D-Wave Systems breaks the 1000 qubit quantum computing barri

[jefk]

[quote="Ozymandias"]
Let me be positive, and instead of using a double negative, say that it's "certainly possible". Only when black tries to win, can a withe win take place.[/quote]

depends how hard Black is trying
Recently it also seems to be based on my data
that Black can equalize against the Yugosloav Dragon,
quite a complicated and sharp variation but maybe offering
more interesting chances for counterplay than the Najdorf.

In other words a human playing 1.e4 against the Sicilian
Dragon has to know what he's doing. And a computer
should have a (very) good book.

jef

PS about this draw conjecture again (sigh) it's a matter i think
also about the burden of proof; in legal system you are
innocent until proven guilty but that's for ethical reasons i
presume. For a system as chess i would reverse the
burden of proof as it is stated currently and would ask
people as mr Hyatt to prove that White always can win.
A similar system as eg. this 'final theory of chess' where
someone is trying to get an advantage with the BDG
gambit but obviously is failing with such strategy.

[JVMerlino]

I doubt if anyone will bother with such a search until the hardware improves. I don't think anyone expects to find a forced checkmate within the first 100 plies, or it very likely would have been discovered already. With nothing but Alpha Beta search on current hardware, it would take millenniums to get deep enough to find something interesting (in all likelihood). Now, a super-fast proof search using GPU cards might prove interesting. We have a super fast GPU move generator, but nobody has bothered to write a proof search yet. The latest cards have a form of recursion and they are getting a lot more memory now, so maybe that sort of thing is not far off.

Of course, it is possible that there is a checkmate in the first 25 plies and we just have not found it yet. But I would not want to spend ten years of computer time to find out, since it seems so improbable.

And I guess this was my roundabout way of agreeing with Bob. If chess is a draw, I believe it will probably never be proven. But if it is a win for White, then the proof is so time-consuming that I think it's less likely that we'll prove it this century than aliens coming down from the sky with their highly-advanced technology and proving it for us.

[jefk]

a quick check

[quote="jefk"]
1. e4 c5 0.00/0 0.0 2. Nf3 0.00/0 0.0 d6 0.00/0 0.0 3. d4 cxd4 0.00/0 0.0 4. Nxd4 0.00/0 0.0 Nf6 0.00/0 0.0 5. Nc3 0.00/0 0.6 a6 0.00/0 0.0 6. Be3 e5 0.00/0 0.0 7. Nb3 0.00/0 0.0 Be7 0.00/0 0.5 8. f3 Be6 0.00/0 0.0 9. Qd2 0.00/0 0.0 O-O 0.00/0 0.0 10. O-O-O 0.00/0 0.0 Nbd7 0.00/0 0.6 11. g4 0.00/0 0.6 b5 0.00/0 0.6 12. g5 0.00/0 0.0 Nh5 0.00/0 0.6 13. Kb1 0.00/0 0.0 Nb6 0.00/0 0.0 14. Na5 0.00/0 0.0 ( 14. Nd5 0.00/0 0.0 ) 14... Rc8!
Whereby i leave it to IM or GM junkies of New in Chess or
Chessbase to find the socalled ' novelties' .
[/quote]

apparently the move 14...Rc8! already is new according to chessbites.com
And after 14.Nd5 Nxd5 15.exd5 Bf5! 16.Na5 f6! seems to be 'new'.

In a similar way after
1. c4 e5 0.00/0 0.1 2. Nc3 0.00/0 0.6 Nf6 0.00/0 0.0 3. g3 0.00/0 0.0 Bb4 0.00/0 0.0 4. Nf3 0.00/0 0.6 Nc6 0.00/0 0.0 5. Bg2 0.00/0 0.0 d6 0.00/0 0.5 6. O-O 0.00/0 0.0 O-O 0.00/0 0.5 7. d3 0.00/0 0.0 a5 0.00/0 0.5 8. Bd2, the move 8... Bf5! already seems to be ' new'.

Although they probably also are listed in the Chessbase 'livebook' ,
(and most likely in the their let's check base).

Thus considering the high scope for 'novelties' for Black my
statement that Black can always equalize is made more plausible.
Similar in other lines for White.

jef

[bob]

Let me be positive, and instead of using a double negative, say that it's "certainly possible". Only when black tries to win, can a withe win take place.

depends how hard Black is trying
Recently it also seems to be based on my data
that Black can equalize against the Yugosloav Dragon,
quite a complicated and sharp variation but maybe offering
more interesting chances for counterplay than the Najdorf.

