17-
lap...@tuxfamily.org
compute that 17- is a win for the first player.
An article will follow in the next weeks, and an improved Glop in the next
months.
In Glop-notation :
we computed that 0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.0.0.AB.}]! is losing
First moves :
0.0.0.0.0.0.0.0.2.}]0.0.0.0.0.0.0.0.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.AB.}0.0.0.2.AB.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.0.AB.CD.}CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.0.A.BC.}BC.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.0.CD.}AB.CD.}]! -----> 0.0.0.0.0.0.0.0.AB.}2AB.}]0.0.0.0.0.0.0.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.1a1a.AB.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.1a1a.A.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.AB.CD.}0.CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.A.BC.}0.BC.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.0.CD.}0.AB.CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.0.0.AB.}0.C.}AB.C.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.AB.CD.}0.0.CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.BC.}0.A.BC.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.0.CD.}0.0.AB.CD.}]! -----> 0.0.0.0.0.0.0.0.AB.}0.0.AB.}]0.0.0.0.A.}0.A.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.AB.CD.}0.0.0.CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.0.BC.}A.BC.}]!
0.0.0.0.0.0.0.0.AB.}0.0.0.0.CD.}0.0.0.AB.CD.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.AB.}0.0.0.2.AB.}]!
0.0.0.0.0.0.0.0.A.}0.0.0.0.0.0.0.1aAa.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.0.1A.}]!
0.0.0.0.0.0.0.0.}]0.0.0.0.0.0.0.A.}0.A.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.0.0.0.}]12.}]!
0.0.0.0.0.0.0.0.}]0.0.0.0.0.0.A.}0.0.A.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.AB.}0.0.C.}0.AB.C.}]!
0.0.0.0.0.0.0.0.}]0.0.0.0.0.A.}0.0.0.A.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.AB.}0.0.0.C.}AB.C.}]!
0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.0.0.A.}]! -----> 0.0.0.0.0.0.0.0.}]0.0.0.0.A.}0.0.1a1a.A.}]!
--
Julien Lemoine & Simon Viennot
Dan Hoey
> Using Glop's new abilities for misere computation, we just managed to
> compute that 17- is a win for the first player.
Congratulations!
Dan
Jeff Peltier
Did you use some sort of algebra for sum of distinct lands? or sum with nimbers?
Congrats!
--
Jeff
--
Jean-François
Dan Hoey
> Using Glop's new abilities for misere computation, we just managed to
> compute that 17- is a win for the first player.
I hope the first player has a strategy that is isomorphic to an
11- strategy for the first few moves. I don't know how far you are
from showing that the first player wins in misère Sprouts when the
remainder (mod 6) is zero, four, or five, except that the first player
wins the one-spot game and loses the four-spot game.
Dan
lap...@tuxfamily.org
>
> Did you use some sort of algebra for sum of distinct lands? or sum with
> nimbers?
The main idea is to replace a land by what Conway calls a "reduced game"
in ONAG p 141.
A "reduced game" is like what we called "canonical game tree" in our
article about surfaces, in which you delete the reversible moves.
For example, Glop gives :
0.0.}]! ~ {2} ("2+" with Conway's notation)
From :
0.0.AB.}AB.}]! ~ {1,{2}}
0.1a1a.}]! ~ 0
0.AB.}0.AB.}]! ~ 0
We deduce :
0.0.0.}]! ~ {0,{1,{2}}}
and {0,{1,{2}}} ~ 1 (reversible move)
so 0.0.0.}]! ~ 1
So, we began to compute these "reduced games" for all the lands that are
in the game tree of the 6-spot game. Then, in the main computation, each
time we met a position with a land we already knew, we replaced this land
by its "reduced game".
More details with the article coming soon.
--
Julien Lemoine
Jeff Peltier
I was wondering how different positions in Sprouts games are from the general games born on day-n.
Did you look in your database issued from the 6-Spots game, if you get for example all 22 reduced games born on day-4 (I don't remember to have met 3+ in my search by hand, but then I don't see a good reason for it not to appear)?
I will wait for your article for getting more details about your ways...
--
Jeff
--
Jean-François
lap...@tuxfamily.org
"Jeff Peltier" <jfpe...@gmail.com> a écrit :
> I was wondering how different positions in Sprouts games are from the
> general games born on day-n.
>
> Did you look in your database issued from the 6-Spots game, if you
> get for example all 22 reduced games born on day-4 (I don't remember
> to have met 3+ in my search by hand, but then I don't see a good
> reason for it not to appear)?
3+ is in the database, for example with ABC.}ABD.}CEF.}DEF.}]! or with
ABCDEFGH.}ABCDEFGH.}]!
But only 16 reduced games born on day-4 are in the database issued from
the 6-spot game.
