . . . # . . . .
. . . . . . . . . . # . . . . . . . .
. . . . . . . . . . # . . . . . . . .
. . . . . . . . . . . . . . # . . . .
. . . . . . . . . . . # # . # . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . # . # . . . . . .
. # # . . . . . . . # . . . . . . . .
O O . O # . . # # . . . # # . . . . .
+ . # O # . . . . . . . . . . . . . .
O O . . . . . . . . . . . . # # . . #
# O . . . . . . . . . . . . . . . . #
# . . # . . . . . . . . . . . . . . .
"Labyrinth"
(by Ralf Gering / published in the "Deutsche Go-Zeitung")
Black to move! Can he save his stone "+"? Do you know the way through the
labyrinth? (314 plies)
Do you know any Go problems with more plies?
Ralf Gering
Robert Jasiek
Ralf Gering wrote:
> Do you know any Go problems with more plies?
If you allow restriction fights and generic board sizes,
then infinite numbers of arbitrarily deep problems can be
constructed...
--
robert jasiek
Ralf Gering
Hello,
I said "Go".
which is a Japanese board game played on an orthogonal 19x19 grid!
Ralf
On Sat, 21 Apr 2001, Robert Jasiek wrote:
> Date: Sat, 21 Apr 2001 23:04:21 +0200
> From: Robert Jasiek <jas...@snafu.de>
> Newsgroups: rec.games.go
> Subject: Re: What is the longest Go problem?
Ted Schuerzinger
in <Pine.LNX.4.30.01042...@linux32.zdv.uni-tuebingen.de>:
>
>Hello,
>
>I said "Go".
>
>which is a Japanese board game played on an orthogonal 19x19 grid!
Bitte mit dem Robert nicht streiten! Er ist ein Expert zu den Themen
Microgo (Go auf Bretten kleiner als 9x9) und die mehrere Regelarten
(Japanisch, Koreanisch, usw.). Er glaubt, 19x19 ist nicht der einzige Art
von Go.
Er hat auch sehr strenge Meinungen nach den mehreren Regelsätzen, und könne
uns alle zu Tode langweiligen mit seinen Meinungen zum Thema: »Warum die
japanische Regeln von 1992 schlechter als die Regeln von 1949 sind« (aber
bitte tue das nicht, Robert!).
--
Ted Schürzinger, Fedya2 bei IGS
fe...@bestweb.net
Jede Buchstabe ist sehr wichtig. Es gibt einen großen Unterschied zwischen
dem FCK und der FKK.
Robert Jasiek
Ralf Gering wrote:
> I said "Go".
> which is a Japanese board game played on an orthogonal 19x19 grid!
It may surprise you but some play it on other board sizes and
some had played it before it was known in Japan:) Seriously, by
exactly which rules do you define Go so that we may invent some
long problem? What do you accept as a problem? E.g. do you
accept "Construct a game with 3600 moves!" as a problem? Then I
would not be particularly surprised if today someone would show
you a game with maybe 100! moves but no repeated position and no
suicide, in case you should insist on certain Japanese rules and
the assumption of a stopped game in case of repetition.
--
robert jasiek
Steve Coltrin
> Do you know any Go problems with more plies?
Black to play and win:
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . , . . . . . , . . . . . , . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . , . . . . . , . . . . . , . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . , . . . . . , . . . . . , . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
Ralf Gering
Robert,
> It may surprise you but some play it on other board sizes and
> some had played it before it was known in Japan:)
It doesn't surprise me because i have a collection of more than 200 Go
books, and play Go for 22 years.
> Seriously, by
> exactly which rules do you define Go so that we may invent some
> long problem?
The standard rules used by the Nihon Kiin and the Kansai Kiin in major
tournaments. Sometimes smaller boards are used such as 9x9 or 13x13, but
these boards are not standard.
> What do you accept as a problem? E.g. do you
> accept "Construct a game with 3600 moves!" as a problem?
No.
This might be interesting, although this is usually not considered to be a
"problem" in game theory. In game theory as well as in most books about
games a problem consists of a defined position (including artificial
positions) and some goal to be reached such as mate your opponent's king,
capture all opponent's pieces, link your stones, etc.
Ralf
Ralf Gering
Steve,
are you still in the kindergarten?