In other words a human playing 1.e4 against the Sicilian
Dragon has to know what he's doing. And a computer
should have a (very) good book.

jef

PS about this draw conjecture again (sigh) it's a matter i think
also about the burden of proof; in legal system you are
innocent until proven guilty but that's for ethical reasons i
presume. For a system as chess i would reverse the
burden of proof as it is stated currently and would ask
people as mr Hyatt to prove that White always can win.
A similar system as eg. this 'final theory of chess' where
someone is trying to get an advantage with the BDG
gambit but obviously is failing with such strategy.

You've not seen me claim such a thing as "white always wins." And I have clearly stated that proving it is close enough to impossible to make that a good adjective to describe the possibility. By the same token, I don't believe the game is a draw for white, nor a loss. I believe that is an "unanswered question."

But this argument of "prove it is a win for white else that proves it is a draw" is a bit "out there". Neither will be proven before the universe collapses and "big bangs" again.

If you want to claim you believe it is a draw, that's fine. But it is NOT a proof the game is a draw. Just because you can't find something (a forced win for white in this case) does NOT mean it doesn't exist. This is the "upside-down A" in CS theoretical discussions, "for all..." Not the existential operator ("backward E") that says "there exists at least one..."

To prove a draw, you have to prove all moves lead to draw which shows there is no winning path. To disprove this, you need just one forced winning line. To prove it is won, you need to prove there is at least one forced winning line, proving one drawing line does nothing.

[jefk]

[quote="bob"]
To prove a draw, you have to prove all moves lead to draw which shows there is no winning path. [/quote]

or, using the Zermol theorem, which has been proven, it should
be ' proven' that Black has a 'drawing strategy' .
Question then is, what is a ' drawing strategy' .

Indeed i claim Black has such a strategy, by having found that Black can 'equalize' all opening lines; and can continue to do so if you extend such lines, starting with the ' best' lines for White.

One can argue this is not a proof, first because it is still ' only' an empirical result, secondly because the engine eval isn't accurate. For me that's nitty gritty, again in physics an empirical result is good enough. Secondly, look at eg endgames with opposing bishops, you need quite a high positional score, (with good engines) to win such an endgame. In other words, Black can always stay within the drawing margin of the game.

jef

PS Maybe/probably chess is too complex to 'prove' this in mathematical terms, well for me that doesn't matter; you also cannot prove with the theoretical particle physics eg quantum gravity, string theory, or dynamic triangular simulation that an apple falls from a tree. yet it does. With the empirical ' law' of gravity.
PS2 And then i'm repeating myself, the Newtonian law action = -reaction also is an empirical ' law' . Well in chess ,using the information of the White move, Black can/should choose his ' best' move, thus being to equalize.
ergo, yes indeed, i claim chess is a draw. with 100 pct certainty
PS3 Other question is whether chess is draw if (only) the 50 move draw rule
wouldn't hold anymore in correspondence chess and/or computer chess; well that one i don't know (yet?); maybe something for a future generation.

[jefk]

let me rephrase my statement(s)

[quote="bob"] To prove a draw, you have to prove *all* moves lead to draw which shows there is no winning path. [/quote]

(emphasized the word all)

ok, why ? because you say so ?
because some mathematicians say so ?
(isn't it possible to prune the move tree ? (*)

Do all mathematicians say this ?
(isn't this a bit dogmatic?)

What about all computer (computational) scientists ?
(are there people besides myself, arshah, and later
probably also chessbase with theire livebook and possibly
chessok with their Aquarium who have looked at huge trees?)

(*)are we not doing that already with alfabeta search which
has been *proven* to be correct ? Isn't it sufficient for Black
o equalize against the *best* White moves, thus then ofcourse
also being able to equalize against other moves, especially if
they fall outside the alfa/beta bound for the tree (on disk) ?
and so on.

[jefk]

[quote="bob"]
But this argument of "prove it is a win for white else that proves it is a draw" is a bit "out there". [/quote]

well it is a bit far-teched, i agree, but i was saying it
as some sort of 'proof by contradition'
https://en.wikipedia.org/wiki/Proof_by_contradiction
It it's not a win for White, then it must be draw. And why
must we ´prove´ it´s not a win for White i wonder+
by now i´ts quite obvious, at least for me.

