# [Computer-go] Alphago and solving Go

uurtamo . uurtamo at gmail.com
Wed Aug 9 22:02:04 PDT 2017

```It's trivial, dude.

On Aug 9, 2017 8:35 AM, "Marc Landgraf" <mahrgell87 at gmail.com> 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 trivial.
>
> Under the in computer go more common rulesets this upper bound is simply
> wrong. Unless we talk about simply the visual aspect, but then this has
> absolutely nothing to do with the discussion abour solving games.
>
> 2017-08-09 14:34 GMT+02:00 Gunnar Farnebäck <gunnar at lysator.liu.se>:
>
>> 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 about how the game’s rules affect the calculation) is outdated since early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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>
>
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