On 21 Apr 2001, Steve Coltrin wrote:
> Date: 21 Apr 2001 17:36:41 -0700
> From: Steve Coltrin <spco...@omcl.org>
> Newsgroups: rec.games.go
> Subject: Re: What is the longest Go problem?
>
Joachim Pimiskern
> are you still in the kindergarten?
Vielleicht solltest Du mal deinen primären Humor-Detektor
neu kalibrieren lassen.
Grüße,
Joachim
Robert Jasiek
Ralf Gering wrote:
> > What do you accept as a problem? E.g. do you
> > accept "Construct a game with 3600 moves!" as a problem?
> No.
> This might be interesting, although this is usually not considered to be a
> "problem" in game theory.
Which game theory...?
> In game theory as well as in most books about
> games a problem consists of a defined position (including artificial
> positions)
This would be The Empty Board, but every other starting position
does it as well.
> and some goal to be reached such as mate your opponent's king,
> capture all opponent's pieces, link your stones, etc.
This would be "Play at least 100! moves!". Really, you should
define "goal" much more precisely! Otherwise I am not the least
impressed by any problem with fewer than 100! moves.
Bantari, we had a discussion on what would be a "problem"
earlier. While we did not come to any agreement, maybe you
could help Ralf here? First I thought he might mean some
sort of perfect play problems (disregarding rules problems),
but a connection problem is not a perfect play problem. So
now I have no idea what Ralf could mean by "problem", except
that he seems to have an antipathy against particularly long
problems...
--
robert jasiek
denis-feldmann
Robert Jasiek <jas...@snafu.de> a écrit dans le message :
3AE310D5...@snafu.de...
>
>
> Ralf Gering wrote:
> > > What do you accept as a problem? E.g. do you
> > > accept "Construct a game with 3600 moves!" as a problem?
> > No.
> > This might be interesting, although this is usually not considered to be
a
> > "problem" in game theory.
>
> Which game theory...?
He is speaking from the problemist point of view. Instead of trying to make
word games with one of the finest "heterodox' go problemist in the world (I
would say the finest, but I may be wrong) , why not try to answer seriously?
>
> > In game theory as well as in most books about
> > games a problem consists of a defined position (including artificial
> > positions)
>
> This would be The Empty Board, but every other starting position
> does it as well.
You must have a proven (or provable) solution. On that count, most go
positions dont qualify. Of course, you know this perfectly well; thisis why
I am accusing you of playing word games.
>
> > and some goal to be reached such as mate your opponent's king,
> > capture all opponent's pieces, link your stones, etc.
>
> This would be "Play at least 100! moves!". Really, you should
> define "goal" much more precisely!
Goal is (usually) one a good human player would identufy as such. It is
(usually) possible, in Go, to settle things so that the goal "Black to play
and win (with x komi)" is the only one : just arrange things such that only
killing some stones say, will win the game.
Otherwise I am not the least
> impressed by any problem with fewer than 100! moves.
Mmmm... See above.
>
> Bantari, we had a discussion on what would be a "problem"
> earlier. While we did not come to any agreement, maybe you
> could help Ralf here? First I thought he might mean some
> sort of perfect play problems (disregarding rules problems),
> but a connection problem is not a perfect play problem.
It can be made so. But his is not necessary: just change the evaluation
function (i.e. decide B wins if she connects her stones, lose otherwise.)
So
> now I have no idea what Ralf could mean by "problem", except
> that he seems to have an antipathy against particularly long
> problems...
Ha :-)
>
> --
> robert jasiek
Ted Schuerzinger
wrote in <3AE30786...@compuserve.com>:
Zu guter letzt! Ein Deutscher, der das amerikanisch Humor versteht! :-)
--
Ted Schürzinger
Ralf Gering
Also, für Witze, die auf dem Niveau von geistig Behinderten liegen, hab
ich im Augenblick nicht viel übrig...
Ralf
On Sun, 22 Apr 2001, Joachim Pimiskern wrote:
> Date: Sun, 22 Apr 2001 18:32:06 +0200
> From: Joachim Pimiskern <JoachimP...@compuserve.com>
> Newsgroups: rec.games.go
> Subject: Re: What is the longest Go problem?
>
Ralf Gering
Hello,
> > > What do you accept as a problem? E.g. do you
> > > accept "Construct a game with 3600 moves!" as a problem?
> > No.
> > This might be interesting, although this is usually not considered to be a
> > "problem" in game theory.
