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## Re: [Bug-gnubg] Measuring Complexity

 From: Massimiliano Maini Subject: Re: [Bug-gnubg] Measuring Complexity Date: Wed, 9 Sep 2009 11:50:35 +0200

```Hmmm, to me the only measure of the "complexity" of a position would
be how often (i.e. a probability) and average player misplays it.

To factor in the magnitude of the potential misplay, I completely
agree with what T.Keith posted on BGonline:

<BEGIN QUOTE>
A mathematical measure might be:

Let err(i) be the amount of equity you lose by playing candidate i.
Let p(i) be the probability that a human player would make that play.

Then the relative complexity of a play would be:

sum of all ( err(i) * p(i) )

The hard part is figuring out p(i). If you had a database of a large
number of human games, you might be able to train a NN to estimate
this probability.
<END QUOTE>

And even this has some issues (besides the technical ones, how to
compute it): whats complex for an intermediate is not necessarily
complex for a world class player ...

Using the NN inputs could tell us how much two moves are different,
but I don't see the link with the complexity of the originating
position.

MaX.

```