UP

For “Up” as a direction on the board see Up and down.

In Combinatorial Game Theory, UP is the name of an infinitesimal, also written ↑. UP is defined as

``uarr = { 0 | ast }``

Left (Black) can play to ``0``, while Right (White) can play to ``ast`` (STAR). UP is positive, favoring Left, who gets the last play, no matter who goes first. The opposite of UP is DOWN, also written ↓.

Some plays with a miai value of 1 chill to UP. (See Chilled Go). Here is an example:

2 + UP  

This position chills to 2↑ (shorthand for 2 + ↑). Black can get the last play locally no matter who plays first.

[edit]

See also

• Go infinitesimals — On the significance of infinitesimals in go
• Corridor infinitesimals — On the (infinitesimal) chilled values of corridors
• Playing infinitesimals — On playing positions of infinitesimal value in the correct order

Notes and discussion

Robert Pauli:
How about this position for exactly UP?

UP ?  

    0
   / \
  1  -1
     / \
    0  -2

Including the white eye, however, is cheating, I know.

Reply:

OC, it is a chilled up.