Tiny

    Keywords: Theory

A tiny is an infinitesimal in combinatorial game theory. In go terms, it is a sente for White. It is positive, favoring Black, because Black can win it by playing the reverse sente if he plays first or by answering the sente if White plays first. It has an atomic weight of 0. The opposite of a tiny is a miny.

Example: In chilled go, this is a tiny.

[Diagram]
Tiny  



[Diagram]
White first  

This is a 1 point sente for White. The local result is +4.

[Diagram]
Black first  

If Black plays the reverse sente, the local result is +5.

In chilled go, however, each play costs one point, and the local result remains +4. The value of the original position in chilled go is thus +4 plus a tiny. Customarily we ignore the local score and just call this a tiny.

Here is the game tree of this tiny. ( / indicates a Black play, \ indicates a White play.)

                   T
                  / \
                 0   U
                    / \
                   0  -2

Because of the -2 result it is called a tiny-2. It is also written as a plus-sign with a subscript: ``+_2`` in this case, or ``+_G = {0" || "0|-G}`` for an arbitrary game ``G``.


Tiny last edited by PJTraill on January 23, 2019 - 01:53
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