>
> Which game theory...?
combinatorial game theory
http://www.ics.uci.edu/~eppstein/cgt/
snip
> While we did not come to any agreement, maybe you
> could help Ralf here? First I thought he might mean some
> sort of perfect play problems (disregarding rules problems),
> but a connection problem is not a perfect play problem.
(perfect play <--> connection tesuji?)
Don't waste my time with your weird nonsense!
> now I have no idea what Ralf could mean by "problem", except
> that he seems to have an antipathy against particularly long
> problems...
If you don't know what I mean, you are in the wrong ng. You abuse this
group with your sophism.
Ralf
Robert Jasiek
Ralf Gering wrote:
> Don't waste my time with your weird nonsense!
> If you don't know what I mean, you are in the wrong ng. You abuse this
> group with your sophism.
If you want a flame war, then you might actually get some...
--
robert jasiek
Robert Jasiek
denis-feldmann wrote:
> > This would be The Empty Board, but every other starting position
> > does it as well.
> You must have a proven (or provable) solution. On that count, most go
> positions dont qualify. Of course, you know this perfectly well; thisis why
> I am accusing you of playing word games.
No, I referred the empty board to the problem of giving
an algorithm for a 100! moves game.
> the goal "Black to play and win (with x komi)"
This would be a reasonable goal if only Ralf spoke about such.
--
robert jasiek
Ralf Gering
Hello,
> He is speaking from the problemist point of view. Instead of trying to make
> word games with one of the finest "heterodox' go problemist in the world (I
> would say the finest, but I may be wrong) ,
Thank you! Well, I will always consider Nakayama Noriyuki as the supreme
master of heterodox Go art. I love his "Treasure Chest Enigma"!
>
> You must have a proven (or provable) solution. On that count, most go
> positions dont qualify. Of course, you know this perfectly well; thisis why
> I am accusing you of playing word games.
what i called "sophism"...
BTW there are beautiful "heterodox" problems in many other games such as
Xiang Qi, Jeu de Dames International and Renju.
Ralf
Ralf Gering
Robert,
my opinion:
if you continue to harrass other users as you did before it might well be
possible that your mental health is in a serious condition.
Ralf
-
From: Ralf Gering <zxm...@mail.uni-tuebingen.de>
> my opinion:
>
> if you continue
> to harrass other
> users as you did
> before it might
> well be possible
> that your mental
> health is in a
> serious condition.
ah, I see ... so it's time for -opinions- again?
On this group we are reviewing matters related to Go,
not whether people are talking to psychiatrists, taking
meds, or on the verge of self-immolation.
- regards
- jb
.
Darren Cook
SECONDED!!!
The first post was interesting. Every other post so far has wasted my
time and bandwidth.
(and to the person who suggested "black to play on empty board" as a
good long problem - I give up, please post the answer).
Darren
Robert Jasiek
Darren Cook wrote:
> >He is speaking from the problemist point of view. [...]
> >why not try to answer seriously?
> The first post was interesting. Every other post so far has wasted my
> time and bandwidth.
Then maybe you could explain what is the problemist point of view?
What is "longest" about the problems in the first post?
--
robert jasiek
denis-feldmann
>
>
> Darren Cook wrote:
> > >He is speaking from the problemist point of view. [...]
> > >why not try to answer seriously?
> > The first post was interesting. Every other post so far has wasted my
> > time and bandwidth.
>
> Then maybe you could explain what is the problemist point of view?
I cannot believe you dont know. I repeat: A problem is defined as a
question of the shape "find a (the) optimal (in the game-theoretic sense)
sequence of legal moves such that a clear objective is attained (by minimax,
say)"; the list of legitimate objectives being extracted from the normal
mechanisms of the game (win, draw, capture some piece, promote, connect,
kill,etc...). In addition, the problem must have a known solution
(preferably unique). It is really possible that no formal definition
exist... But chess problemists have worked for hundred of years, and
codified their practice; go problemists have a similar history, and (though
they never codified it) similar practice and exigences.
> What is "longest" about the problems in the first post?
See above. Read some chess problem theory. Try to understand why the name of
O.Blathy is still well-known. Try to get some sense of awe from the problem
in question (for a start, try to solve it :-))
>
> --
> robert jasiek
Robert Jasiek
denis-feldmann wrote:
> > Then maybe you could explain what is the problemist point of view?
