Infinitesimals in Gone

Star  

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

Black moves to 0  

After each player has one move, for a zero.

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 (^).

White moves to 0  

After each player has two moves, for 0.

Black moves to *  

After each player can move to 0.

Black moves to 0.  

After 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.

Black moves to 0  

This is a reversal sequence. forces .

Zero  

and are miai. Now neither player can move.

Zero  

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

Black moves to *  

Another reversal.

Now each player can move to 0.

White moves to 0  

After each player has one move, for a zero.

Black moves to 0  

After each player has one move.

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

White moves to 0  

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

Zero, var. 1  

After each player has one move, still a zero.

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

Zero, var. 2  

After each player has one move, still zero.

(And the play could also go - .)

White moves to *  

After each player can move to 0.

Black moves to 0  

After each player has one move, for zero.

White moves to 0  

After each player has one move.

Up-star (^*)

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

White moves to 0 (1)  

After each player has one move, for a zero.

White moves to 0 (2)  

After each player has one move.

Black moves to 0  

After each player has one move, for a zero.

Black moves to *  

leaves a * in the top left corner.