In relation to required methodlogy my example of an apple might also seem a bit odd, but what i'm in fact referring to is the phenomenon of
'emergence' (nowadays many physicists also see gravity as
an emergent phenomenon'.
https://en.wikipedia.org/wiki/Emergence
Emergence not only occurs in biological systems, but
also in some physical systems.
https://en.wikipedia.org/wiki/Emergence ... al_systems
And even in mathematical systems, eg cellular automata
https://en.wikipedia.org/wiki/Cellular_automaton
Stephen Wolfram wrote a book about such a ´new kind of science´
https://en.wikipedia.org/wiki/A_New_Kind_of_Science
Now there is not much talk about chess in this book,
and chess also doesn´t of cellular automata, but for
me there is some similarity, from individual moves
you can get a pattern, White trying to win, Black equalizing,
and thus the game, in the end with less pieces, ending
in a draw. An emergent fact.
Most emergent facts cannot be proven, they only
can be simulated. Yet when such simulations are
done accurately and rigorously enough, often a resulting
conclusions may be regarded as a fact and there is
no need for a further more detailed proof.
That is my basic argument

jef

[bnemias]

I believe the game is a draw with perfect play. There are even rational reasons to think that. But that doesn't make it so, and it is certainly not proof.

or, using the Zermol theorem, which has been proven, it should
be ' proven' that Black has a 'drawing strategy' .
Question then is, what is a ' drawing strategy' .

Zermelo's Theorem doesn't apply. It is for games that cannot end in a draw.

Indeed i claim Black has such a strategy, by having found that Black can 'equalize' all opening lines; and can continue to do so if you extend such lines, starting with the ' best' lines for White.

This is irrelevant. Define equalize for one. It's easy enough to construct positions where engines report 0.0 that are clearly decisive. This means you can't just look at selected positions and then trust some eval about the result.

Your draw strategy doesn't account for the possibility of a drawing structure being forced to collapse via zugzwang.

PS Maybe/probably chess is too complex to 'prove' this in mathematical terms, well for me that doesn't matter; you also cannot prove with the theoretical particle physics eg quantum gravity, string theory, or dynamic triangular simulation that an apple falls from a tree. yet it does. With the empirical ' law' of gravity.
PS2 And then i'm repeating myself, the Newtonian law action = -reaction also is an empirical ' law' . Well in chess ,using the information of the White move, Black can/should choose his ' best' move, thus being to equalize.
ergo, yes indeed, i claim chess is a draw. with 100 pct certainty

The bolded segments are contradictory.

[jefk]

[quote="bnemias"]
[url=https://en.wikipedia.org/wiki/Zermelo%2 ... _theory%29]Zermelo's Theorem[/url] doesn't apply. It is for games that cannot end in a draw.[/quote]

hmm, but Zermelo apparently applied it himself to the game of chess
' Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels'
(also mentioned in this wikipedia article. That remark about
games which 'cannot end in a draw' is mentioned in this
wikipedia article, but i suspect it is not entirely correct.

Are you a mathematician btw ? (just curious);
or just an IT guy.

[quote]
[quote]PS Maybe/probably chess is [b]too complex to 'prove' this in mathematical[/b] terms, well for me that doesn't matter;
[b]yes indeed, i claim chess is a draw. with 100 pct certainty[/b][/quote]
The bolded segments are contradictory.[/quote]

not for me. something can exist in reality witout
proven in rigid mathematical terms; due to
the socalled emergence which i mentioned in an earlier posting
(whereby i hadn't seen your message yet).

And if i say i claim with 100 pct certainty, i ofcourse
mean that that for *me* it is with 100 pct certainty.

Those with the illusory ' hope' (?) of still finding a
win for White can continue their search to the end,
which is possible in a few decades i think with alfa/beta
engine search combined with a positional tree on disk
(as in Aquarium IDea) and bearing in mind the large
amount of transpositions which occur thus making
it a finite tree and such a search imho feasible
contrary to what Bob H apparently currently believes.
In the end such a search would only confirm my
statement, ie strong conjecture, ie empirical finding
that chess is a draw.

jef

PS you talked about zugzwang ? Irrelevant in the middlegame,
with positional manoeuvring you often get triangles and
thus zugzwang plays no role. Fortresses ? Yes that is
an additional argument why Black can draw (besides
the high drawing margin eg when having oppositie
bishops in the endgame).

[jefk]

just a quick addition with 2 refs

[quote="jefk"]That remark about
games which 'cannot end in a draw' is mentioned in this
wikipedia article, but i suspect it is not entirely correct.
[/quote]

apparently there are various variations on this
(specific, gametheoretic ) Zermelo theorem; see eg
http://www.math.harvard.edu/~elkies/FS2 ... ermelo.pdf
and /or
https://theoryclass.wordpress.com/2009/ ... s-theorem/

which i will study later in more detail;
with respect to chess at least

In the meantime i will obviously not revise my statement.
(with the 100 pct = 99.999999999999999999... and so on pct).

jef