> I cannot believe you dont know. I repeat: A problem is defined as a
> question of the shape "find a (the) optimal (in the game-theoretic sense)
> sequence of legal moves such that a clear objective is attained (by minimax,
> say)"; the list of legitimate objectives being extracted from the normal
> mechanisms of the game (win, draw, capture some piece, promote, connect,
> kill,etc...). In addition, the problem must have a known solution
> (preferably unique). It is really possible that no formal definition
> exist... [...] go problemists have a similar history, and (though
> they never codified it) similar practice and exigences.
It is clear what is meant by
- optimal in the [CGT-]game-theoretic sense,
- minmax
It is more or less clear what is supposed to be
- legal moves
It is unclear
- what is a legitimate objective in contrast to a non-legitimate
objective,
- why a unique solution should be preferred,
- why only rules that do not allow a game-theoretic analysis in
general should be valid
IIUYC, then you consider a particular genre of go problems -
the genre of "historical problems", which need objectives that
might have been chosen by problemists hundreds of years ago and
that use only such rules that have existed for hundreds of years.
If I tolerate studying a particular genre, then why wouldn't you
tolerate my study of other go genres? OC, I tolerate the
historical genre now that I recognize it is a particular one
because now I even (believe to) know what is meant by it. Please
correct me if my understanding that you rely on invariants during
hundreds of years of problem history is still wrong. How do you
classify old problems that do not belong to the historical genre
because, e.g., they rely on other rules, see, e.g., Shimada's
problems?
--
robert jasiek
hh
philosophical hair splitting issues arise. Starting from a simple
looking question, one may ask: what is a problem? what is a game? what
is a rule? what is a definition? what is an abstract concept? in which
logical framework do abstract concepts have a meaning?
If we don't stray into philosophy, let's try to define "problem" and
"length".
A problem in a game is a question of the sort: "can a [specified] player
reach a [specified] goal starting from a [specified] situation, whatever
the opponent[s] play[s]?".
The length of the solution is the minimax value of the number of plies
of all legal sequences starting from the initial situation and ending
when the aim is reached.
The string capture game, or the ladder game for example, are subgames of
Go that can be easily defined unequivocally. Problems involving
life/death ("kill/save") and connections are more difficult to define,
and not everyone will agree with any reasonable definition.
"Play at least 100! moves" is a legitimate goal IMHO, but not a
traditional one.
Jean-Pierre Vesinet - j...@NaOtStPhAiMs.com (remove NOSPAM)
hh
Thanks for posting!
This is a puzzling one. Does your problem have a solution?
It seems that the black string gets captured at move 314 - see SGF
below. Or did I miss something?
BTW, what is the length of the solution of a problem that doesn't have
one?
This sounds like a zen koan. ;-)
(;SZ[19]AB[qa][ra][ab][ac][ec][qd][ge][je][ke][qe][of][og][kh][ki][oj][lk][mk]
[ok][km][mm][bn][cn][kn][eo][mo][no][ap][cp][ep][oq][pq][sq][ar][sr][as][ds]
[ho][io][dc][fe]AW[ao][bo][do][dp][aq][bq][br]TR[ap]PL[B]
;B[bp];W[co];B[cq];W[dq];B[cr];W[dr];B[cs];W[bs];B[es];W[er];B[fs];W[fr];B[gs]
;W[gr];B[hs];W[hr];B[is];W[ir];B[js];W[jr];B[ks];W[kr];B[ls];W[lr];B[ms];W[mr]
