> Shouldnt that number at most be 722^#positions? Since adding a black or a
> white stone is something fundamentally different?
The upper bound of 361^L(19,19) games is from Theorem 7 on page 31 of
http://tromp.github.io/go/gostate.pdf, where you will find a proof.
As the paragraph preceding that
On 09.08.2017 20:50, John Tromp wrote:
The number of games is at most 361^#positions.
This misses passes, rules distinguishing situations etc. and infinite
sequences under some rulesets.
--
robert jasiek
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Why do you think that there is a 3 in the denominator?
On Aug 9, 2017 2:29 PM, "Marc Landgraf" wrote:
> I don't mind your terminology, in fact I feel like it is a good way to
> distinguish the two different things. It is just that I considiered one
> thing wrongly used
It's trivial, dude.
On Aug 9, 2017 8:35 AM, "Marc Landgraf" wrote:
> Under which ruleset is the 3^(n*n) a trivial upper bound for the number of
> legal positions?
> I'm sure there are rulesets, under which this bonds holds, but I doubt
> that this can be considered
I don't mind your terminology, in fact I feel like it is a good way to
distinguish the two different things. It is just that I considiered one
thing wrongly used instead of the other for the discussion here.
But if we go with the link you are suggesting here:
Shouldnt that number at most be
> And what is the connection between the number of "positions" and the number
> of games
The number of games is at most 361^#positions.
> or even solving games? In the game trees we do not care about
> positions, but about situations.
We care about lots of things, including intersections,
And what is the connection between the number of "positions" and the number
of games or even solving games? In the game trees we do not care about
positions, but about situations. For the game tree it indeed matters whos
turn it is, which moves are legal, and if super-ko rules are used which
> Under which ruleset is the 3^(n*n) a trivial upper bound for the number of
> legal positions?
Under all rulesets.
> Unless we talk about simply the visual aspect
Yes, we do.
> but then this has
> absolutely nothing to do with the discussion abour solving games.
If you want the notion of
Under which ruleset is the 3^(n*n) a trivial upper bound for the number of
legal positions?
I'm sure there are rulesets, under which this bonds holds, but I doubt that
this can be considered trivial.
Under the in computer go more common rulesets this upper bound is simply
wrong. Unless we talk
361! seems like an attempt to estimate an upper bound on the number of
games where nothing is captured.
On Wed, Aug 9, 2017 at 2:34 PM, Gunnar Farnebäck
wrote:
> Except 361! (~10^768) couldn't plausibly be an estimate of the number of
> legal positions, since ignoring the
Except 361! (~10^768) couldn't plausibly be an estimate of the number of
legal positions, since ignoring the rules in that case gives the trivial
upper bound of 3^361 (~10^172).
More likely it is a very, very bad attempt at estimating the number of
games. Even with the extremely unsharp bound
On Mon, Aug 7, 2017 at 12:52 PM, Darren Cook wrote:
> > https://en.wikipedia.org/wiki/Brute-force_search explains it as
> > "systematically enumerating all possible candidates for the
> > solution".
> >
> > There is nothing systematic about the pseudo random variation
> >
> https://en.wikipedia.org/wiki/Brute-force_search explains it as
> "systematically enumerating all possible candidates for the
> solution".
>
> There is nothing systematic about the pseudo random variation
> selection in MCTS;
More semantics, but as it is pseudo-random, isn't that systematic?
BTW, if anyone is wondering about the "roughly" part,
361! = 1.438 * 10^768 while L19 = 2.081681994 * 10^170.
On Sun, Aug 06, 2017 at 07:14:42PM -0700, David Doshay wrote:
> Yes, that zeroth order number (the one you get to without any thinking about
> how the game’s rules affect the
Yes, that zeroth order number (the one you get to without any thinking about
how the game’s rules affect the calculation) is outdated since early last year
when this result gave us the exact number of legal board positions:
https://tromp.github.io/go/legal.html
On 08/06/2017 04:39 PM, Vincent Richard wrote:
No, simply because there are way to many possibilities in the game,
roughly (19x19)!
Can we lay this particular number to rest? Not that "possibilities in
the game" is very well defined (what does it even mean?) but the number
of permutations of
gt; *Sent:* Sunday, August 6, 2017 2:52 PM
> *To:* Brian Sheppard <sheppar...@aol.com>
> *Cc:* computer-go <computer-go@computer-go.org>
>
> *Subject:* Re: [Computer-go] Alphago and solving Go
>
>
>
> This is semantics. Yes, in the limit of infinite time, it is brute
PM
To: Brian Sheppard <sheppar...@aol.com>
Cc: computer-go <computer-go@computer-go.org>
Subject: Re: [Computer-go] Alphago and solving Go
This is semantics. Yes, in the limit of infinite time, it is brute-force.
