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Offline phillip1882
 Post subject: logarithmic go
Post #1 Posted: Tue Feb 03, 2015 7:44 pm 
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for each area, take the logarithm and add.
exe:
Click Here To Show Diagram Code
[go]$$c scoring
$$ ---------------------------------------
$$ | . O X . X O . . . . O O O X . . . . . |
$$ | O . X X X O . . . . O X X X . . . . . |
$$ | X X X X X O . . . . O X . . . . . . . |
$$ | O O O O O O . . . , . O X . . , . . . |
$$ | . O X O X O O . . . . O X . . . . X X |
$$ | O O X X X X O . . . . O X X X X X O X |
$$ | X X X . . X O . . . . O X O O X O O O |
$$ | . . . . . X O . . . O X X O . O . . . |
$$ | . . . . . . X O . . O X O O O . . O O |
$$ | . . . , . . X O O O O O . . . O O O X |
$$ | . . X X X X X O X O O X O O O O X X X |
$$ | . . X O O O X X X X X X O X X O X X . |
$$ | . . X X X O O X . . . X X X O O O X . |
$$ | . . X O X O O X . . . X O O X X X X . |
$$ | . . X O O O . O X X X O O X X . . . . |
$$ | . . X O O . . O O O O O . O X X . . . |
$$ | . . . X O . . . . . . . . O O X . . . |
$$ | . . . X X O O O . . . . . . O X X . . |
$$ | . . . . X X X O . . . . . . O O X . . |
$$ ---------------------------------------[/go]



black top left: log(11)
black side: log(99)
black top right corner: log(64)
black bottom right corner: log(36)
black total score = 6.399

white top left: log(3)
white mid top and right side: log(106)
white bottom side: log(58)
white komi: log(6.5)
white total score = 5.079
black wins.

thoughts?
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Offline emeraldemon
 Post subject: Re: logarithmic go
Post #2 Posted: Tue Feb 03, 2015 8:15 pm 
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Well it would be to each players' advantage to create as many small living groups as possible. In the example above each player could probably do better by splitting those big spaces up rather than connecting, for example white's bottom territory:

Click Here To Show Diagram Code
[go]$$c scoring
$$ ---------------------------------------
$$ | . O X . X O . . . . O O O X . . . . . |
$$ | O . X X X O . . . . O X X X . . . . . |
$$ | X X X X X O . . . . O X . . . . . . . |
$$ | O O O O O O . . . , . O X . . , . . . |
$$ | . O X O X O O . . . . O X . . . . X X |
$$ | O O X X X X O . . . . O X X X X X O X |
$$ | X X X . . X O . . . . O X O O X O O O |
$$ | . . . . . X O . . . O X X O . O . . . |
$$ | . . . . . . X O . . O X O O O . . O O |
$$ | . . . , . . X O O O O O . . . O O O X |
$$ | . . X X X X X O X O O X O O O O X X X |
$$ | . . X O O O X X X X X X O X X O X X . |
$$ | . . X X X O O X . . . X X X O O O X . |
$$ | . . X O X O O X . . . X O O X X X X . |
$$ | . . X O O O . O X X X O O X X . . . . |
$$ | . . X O O . O O . O O O . O X X . . . |
$$ | . . . X O . . O . O . . . O O X . . . |
$$ | . . . X X O O O . O . . . . O X X . . |
$$ | . . . . X X X O . O . . . . O O X . . |
$$ ---------------------------------------[/go]


now white has log(26) + log(28) = 6.59, compared with log(58) = 4.06 , so giving those four points up was a pretty big gain. There would be a huge incentive not to connect any stones unless absolutely necessary. (note also that the move to live doesn't cost anything in area territory)
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Offline DrStraw
 Post subject: Re: logarithmic go
Post #3 Posted: Wed Feb 04, 2015 4:29 am 
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And the point is?

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

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Offline phillip1882
 Post subject: Re: logarithmic go
Post #4 Posted: Wed Feb 04, 2015 11:13 am 
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dunno, just trying to think of a go variant that might be interesting.
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Offline Matti
 Post subject: Re: logarithmic go
Post #5 Posted: Thu Feb 05, 2015 3:22 am 
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If one plays inside own territory to split it into two would you add the logarithms of the sizes of the territories?
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Offline DrStraw
 Post subject: Re: logarithmic go
Post #6 Posted: Thu Feb 05, 2015 7:23 am 
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There is something intrinsically wrong with these numbers:

Click Here To Show Diagram Code
[go]$$ 0 points
$$ | X X X X X X X X X|
$$ | X . X . X . X . X|
$$ | X X X X X X X X X|[/go]


Click Here To Show Diagram Code
[go]$$ 1.098 points
$$ | X X X X X X X X X|
$$ | X . . . X . X . X|
$$ | X X X X X X X X X|[/go]


Click Here To Show Diagram Code
[go]$$ 1.386 points
$$ | X X X X X X X X X|
$$ | X . . X . . X . X|
$$ | X X X X X X X X X|[/go]


Click Here To Show Diagram Code
[go]$$ 1.609 points
$$ | X X X X X X X X X|
$$ | X . X . . . . . X|
$$ | X X X X X X X X X|[/go]


Click Here To Show Diagram Code
[go]$$ 1.946 points
$$ | X X X X X X X X X|
$$ | X . . . . . . . X|
$$ | X X X X X X X X X|[/go]


Click Here To Show Diagram Code
[go]$$ 2.197 points
$$ | X X X X X X X X X|
$$ | X . . . X . . . X|
$$ | X X X X X X X X X|[/go]

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).
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Offline HermanHiddema
 Post subject: Re: logarithmic go
Post #7 Posted: Thu Feb 05, 2015 7:34 am 
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@DrStraw: The original post uses area, not territory, so each of your examples would score log(27).
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Offline DrStraw
 Post subject: Re: logarithmic go
Post #8 Posted: Thu Feb 05, 2015 8:07 am 
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HermanHiddema wrote:
@DrStraw: The original post uses area, not territory, so each of your examples would score log(27).


Oh! I guess that just makes it even more confusing. I am just not used to thinking in area terms.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).
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Offline skydyr
 Post subject: Re: logarithmic go
Post #9 Posted: Thu Feb 05, 2015 8:38 am 
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I imagine that for most players, first they would play a game, and then they would be surprised at the result.

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Offline Matti
 Post subject: Re: logarithmic go
Post #10 Posted: Tue Feb 10, 2015 7:11 am 
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Do you allow suicide? One might decide to suicide an own group to unite several opponents groups.

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Offline uPWarrior
 Post subject: Re: logarithmic go
Post #11 Posted: Tue Feb 10, 2015 10:03 am 
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Click Here To Show Diagram Code
[go]$$c
$$ ---------------------------------------
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X O . . . . , . . . . . , . . . |
$$ | X X X X O . . . . . . . . . . . . . . |
$$ | O O O O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . O O O O O |
$$ | . . . , . . . . . , . . . O X X X X X |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ ---------------------------------------[/go]


Black's optimal move is to pass, as 2*log(20) > log(321). White can't win.

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Offline cyclops
 Post subject: Re: logarithmic go
Post #12 Posted: Thu Jun 04, 2015 3:21 pm 
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Simply multipling gives the same result but doesn't need a calculator.

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I think I am so I think I am.
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Offline Pio2001
 Post subject: Re: logarithmic go
Post #13 Posted: Fri Jun 05, 2015 11:15 am 
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So it seems that the goal would be to get the most possible groups.

But what do you call a "group" ?
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