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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.puzzle
Subject: Re: imperfect information game theory
Message-ID: <1038@brl-tgr.ARPA>
Date: Wed, 25-Dec-85 16:08:01 EST
Article-I.D.: brl-tgr.1038
Posted: Wed Dec 25 16:08:01 1985
Date-Received: Sat, 28-Dec-85 12:29:56 EST
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Organization: Ballistic Research Lab
Lines: 23

Thanks, Bill!

It is important to realize that all "probability" measures
are actually CONDITIONAL probabilities, dependent on the
information available.  In some contexts, there is a common
condition, which may then be suppressed so that probabilities
appear to be absolute measures.  However, changed circumstances
may require re-introducing the suppressed condition.

For people who have never heard this before:  P(A|B) is used
to denote "probability of A, given B" where A and B are events.
For example, one of the elementary probability formulae is:
	P(A and B | C) = P(A|BC) P(B|C)
which, assuming the common context C, may be written
	P(A and B) = P(A|B) P(B)
Assuming events A and B are statistically independent, then
	P(A|BC) = P(A|C)	or, given C:	P(A|B) = P(A)
so one often sees the formula
	P(A and B) = P(A) P(B)
But there are two assumptions buried in this.

The moral is, beware of applying formulae when you don't
fully understand the conditions under which they are valid.