Infinitesimals Optimal Play

Path: <= CGT path =>
    Keywords: EndGame

This page describes the optimal play for Black when the only go infinitesimals around are *, , , and Tinies and Minies. For White, Minies and Tinies switch roles with each other. This page may not apply if there are kos or future kos on the board. It also describes optimal play in go numbers. These kinds of endgames are common.

[Diagram]
Miny-3  

Minies (which are sente) should be played first, starting with those whose threats are largest.

[Diagram]
2.5 point gote  

It is better to threaten an ``n`` point gote than to play on an ``n`` point gote.

[Diagram]
{Miny-1|0}  

Next, attack longer corridors ending in minies, starting with corridors ending in smallest miny.

[Diagram]
{Miny-1|0||0}  

Longer corridors are attacked after shorter corridors if minies at the end are equal.

[Diagram]
{Miny-2|0}  
[Diagram]
{Miny-2|0||0}  
[Diagram]
vvv  

Attacks on corridors ending in STARs (simple 1 point gote by miai value) are all worth the same.

[Diagram]
*  

Stars are next. Caveat: Even number of stars add to zero and should be ignored.

Patrick Traill: Is that ‘may be ignored’ or ‘should be ignored’? I.e. is anything lost by playing them?

Bill: Something may be lost. For instance, ↑ + * + * = ↑ > 0, so Black wins by taking the ↑. If Black takes one of the *s, he leaves ↑*, which is confused with 0, so White wins by playing in the ↑ to * + * = 0. See example below.

[Diagram]
UP + * + *  
[Diagram]
Black wins  
[Diagram]
Black loses  
[Diagram]
{0||0|Tiny-1}  

Next, block corridors ending in tinies (reverse sente) or STARs.

[Diagram]
1/8  

Next are numbers. Start on numbers with largest denominator.

[Diagram]
-1/4  

Most of these results are proved on other pages.


See also:


Path: <= CGT path =>
Infinitesimals Optimal Play last edited by PJTraill on January 30, 2019 - 20:04
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