;B[ns];W[nr];B[os];W[or];B[ps];W[pr];B[qs];W[qr];B[rs];W[rr];B[ss];W[rq];B[sp]
;W[rp];B[so];W[ro];B[sn];W[rn];B[sm];W[rm];B[sl];W[rl];B[sk];W[rk];B[sj];W[rj]
;B[si];W[ri];B[sh];W[rh];B[sg];W[rg];B[sf];W[rf];B[se];W[re];B[sd];W[rd];B[sc]
;W[rc];B[sb];W[rb];B[sa];W[qb];B[pa];W[pb];B[oa];W[ob];B[na];W[nb];B[ma];W[mb]
;B[la];W[lb];B[ka];W[kb];B[ja];W[jb];B[ia];W[ib];B[ha];W[hb];B[ga];W[gb];B[fa]
;W[fb];B[ea];W[eb];B[da];W[db];B[ca];W[cb];B[ba];W[bb];B[aa];W[bc];B[ad];W[bd]
;B[ae];W[be];B[af];W[bf];B[ag];W[bg];B[ah];W[bh];B[ai];W[bi];B[aj];W[bj];B[ak]
;W[bk];B[al];W[bl];B[am];W[an];B[bm];W[dn];B[cm];W[dm];B[cl];W[dl];B[ck];W[dk]
;B[cj];W[dj];B[ci];W[di];B[ch];W[dh];B[cg];W[dg];B[cf];W[df];B[ce];W[de];B[cd]
;W[cc];B[dd];W[ed];B[fc];W[fd];B[gc];W[gd];B[hc];W[hd];B[ic];W[id];B[jc];W[jd]
;B[kc];W[kd];B[lc];W[ld];B[mc];W[md];B[nc];W[nd];B[oc];W[od];B[pc];W[qc];B[pd]
;W[pe];B[qf];W[pf];B[qg];W[pg];B[qh];W[ph];B[qi];W[pi];B[qj];W[pj];B[qk];W[pk]
;B[ql];W[pl];B[qm];W[pm];B[qn];W[pn];B[qo];W[po];B[qp];W[pp];B[qq];W[op];B[nq]
;W[np];B[mq];W[mp];B[lq];W[lp];B[kq];W[kp];B[jq];W[jp];B[iq];W[ip];B[hq];W[hp]
;B[gq];W[gp];B[fq];W[eq];B[fp];W[fo];B[en];W[fn];B[em];W[fm];B[el];W[fl];B[ek]
;W[fk];B[ej];W[fj];B[ei];W[fi];B[eh];W[fh];B[eg];W[fg];B[ef];W[ee];B[ff];W[he]
;B[gf];W[hf];B[gg];W[hg];B[gh];W[hh];B[gi];W[hi];B[gj];W[hj];B[gk];W[hk];B[gl]
;W[hl];B[gm];W[hm];B[gn];W[go];B[hn];W[jo];B[in];W[jn];B[im];W[jm];B[il];W[jl]
;B[ik];W[jk];B[ij];W[jj];B[ii];W[ji];B[ih];W[jh];B[ig];W[jg];B[if];W[ie];B[jf]
;W[kf];B[le];W[lf];B[me];W[mf];B[ne];W[oe];B[nf];W[oh];B[ng];W[nh];B[mg];W[mh]
;B[lg];W[kg];B[lh];W[kj];B[li];W[lj];B[mi];W[mj];B[ni];W[nj];B[oi];W[nk];B[ol]
;W[nl];B[om];W[nm];B[on];W[nn];B[oo];W[mn];B[lo];W[ko];B[ln];W[kl];B[lm];W[ll]
;B[ml];W[kk])
denis-feldmann
>
>
> denis-feldmann wrote:
> > > Then maybe you could explain what is the problemist point of view?
> > I cannot believe you dont know. I repeat: A problem is defined as a
> > question of the shape "find a (the) optimal (in the game-theoretic
sense)
> > sequence of legal moves such that a clear objective is attained (by
minimax,
> > say)"; the list of legitimate objectives being extracted from the normal
> > mechanisms of the game (win, draw, capture some piece, promote, connect,
> > kill,etc...). In addition, the problem must have a known solution
> > (preferably unique). It is really possible that no formal definition
> > exist... [...] go problemists have a similar history, and (though
> > they never codified it) similar practice and exigences.
>
> It is clear what is meant by
> - optimal in the [CGT-]game-theoretic sense,
> - minmax
>
> It is more or less clear what is supposed to be
> - legal moves
No, this is only a problem for Go in the classical ages, where there was no
"official rules". In a formalized approch, leagal moves are part of the
definition of the game anyway (see Conway, On Games and Numbers, for
instance)
>
> It is unclear
> - what is a legitimate objective in contrast to a non-legitimate
> objective,
Yes. This will *strongly* depend of the class of problems considered. In
Chess, for instance, a lot of variations (orthodox two-movers, studies,
fairy chess...) are possible. The point, let's say, is that the objective
must be formalizable. The rest is a matter of history (for instance, some
really old chess problems (18th and 19th century mainly :-)) have goals like
: "To mate after the knight has made three complete rounds of the board"
Many modern problemists find this illegitimate (and hideous, by the way).
