Infinitesimals in Gone

   

Infinitesimals occur often in no-capture go, aka gone, a variant of go in which passes, captures, and suicide are illegal, and the player without a move loses.

Star (*)

[Diagram]

Star

The infinitesimal, STAR (*), is like a dame in go. Each player can move to 0. The first player wins in a Star.



[Diagram]

Black moves to 0

After B1 each player has one move, for a zero.

[Diagram]

White moves to 0



Down (v)

Down (v) is a negative infinitesimal (White wins). White can move to 0, Black can move to *.

The opposite of Down is Up (^).

[Diagram]

Down



[Diagram]

White moves to 0

After W1 each player has two moves, for 0.

[Diagram]

Black moves to *

After B1 each player can move to 0.

[Diagram]

White moves to 0.



[Diagram]

Black moves to 0.

After B1 each player has one move, for a zero.

Star-2 (*2)

Star-2 is like a Nim heap of size two. Each player can move to * or 0.

[Diagram]

*2



[Diagram]

Black moves to 0

This is a reversal sequence. W2 forces B3.



[Diagram]

Zero

W1 and B2 are miai. Now neither player can move.



[Diagram]

Zero

Or this position could be reached, where each player has one move, also a zero.

[Diagram]

Black moves to *

Another reversal.

Now each player can move to 0.

[Diagram]

White moves to 0

After W1 each player has one move, for a zero.

[Diagram]

Black moves to 0

After B1 each player has one move.

(Note that in this * the players have different moves.)

[Diagram]

White moves to 0

It may not be obvious that this is a zero. There are some variations in the remaining play.

[Diagram]

Zero, var. 1

After W2 each player has one move, still a zero.

(OC, with White to play the play could go W2 - B1.)

[Diagram]

Zero, var. 2

After W2 each player has one move, still zero.

(And the play could also go W2 - B1.)

[Diagram]

White moves to *

After W3 each player can move to 0.

[Diagram]

Black moves to 0

After B1 each player has one move, for zero.

[Diagram]

White moves to 0

After W1 each player has one move.

Up-star (^*)

^* = {0,* | 0}. As the name suggests, it is equivalent to the sum of ^ and *.

[Diagram]

^*



[Diagram]

White moves to 0 (1)

After W1 each player has one move, for a zero.

[Diagram]

White moves to 0 (2)

After W1 each player has one move.

[Diagram]

Black moves to 0

After B1 each player has one move, for a zero.

[Diagram]

Black moves to *

B1 leaves a * in the top left corner.



This is a copy of the living page "Infinitesimals in Gone" at Sensei's Library.
(OC) 2012 the Authors, published under the OpenContent License V1.0.
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