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/6/204b188eadd70d98da49b660f533902a.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/42/d8dd9b2c68a7386e8858e63507d1cf63.png)
Black moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/40/cde5083b76374ac8c2e4d5dba76993bb.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/13/2918ee71fd08b7441eea773ea43b7730.png)
Down
![[Diagram]](../../diagrams/46/ba41386ee84848187729bbdcd8db1b52.png)
White moves to 0
After
each player has two moves, for 0.
![[Diagram]](../../diagrams/27/8b340e0ef79fd80e6d16a7ba1718ad91.png)
Black moves to *
After
each player can move to 0.
![[Diagram]](../../diagrams/29/593e5328830e4c70a3fdc38cf984879f.png)
White moves to 0.
![[Diagram]](../../diagrams/36/e827d949981190659d90f4faf0c5fc7a.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/14/48ced094a4fd71d19c0c0ac4bddc7d27.png)
*2
![[Diagram]](../../diagrams/39/4abb779c13173f0e124413cb0f6d51c4.png)
Black moves to 0
This is a reversal sequence.
forces
.
![[Diagram]](../../diagrams/49/73f4ad17b180b972197e55d2a5ea904c.png)
Zero
and
are miai. Now neither player can move.
![[Diagram]](../../diagrams/1/becdded46d9c6e7cc63367ac246472ac.png)
Zero
Or this position could be reached, where each player has one move, also a zero.
![[Diagram]](../../diagrams/35/4dc974d7e9eedd1cf92eadbf062d7d34.png)
Black moves to *
Another reversal.
Now each player can move to 0.
![[Diagram]](../../diagrams/9/33ed42398d73415b910030df338aadb0.png)
White moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/23/a3e7cc67a63dfb8602840f812da401c7.png)
Black moves to 0
After
each player has one move.
(Note that in this * the players have different moves.)
![[Diagram]](../../diagrams/36/0b11bb002f1ab3414015cce75f800be2.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/47/ab7448ad0bc646071d674120a960f15a.png)
Zero, var. 1
After
each player has one move, still a zero.
(OC, with White to play the play could go
-
.)
![[Diagram]](../../diagrams/51/2c3f0912800dc225c92f76a8b94cf196.png)
Zero, var. 2
After
each player has one move, still zero.
(And the play could also go
-
.)
![[Diagram]](../../diagrams/37/05445f7027f76ddf892e2546246ff383.png)
White moves to *
After
each player can move to 0.
![[Diagram]](../../diagrams/21/0b5a800e05dc6df1f2eb4c8476169212.png)
Black moves to 0
After
each player has one move, for zero.
![[Diagram]](../../diagrams/20/07e5d59b70e2c9b0481c4f06bd893e93.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/6/4f83c4988de6626050e8241e3135dd4d.png)
^*
![[Diagram]](../../diagrams/30/760640f1da689f9a91fba676700ddfe7.png)
White moves to 0 (1)
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/13/7b73837a463a6d558df2f49098edbc37.png)
White moves to 0 (2)
After
each player has one move.
![[Diagram]](../../diagrams/6/60569e6a98bf04b793f36566243be31e.png)
Black moves to 0
After
each player has one move, for a zero.
![[Diagram]](../../diagrams/5/189acdf66d3361730f14931c470fddd3.png)
Black moves to *
leaves a * in the top left corner.