> - why a unique solution should be preferred,
Interesting question. In chess, this is very important. Maybe the reson this
is somewhat relaxed in Go is the difficulty of eliminating
irrelevant ko threats and the like?
> - why only rules that do not allow a game-theoretic analysis in
> general should be valid
Sorry? I dont understand this.
>
> IIUYC, then you consider a particular genre of go problems -
> the genre of "historical problems", which need objectives that
> might have been chosen by problemists hundreds of years ago and
> that use only such rules that have existed for hundreds of years.
Yes, mostly that. Of course, I am also interested in rule problems,
theoretical yose problems, etc. And things like "what is the maximum number
of living groups on a regular goban " But , as in chess, I somehoiw find
those problems less interesting and less artistic. matter of taste,
obviously.
> If I tolerate studying a particular genre, then why wouldn't you
> tolerate my study of other go genres?
Oh, but I do. I was just wondering why you were insistingso much on a
formalisation of the problem, when I felt the question was clear (and
somewhat interesting). Why does all this reminds me of a mathematician,
friend of mine, who never wanted to learn how to play Go because, said he
(that was before your efforts, Robert:-)) the rules of the game seemed
unclear and incomplete?
OC, I tolerate the
> historical genre now that I recognize it is a particular one
> because now I even (believe to) know what is meant by it. Please
> correct me if my understanding that you rely on invariants during
> hundreds of years of problem history is still wrong.
Well, not exactly. All this was completely theorized (for chess) in the late
19th and early 20th century. A lot of concepts were formalized then (like
what is a real threat, a virtual threat, conjugate cases and opposition,
etc.) Nothing of the kind seems to exist for Go, but adaptation of existing
concepts is possible (like getting a formal definition of Yosumiru (probe),
by inspection of the game tree)
How do you
> classify old problems that do not belong to the historical genre
> because, e.g., they rely on other rules, see, e.g., Shimada's
> problems?
In the category "others"? :-) (after all, there are probably not many of
those...) Seriously, of course, those are "rule problems", or "unusual
positions" (in that they necessitate the application of exceptional rules
to solve them)
>
> --
> robert jasiek
Robert Jasiek
denis-feldmann wrote:
> this is only a problem for Go in the classical ages, where there was no
> "official rules". In a formalized approch, leagal moves are part of the
> definition of the game anyway (see Conway, On Games and Numbers, for
> instance)
Sure.
> > - why a unique solution should be preferred,
> Interesting question. In chess, this is very important. Maybe the reson this
> is somewhat relaxed in Go is the difficulty of eliminating
> irrelevant ko threats and the like?
I like multiple solutions because that is more realistic and
because one can study side-conditions.
> > - why only rules that do not allow a game-theoretic analysis in
> > general should be valid
> Sorry? I dont understand this.
Presuming logical rules, no surprise:)
> Oh, but I do.
No doubt. I didn't mean "you" personally.
> I was just wondering why you were insistingso much on a
> formalisation of the problem, when I felt the question was clear (and
> somewhat interesting).
Until today I viewed upon all problems equally without classifying
them because I classified their study methods instead. It simply
didn't occur to me that there would be anything like a particular
problem genre. E.g., using the study method time of invention I
would have recognized an old problem as old but I did not classify
it as being part of a historical problems genre. I did about the
same for the study method board size.
> Why does all this reminds me of a mathematician,
> friend of mine, who never wanted to learn how to play Go because, said he
> (that was before your efforts, Robert:-)) the rules of the game seemed
> unclear and incomplete?
If I would not have been convinced of the complexity, etc. of
go before hearing about its many unclear and incomplete rules
shortly after starting to play, then my fate might indeed have
been the same;)
> what is a real threat, a virtual threat, conjugate cases and opposition,
> etc.) Nothing of the kind seems to exist for Go,
Some people here have started studying such during the last, say,
4 years. Wait another decade and you will see similar things for
go.
--
robert jasiek
Robert Jasiek
Bruno Wolff III wrote:
> >Do you know any Go problems with more plies?
> You might find "Mathematical Go: Chilling gets the last point" interesting.
> It provides some very complicated endgame positions that can be solved
> use combanatorial game theory. They are exactly like your ladder situations
> and you may not be looking for that kind of problem.
