Use of Probability

[John Aspinall <jga@xxxxxxx>]

A couple of times in the past few months, some list members have suggested
using probability measures as part of the evaluation function.  There may
be some interesting ideas here, and I do not want to discourage people from
thinking more about it.

But...

It is an error to think that there is a single number - "the probability" -
that can represent the uncertainty associated with a game decision.  Nearly
every probability is a conditional probability; it depends on other
assumptions.  There may be many different probabilities for an event --
dependent upon what the event is conditioned on.

Example: let A be the event that black group A lives, similarly let B be
the event that black group B lives.

The standard notation is P(A|X) - meaning the probability of event A, given X.
 "<>" is "not equal"

Then P(A|white to move)  <>  P(A|black to move) which we all know.  There
are positions which live or die with sente.

Also P(A|B)  <>  P(A|not-B).  That is, if group B is alive it might affect
whether group A can live.  (Maybe, an option for A is to connect to B.)

What about both A and B living?
P(A,B|X) = P(A|X) * P(B|X) only if A and B are independent.  I'll claim
that this is very rare.
P(A,B|X) < P(A|X) * P(B|X) if (for example) A and B both live in sente
only.  Then if black spends his move saving A, white will have sente to
move on B.
P(A,B|X) > P(A|X) * P(B|X) is also possible, if A and B can link up.

Summary: You can't just talk about "the probability".  There's no such
animal.  There's "the probability of A given X", and "the probability of A
given Y".  They're not the same.  Representing and combining them is the
hard part.

Recommended reading: E.T. Jaynes' textbook on Bayesian reasoning.
Available on the net from http://omega.albany.edu:8080/JaynesBook