[Computer-go] Alphago and solving Go

Erik van der Werf erikvanderwerf at gmail.com
Wed Aug 9 06:29:25 PDT 2017


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 <gunnar at lysator.liu.se>
wrote:

> 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 given in
> https://tromp.github.io/go/gostate.pdf
>
> 10^(10^48) < number of games < 10^(10^171)
>
> the 361! estimate comes nowhere close to that interval.
>
> /Gunnar
>
> On 08/07/2017 04:14 AM, David Doshay wrote:
>
>> 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 about how the game’s rules affect the calculation) is outdated since early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
>>
>> So, a complete game tree for 19x19 Go would contain about 2.08 * 10^170
>> unique nodes (see the paper for all 171 digits) but some number of
>> duplicates of those nodes for the different paths to each legal position.
>>
>> In an unfortunate bit of timing, it seems that many people missed this
>> result because of the Alpha Go news.
>>
>> Cheers,
>> David G Doshay
>>
>> ddoshay at mac.com <mailto:ddoshay at mac.com>
>>
>>
>>
>>
>>
>> On 6, Aug 2017, at 3:17 PM, Gunnar Farnebäck <gunnar at lysator.liu.se
>>> <mailto:gunnar at lysator.liu.se>> wrote:
>>>
>>> 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 19x19 points has no meaningful connection to the game of go
>>> at all, not even "roughly".
>>>
>>> /Gunnar
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>>
>>
>>
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