Re: Use of Probability

[Dave Dyer <ddyer@xxxxxxxxxxx>]

This discussion is a move in the right direction - using a Baysean
framework to represent the state as a tree of conditional probabilities
is an improvement - but it is also a dead end

The problem is that Baysean reasoning requires you to assign a probability
to every event, and the whole edifice collapses if events assigned low 
probabilities actually occur.  

In fact, in problems such as Go there is a large amount of uncertainty
in almost all such probabilities, and uncertainty is a completely different
beast from probability. Worse, there is no satisfactory formal framework
for reasoning about uncertainty.

Lets take a simple example; Suppose the situation on the board is 
that black can kill either of two groups, depending on his next move.
A baysian frame work might represent each of the white groups with a
50% chance of survival.  Suppose group A is "standalone" and group
B is a supporting group for Group C, such that if group B dies, C has
a 50% chance of survival, and if B lives has a 90% chance of survival.
A Bayesean framework would calculate C chance of survival as 

	.9*(1.0-.5)+.5*.5 = .7

Which is complete nonsense, because a rational black player will always
choose to kill B rather than A.  

Baysean probabilities can only be added (as in the above example) if 
they are independant, and in game situations that would certainly not
be the case.  The status of C will depend not just on B but also on 
a bunch of other groups of both colors, so the true "status of C" equation 
requires conditional probabilities for all combinations of outcomes of all 
the relevant groups. So for example, if E is also a factor, we would
need 
		Prob C lives given (B and E die)
		Prob C lives given (B lives E dies) 
		Prob C lives given (B dies E lives)
		Prob C lives given (B lives E lives)

All of these conditional probabilities would have to be assigned
somehow, and of couse, the web of conditionality is circular (E
probably influences if B lives).