Optimal play

    Keywords: Theory

Optimal play is play that achieves the best results for the player, given subsequent optimal play by both players.

(Note: This is not a circular definition if play eventually ends, as it does in go, with rare exceptions.)


See also:

For a mathematical approach

For a philosophical? approach

PS they all link to the same page


Discussion

Bill: Note to Willemien: While optimal play may be perfect in one sense, it is not the same. For example perfect play may also be play that yields the best chance of winning (but cannot be refuted, turning a win into a loss), even if the margin of the win is less than that by optimal play. The reason for using the term, 'optimal', is to distinguish it from other notions of perfect play. :)

Willemien: Thanks Bill, I know we are splitting hairs and YOU are the expert and I not even a deshi of you.

Can you give an example? (I like examples even if it is only an CGT tree )

Bill: No, I am not an expert. I am just reflecting my experience with the terminology. If perfect were not ambiguous, there would be no need for optimal. :)

Herman: Here's an attempt at an example:

[Diagram]

Example

Question: How should black respond to W2, a or b? (No komi).

[Diagram]

Simple block

B3 is simple, and leads to a 1 point victory for black

[Diagram]

Complicated invasion

If black decides to hane, play might continue like this.


The first diagram might be considered perfect play for black. There are very few variations, and black wins.

The second diagram might be optimal play. Black is likely to win by more points than in the first diagram, because B5 was sente, so black got first play in both corners. (of course, white might ignore B5 to further complicate matters). Here, black is perhaps playing optimally, but is also taking a risk...

MrMormon: The idea of taking a risk directly contradicts the idea of optimal play.

anonymous: on the page [ext] http://senseis.xmp.net/?DoesKamiNoItteExist a proof was given that a winning strategy must exist for one of White or Black in no-komi go. It wasn't mentioned there that Black must have a winning strategy in no komi go. If White had a winning strategy then Black could pass on the first move and then follow the White winning strategy with colors reversed


This is a copy of the living page "Optimal play" at Sensei's Library.
(OC) 2014 the Authors, published under the OpenContent License V1.0.
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