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]](../../diagrams/38/0e89b40ff0f107ff50a0dd663d28a571.png)
Star
The infinitesimal, STAR (*), is like a dame in go. Each player can move to 0. The first player wins in a Star.
![[Diagram]](../../diagrams/10/216651e4dcbc3191c270b9118ebda318.png)
Black moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/17/a138cbf2252b6db23e4cc347bcdb51a4.png)
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]](../../diagrams/18/a3e2f90500a977590f84d6c67519e886.png)
Down
![[Diagram]](../../diagrams/45/0a46c4c78b455a50e92f643808f17152.png)
White moves to 0
After
each player has two moves, for 0.
![[Diagram]](../../diagrams/25/bb436e10484c192c1d7af235c049b6a9.png)
Black moves to *
After
each player can move to 0.
![[Diagram]](../../diagrams/47/58e87631a44794b198395bad39fa32d3.png)
White moves to 0.
![[Diagram]](../../diagrams/21/e7faa82f9e0de08280c864902c09fda1.png)
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.
![[Diagram]](../../diagrams/4/31e868af9bef94cb33df5bc608b8d2ba.png)
*2
![[Diagram]](../../diagrams/47/a5c8a8b484effdf89abe15df480f67d7.png)
Black moves to 0
This is a reversal sequence.
forces
.
![[Diagram]](../../diagrams/32/affc2042d7666f26e8e62eaf5791ddf1.png)
Zero
and
are miai. Now neither player can move.
![[Diagram]](../../diagrams/38/5e08b3faaed7091f996440c7c4fe850f.png)
Zero
Or this position could be reached, where each player has one move, also a zero.
![[Diagram]](../../diagrams/1/a0cd4fce201086fc9b7c3bf5ae0d71b4.png)
Black moves to *
Another reversal.
Now each player can move to 0.
![[Diagram]](../../diagrams/52/a2aeb9c56bcb34f01603c6a2daed9ae4.png)
White moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/17/d0bd5c92c4e51d2baecc2a848949eba3.png)
Black moves to 0
After
each player has one move.
(Note that in this * the players have different moves.)
![[Diagram]](../../diagrams/22/3a66ab990b8d1bdbc7d123ba79bd3a0d.png)
White moves to 0
It may not be obvious that this is a zero. There are some variations in the remaining play.
![[Diagram]](../../diagrams/32/1c7abee54fe425da6d98f011bca7c557.png)
Zero, var. 1
After
each player has one move, still a zero.
(OC, with White to play the play could go
-
.)
![[Diagram]](../../diagrams/21/bb1edc333303e05dc166a29a0d66f623.png)
Zero, var. 2
After
each player has one move, still zero.
(And the play could also go
-
.)
![[Diagram]](../../diagrams/49/5df02ee58ed4f6b0796a6001e85228b9.png)
White moves to *
After
each player can move to 0.
![[Diagram]](../../diagrams/38/ceb40ec3731ab1636f57971d520ac5d9.png)
Black moves to 0
After
each player has one move, for zero.
![[Diagram]](../../diagrams/28/ad646bb4f9fac481520169711b1019c8.png)
White moves to 0
After
each player has one move.
^* = {0,* | 0}. As the name suggests, it is equivalent to the sum of ^ and *.
![[Diagram]](../../diagrams/27/c3688cd8aeb0c8301fe97a29b58bb574.png)
^*
![[Diagram]](../../diagrams/49/8572a60003f0e6d2a3af0ce549d93993.png)
White moves to 0 (1)
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/49/59d8e1f0cf5c5e621c2e3f7b3c78b0e0.png)
White moves to 0 (2)
After
each player has one move.
![[Diagram]](../../diagrams/37/385f2209c96f8e16f708fa3151ace6b6.png)
Black moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/1/639f53600cade76d028b67a7206ed6f2.png)
Black moves to *
leaves a * in the top left corner.