Go with a prohibition of repeated positions can have quite long
problems: (use a fixed width font)
X X X X X X X X X X X X X X X X X X X X to play and prepare
O X O X . X . X . X . X . X . X X X X against O's toughest
. O . O X O X O X O X O X O X O O O O (i.e. longest) perfect
O O O O O O O O O O O O O O O O O O O play resistance
X X X X X X X X X X X X X X X X X X X
O O O O O O O O O O O O O O O O X X .
. O . O X O X O X O X O X O X O X X X
O X O X . X . X . X . X . X . X O O .
X X X X X X X X X X X X X X X X O O O
O O O O O O O O O O O O O O O O O O O
X X X X X X X X X X X X X X X X O O O
O X O X . X . X . X . X . X . X O O .
. O . O X O X O X O X O X O X O X X X
O O O O O O O O O O O O O O O O X X .
X X X X X X X X X X X X X X X X X X X
O O O O O O O O O O O O O O O O O O O
. O . O X O X O X O X O X O X O O O O
O X O X . X . X . X . X . X . X X X X
X X X X X X X X X X X X X X X X X X X
There are 4 8-tuple-kos on the board. According to the proof
for the theorem by Bill Spight, which relies on concepts
proposed by James Davies and John Rickard and is attached inline,
X can destroy exactly one 8-tuple-ko-coexistence after, if I have
understood the proof correctly after quickly skimming through it,
at most 2 * (8*7)^4 = 19.668.992 plays on the board because
within each 8-tuple-ko there are 8*7 defensive positions with
exactly two O ko stones, because the number of 8-tuple-kos is 4,
and because defensive and attacking positions alternate giving
the factor 2.
X wants to win one of the two biggest 8-tuple-kos while O
wants to keep them. If all four would be equally big, then
O could pass at move 19.668.992. (If you can set up 4 equally
big 8-tuple-kos on a 19x19-board, then calculation is easier.)
However, O will pass earlier, namely the last time when X can
attack a small 8-tuple-ko. I am not sure, which such last time
moment is the earliest for X? Anyway, it will be fewer than
19.668.992 moves until one of the 4 8-tuple-kos is dissolved.
Then I suppose there to be an endgame ko fight about 4 points
(or about even more?). O should be able to turn at least one
standard ko within the remaining 3 8-tuple-kos from an X to a
O ko stone. Does this take only a few moves or many moves?
How long is this problem really in case of O's toughest
resistance while still following perfect play? It looks like
many millions of moves or have I made severe mistakes while
applying the proof? What is the correct komi?
--
robert jasiek
Subject: Re: Two quad-kos and more
Date: Sat, 27 Sep 1997 03:49:47 -0400 (EDT)
From: BillS...@aol.com
To: go-r...@lists.io.com
All:
Before I said that James Davies' note on two quadruple kos
was excellent. Let me amend that. It is most excellent!!!!!
I did not understand Davies' method at first. But when I
did, I realized that it shows that enough basic n-tuple kos allow
the attacker to break the final standoff under superko rules, and
tells the attacker how to play.
Definitions:
Basic multiple ko. A superko comprised of simple ko mouths
in which, if either player has a stone in all of the ko mouths,
he captures all of the opponent's stones, and neither player can
capture any stones except single ko stones otherwise.
Attack position. 1. A position in a basic multiple ko in
which one player (the attacker) has stones in all but one of the
ko mouths.
2. A position in a superko comprised of basic multiple kos
in which one of the multiple kos is in an attack position.
Standoff position. 1. A position in a basic multiple ko in
which one player (the attacker) has stones in all but two of the
ko mouths. This is said to be a standoff favoring the attacker.
2. A position in a superko comprised of basic multiple kos
in which all of the multiple kos are in standoff positions
favoring the attacker.
Break the standoff. Reach an attack position from which the
defender is barred from returning to a standoff position by the
superko rule.
Proposition:
Given int(n/2) n-tuple kos (n > 2) (the superko) in standoff
position favoring the attacker (and given that the last play was
not a play by the defender in the superko), the attacker to move
can break the standoff.
Davies' method:
For each standoff position determine an attack position
which the attacker can reach by one move. Then from each
standoff position the attacker may move to the corresponding
attack position without repeating a prior superko position (if
the attacker was the first to play from the initial superko
position). Since the defender can move to at most all but one of
the standoff positions from the attack positions without
repeating a superko position, and the attacker has a
non-repeating move from each of these, the defender must run out
of legal plays in the multiple n-tuple ko before the attacker
does.