The missing games are (in Conway notation) :
2++ ; 2+0 ; 2+2 ; 2+20 ; 2+21 ; 2+32
--
Julien Lemoine
Josh Purinton
> But only 16 reduced games born on day-4 are in the database issued from
> the 6-spot game. The missing games are (in Conway notation) :
> 2++ ; 2+0 ; 2+2 ; 2+20 ; 2+21 ; 2+32
I didn't see one in the 6-spot game tree, but there is a *2+*2 in the
7-spot game tree. It's 2.A.}2A2B.}aBaCD.}C.D.}]!
lap...@tuxfamily.org
"Josh Purinton" <josh.p...@gmail.com> a écrit :
>> But only 16 reduced games born on day-4 are in the database issued from
>> the 6-spot game. The missing games are (in Conway notation) :
>> 2++ ; 2+0 ; 2+2 ; 2+20 ; 2+21 ; 2+32
>
> I didn't see one in the 6-spot game tree, but there is a *2+*2 in the
> 7-spot game tree. It's 2.A.}2A2B.}aBaCD.}C.D.}]!
I think there is a misunderstanding due to the multiple notations :
for Conway (p141 of ONAG), 2+2 means {2+;2}, ie a position with 2 sons : 2
and 2+. What he calls 2+ is the position with 1 son, which is 2.
But this is not what you call *2+*2 : *2+*2 has 2 sons, *2+*1=*3 and
*2+*0=*2, so this is what Conway calls 32.
You don't need the 7-spot game tree to find such a position : for example,
you have ABCD.EF.}ABCD.GH.}EF.}GH.}]! in the 4-spot game tree.
Do you agree with this, or did I miss something ?
--
Julien Lemoine
Josh Purinton
also says that ABCD.EF.}ABCD.GH.}EF.}GH.}]! = {*2,*3} = *2+*2. As you
say, there are many positions like this in the 6-spot database. I was
just searching the database incorrectly.
Josh Purinton
After discussing this with Jeff, I have a question.
Let G = ABCDEFGH.}ABCDEFGH.}]! I understand that Glop found that G =
3+ = {*3}. However, according to Aunt Beast, this is not the case. I
would like to resolve the discrepancy.
Let G' = ABCD.}ABCEFG.}DEFG.}]!. Note that G' is an option of G.
If G = {*3}, then G' = *3. Since *3 has a *0 option, G' must have an
option G'' such that G'' = *0. What is G'' in Glop notation?
lap...@tuxfamily.org
"Josh Purinton" <josh.p...@gmail.com> a écrit :
>> 3+ is in the database, for example with ABC.}ABD.}CEF.}DEF.}]! or with
>> ABCDEFGH.}ABCDEFGH.}]!
>
> After discussing this with Jeff, I have a question.
>
> Let G = ABCDEFGH.}ABCDEFGH.}]! I understand that Glop found that G =
> 3+ = {*3}. However, according to Aunt Beast, this is not the case. I
> would like to resolve the discrepancy.
>
> Let G' = ABCD.}ABCEFG.}DEFG.}]!. Note that G' is an option of G.
>
> If G = {*3}, then G' = *3. Since *3 has a *0 option, G' must have an
> option G'' such that G'' = *0. What is G'' in Glop notation?
You're right when you say that G' don't have an option G'' such that G'' =
*0.
But G' have the option G'' = ABC.}ABD.}CEF.}DEF.}]! = {*3}, so this is a
reversible move.
--
Julien Lemoine
Dan Hoey
> On Tue, Jan 20, 2009 at 10:24 AM, <lap...@tuxfamily.org> wrote:
>> 3+ is in the database, for example with ABC.}ABD.}CEF.}DEF.}]! or with ABCDEFGH.}ABCDEFGH.}]!
>
> After discussing this with Jeff, I have a question.
>
> Let G = ABCDEFGH.}ABCDEFGH.}]! I understand that Glop found that G =
> 3+ = {*3}. However, according to Aunt Beast, this is not the case. I
> would like to resolve the discrepancy.
>
> Let G' = ABCD.}ABCEFG.}DEFG.}]!. Note that G' is an option of G.
>
> If G = {*3}, then G' = *3.
That's where you go wrong. G' = *[3/(2/3210)(2/321)21], where I write
"/" instead of "+" in the compact Conway notation. That is to say,
G'={{*3}, {{*2},*3,*2,*1,*0}, {{*2},*3,*2,*1}, *2, *1}
G' is an option of G, but G' is not an option of the canonical form of
G. Instead, G' is a reducible option. That is to say, we may treat G
as if its only option is *3, because if anyone were to play G', the
the opponent could immediately play to the {*3} option of G'.
I haven't found out what position is the {*3} option of G' yet; my tools
for examining the Lemoine-Viennot database are somewhat primitive.
Dan
Josh Purinton
> You're right when you say that G' don't have an option G'' such that G'' =
> *0.
>
> But G' have the option G'' = ABC.}ABD.}CEF.}DEF.}]! = {*3}, so this is a
> reversible move.
Oh, of course. I understand now. Thanks again for the explanation.