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logarithmic go

https://lifein19x19.com/viewtopic.php?t=11434

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logarithmic go

Posted: Tue Feb 03, 2015 7:44 pm
by phillip1882
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?

Re: logarithmic go

Posted: Tue Feb 03, 2015 8:15 pm
by emeraldemon
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)

Re: logarithmic go

Posted: Wed Feb 04, 2015 4:29 am
by DrStraw
And the point is?

Re: logarithmic go

Posted: Wed Feb 04, 2015 11:13 am
by phillip1882
dunno, just trying to think of a go variant that might be interesting.

Re: logarithmic go

Posted: Thu Feb 05, 2015 3:22 am
by Matti
If one plays inside own territory to split it into two would you add the logarithms of the sizes of the territories?

Re: logarithmic go

Posted: Thu Feb 05, 2015 7:23 am
by DrStraw
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]

Re: logarithmic go

Posted: Thu Feb 05, 2015 7:34 am
by HermanHiddema
@DrStraw: The original post uses area, not territory, so each of your examples would score log(27).

Re: logarithmic go

Posted: Thu Feb 05, 2015 8:07 am
by DrStraw
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.

Re: logarithmic go

Posted: Thu Feb 05, 2015 8:38 am
by skydyr
I imagine that for most players, first they would play a game, and then they would be surprised at the result.

Re: logarithmic go

Posted: Tue Feb 10, 2015 7:11 am
by Matti
Do you allow suicide? One might decide to suicide an own group to unite several opponents groups.

Re: logarithmic go

Posted: Tue Feb 10, 2015 10:03 am
by uPWarrior
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.

Re: logarithmic go

Posted: Thu Jun 04, 2015 3:21 pm
by cyclops
Simply multipling gives the same result but doesn't need a calculator.

Re: logarithmic go

Posted: Fri Jun 05, 2015 11:15 am
by Pio2001
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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