[extropy-chat] what is probability?

[gts]

On Mon, 15 Jan 2007 18:44:23 -0500, Rafal Smigrodzki  
<rafal.smigrodzki at gmail.com> wrote:

> ### I would see it this way: The meaning of "random" is "obeying the
> principle of indifference, where the sample space is unambiguously
> described". If the sample space is exactly two outcomes, then each one
> must occur 50% of the time, or else the coin is weighted, and the
> tosses are not quite random anymore.

Hmm, I think this is not at all what is or should be the definition of  
"random".

As the word is normally defined, a series of tosses of an unfair coin  
still result in a completely random sequence! How can you suggest  
otherwise?

In objectivist terms, all that matters for the sake of randomness is that  
the sequence satisfy what von Mises called "The Law of Excluded Gambling  
Systems", which is just to say (roughly) that the sequence must contain no  
predictable sub-sequences, i.e., that the result of each toss is  
independent of the others. (Subjectivists have a different way of saying  
essentially the same thing.)

-gts