Meanwhile, in the real world, AlphaGo chooses to balance its finite
Aren't you a little bit too old now to be troling this list?
On Sun, Aug 6, 2017 at 3:49 PM, Cai Gengyang wrote:
> Is Alphago brute force search?
> Is it possible to solve Go for 19x19 ?
> And what does perfect play in Go look like?
> How far are current top pros from
[mailto:lightvec...@gmail.com]
Sent: Sunday, August 6, 2017 2:54 PM
To: Brian Sheppard <sheppar...@aol.com>; computer-go@computer-go.org
Cc: Steven Clark <steven.p.cl...@gmail.com>
Subject: Re: [Computer-go] Alphago and solving Go
Saying in an unqualified way that AlphaGo is brute fo
From: Steven Clark [mailto:steven.p.cl...@gmail.com
<mailto:steven.p.cl...@gmail.com> ]
Sent: Sunday, August 6, 2017 1:14 PM
To: Brian Sheppard <sheppar...@aol.com <mailto:sheppar...@aol.com> >;
computer-go <computer-go@computer-go.org <mailto:computer-go@computer-go.org>
12 errors
> per game, but you can reasonably get other numbers based on your model.
>
>
>
> Best,
>
> Brian
>
>
>
> *From:* Computer-go [mailto:computer-go-boun...@computer-go.org] *On
> Behalf Of *Cai Gengyang
> *Sent:* Sunday, August 6, 2017 9:49 AM
truly excels. (AlphaGo also excels at whole board evaluation, but
> that is a separate topic.)
>
>
>
>
>
> *From:* Steven Clark [mailto:steven.p.cl...@gmail.com]
> *Sent:* Sunday, August 6, 2017 1:14 PM
> *To:* Brian Sheppard <sheppar...@aol.com>; computer-go <
> compu
mputer-go
<computer-go@computer-go.org>
Subject: Re: [Computer-go] Alphago and solving Go
Why do you say AlphaGo is brute-force? Brute force is defined as: "In computer
science, brute-force search or exhaustive search, also known as generate and
test, is a very general problem-
half Of *Cai Gengyang
> *Sent:* Sunday, August 6, 2017 9:49 AM
> *To:* computer-go@computer-go.org
> *Subject:* [Computer-go] Alphago and solving Go
>
>
>
> Is Alphago brute force search?
>
> Is it possible to solve Go for 19x19 ?
>
> And what does perfect play in Go loo
errors per game, but you can
reasonably get other numbers based on your model.
Best,
Brian
From: Computer-go [mailto:computer-go-boun...@computer-go.org] On Behalf Of Cai
Gengyang
Sent: Sunday, August 6, 2017 9:49 AM
To: computer-go@computer-go.org
Subject: [Computer-go] Alphago
Actually, a better Go-God for handicap games would probably be one that
ignores score margin as long as it's behind and simply maximizes the
entropy measure for the lowest-entropy proof tree that proves that Black is
winning. (And only counts the entropy for the black moves, not the white
moves in
*Is Alphago **brute **force search? *
No, simply because there are way to many possibilities in the game,
roughly (19x19)!
Alphago tries to consider the game like the human do: it evaluates the
board from only a limited set of moves, based on its "instinct". This
instinct is generated from
* A little but not really.
* No, and as far as we can tell, never. Even 7x7 is not rigorously solved.
* Unknown.
* Against Go-God (plays move that maximizes score margin, breaking ties by
some measure of the entropy needed to build the proof tree relative to a
human-pro-level policy net), I guess
No (have you read any of the papers about it?)
No
We don't know
We don't know (pros used to claim they were 2-3 stones away from God, but
AlphaGo might have encouraged them to be a bit more humble)
On Sun, Aug 6, 2017 at 9:49 AM, Cai Gengyang wrote:
> Is Alphago brute
No, it is not possible to solve go on a 19x19 board. The closest we have is
5x5, I believe. We have a pretty good idea what optimal play looks like on
7x7. The difficulty of finding optimal play on large boards is
unfathomable.
Álvaro.
On Sun, Aug 6, 2017 at 10:06 AM Cai Gengyang
Is Alphago brute force search?
Is it possible to solve Go for 19x19 ?
And what does perfect play in Go look like?
How far are current top pros from perfect play?
Gengyang
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