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Easy capture game problem
http://www.lifein19x19.com/viewtopic.php?f=11&t=11857
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Author:  Bill Spight [ Wed May 20, 2015 2:28 pm ]
Post subject:  Easy capture game problem

The object of the capture game is to capture one or more of the opponent's stones. It is a form of no pass go, so eventually someone will win.

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X . . |
$$ | O X . O . |
$$ -----------[/go]


Enjoy!

Author:  skydyr [ Wed May 20, 2015 2:37 pm ]
Post subject:  Re: Easy capture game problem

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X 3 |
$$ | O X X 2 1 |
$$ | O X . O . |
$$ -----------[/go]


Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X 3 1 |
$$ | O X . O 2 |
$$ -----------[/go]


Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X 3 1 |
$$ | O X 2 O . |
$$ -----------[/go]

Author:  Pio2001 [ Thu May 21, 2015 4:19 pm ]
Post subject:  Re: Easy capture game problem

Nice one :)

I agree with skydyr's answer.

Author:  Bill Spight [ Thu May 21, 2015 7:26 pm ]
Post subject:  Re: Easy capture game problem

Yup. Skydyr solved it. :)

For more analysis, see below.

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X . . |
$$ | O X . O . |
$$ -----------[/go]


The top left is seki in the capture game. In regular go White is dead. It takes Capture-4 or more for Black to be able to kill White, since she has to sacrifice 3 stones in order to make the capture. (As the number of stones to capture increases, the capture game gets more like regular go.)

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X 3 |
$$ | O X X 2 1 |
$$ | O X . O . |
$$ -----------[/go]


:w4: resigns.

The bottom right after :w2: is a seki, both in regular go and the capture game. After :b3: Black is dead in regular go (except for being able to capture White in the top left, OC ;)), but there is still a seki in the capture game, because White would have to sacrifice 6 stones to kill Black.

After :b3: with these two sekis on the board the score is 0, but in no pass games 0 is a loss for the player with the move, so White loses.

The position after :w2: also has a score.

Click Here To Show Diagram Code
[go]$$Bc Black +1
$$ ----------
$$ | X . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X O X |
$$ | O X . O . |
$$ -----------[/go]


White to play loses, OC, but Black to play has a move. This position is worth 1 move for Black. Black's move, OC, is in the eye at E-03. In the Capture Game that is one point of Black territory in the seki. That is no accident.

Since this position has a score, the players could agree to stop play and count the score instead of playing the game out. They would find that Black wins by 1 point (move).

Now, it is a little known fact that no pass go can be scored using territory scoring. It is not true that in each form of no pass go one point of territory is equivalent to one move. However, that is true, with some exceptions, for the various forms of the capture game.

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ----------
$$ | O . O O X |
$$ | . O O X X |
$$ | O O X X . |
$$ | O X X O X |
$$ | O X . O . |
$$ -----------[/go]


In Capture-7, for instance, Black cannot afford to fill the point at E-03. It is not a point of territory in the seki. (Sound familiar? ;))

Territory is an emergent property of no pass go. :D

Furthermore, as it becomes necessary to capture a number of stones to win capture go, it becomes apparent that -- again, with some exceptions --, one captured stone is also worth 1 point. (Sound familiar? :)) If you allow a player, instead of playing a stone on the board, to hand over a stone as a captive, then the correspondence is exact. :)

Since the concept of territory, as well as that of dead and captured stones as points, emerges naturally in Capture Go, it is a good way to introduce beginners to go with territory scoring. :)

It is also quite possible that a game like capture go was a precursor of go. :)

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