How to determine the corresponding attack positions:
Definition:
Order of a standoff position:
Represent a ko mouth occupied by the attacker by X and one
occupied by the defender by O. For the standoff position arrange
the ko mouths in a circle. Given this arrangement, the order of
the standoff position is the minimum number of Xs between the Os.
Examples:
In a 7-tuple ko the order of the following position is 2.
X X O X X O X.
In an 11-tuple ko the order of the following position is 4.
X X O X X X X X O X X (the last X is adjacent to the first
in the circle).
For a given circular arrangement, each standoff position in
an n-tuple ko has possible orders from 0 to int(n/2) - 1.
Phase 1: For each n-tuple ko standoff position determine an
attack position.
For the circle representing the standoff position identify a
direction and a "leftmost point". We may write the circle as a
line in which the direction is left to right except from the
rightmost point, where the direction is to the leftmost point.
For a position of order r replace the O which has r Xs to its
left between it and the other O. Order n/2 - 1 is ambiguous.
For it replace the rightmost O in the line.
Phase 2: Given the standoff positions and attack positions
of each of the n-tuple kos, determine an attack position for each
standoff position in the superko.
Number the individual n-tuple kos from 0 to int(n/2) - 1.
Add the orders of the standoff positions modulo int(n/2).
The attack position in the n-tuple ko with the same number as the
sum, along with the standoff positions is the superko attack
position.
That is it!
I realize that that may not look too much like what Davies
did, but it comes to the same thing.
To demonstrate that, here is how the method as I describe it
applies to 2 quadruple kos.
Order 0 standoff positions and corresponding attack
positions:
OOXX OXXX
XOOX XOXX
XXOO XXOX
OXXO XXXO
Order 1 standoff positions and corresponding attack
positions:
OXOX OXXX
XOXO XOXX
Next the method I describe differs slightly from what Davies
did, but the difference is minor. He divided the positions
equally, instead of by orders.
Let the right quadruple ko have number 0 and the left have
number 1. Then if both individual standoff positions have order
0, the sum is 0, so the attacker should play in the right
quadruple ko. If one individual standoff position has order 0
and the other has order 1, the sum is 1, and the attacker should
play in the left quadruple ko. If both standoff positions have
order 1, the sum is 1 + 1 = 0 (mod 2), so the attacker should
play in the right quadruple ko.
Now let's look at 4 9-tuple kos:
Order 0
OOXXXXXXX OXXXXXXXX
XOOXXXXXX XOXXXXXXX
. . . . . .
OXXXXXXXO XXXXXXXXO
Order 1
OXOXXXXXX OXXXXXXXX
XOXOXXXXX XOXXXXXXX
. . . . . .
XOXXXXXXO XXXXXXXXO
Order 2
OXXOXXXXX OXXXXXXXX
XOXXOXXXX XOXXXXXXX
. . . . . .
XXOXXXXXO XXXXXXXXO
Order 3
OXXXOXXXX OXXXXXXXX
XOXXXOXXX XOXXXXXXX
. . . . . .
XXXOXXXXO XXXXXXXXO
Orders of 9-tuple kos Number of 9-tuple ko in which to play
0 + 0 + 0 + 0 = 0 (mod 4)
0 + 0 + 0 + 1 = 1 (mod 4)
. . . ...
0 + 0 + 1 + 1 = 2 (mod 4)
. . . ...
1 + 2 + 3 + 0 = 2 (mod 4)
. . . ...
3 + 1 + 1 + 2 = 3 (mod 4)
. . . = ...
3 + 3 + 3 + 3 = 0 (mod 4)
You can see that each attack position is different. Given
the orders of three of the 9-tuple kos, the order of the fourth
uniquely determines which of the kos to play in.
Many thanks, James!
Bill Spight
denis-feldmann
poster wanted longest problem *without* ko capture, but the incredible
problem below is without doubt pertinent to the question :-) Ok, what *is*
the longest problem *without* ko capture?
Robert Jasiek <jas...@snafu.de wrote in message :
3AE7115C...@snafu.de...
Tim Tyler
: Ok, what *is* the longest problem *without* ko capture?
Since simple ko is not the only way of getting forced repetitions in go,
I imagine the longest non-ko problem would involve them instead.
--
__________
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