Re: [Computer-go] Alphago and solving Go

[John Tromp]

> 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 theorem explains, the difference from your
suggestion is due to the average position having only 361/3 empty points
available for play.

-John
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Re: [Computer-go] Alphago and solving Go

[Robert Jasiek]

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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Re: [Computer-go] Alphago and solving Go

[uurtamo .]

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 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 722^#positions? Since adding a black or a
> white stone is something fundamentally different?
>
> 2017-08-09 20:50 GMT+02:00 John Tromp :
>
>> > 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, stones,
>> liberties, strings, positions, sets of previous positions.
>>
>> > I'm actually surprised that this "absurd" to you...
>>
>> I said that referring to a board configuration together with the set
>> of all previously occurring board configurations (and turn to move) as
>> "position" is absurd.
>> We need a simple word to denote a board configuration, and "position" fits
>> that requirement. A good word for all the relevant historical
>> information leading up to a position is "situation".
>>
>> -John
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>
>
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