quick probability note (was bg termination)

[Robert Koca]

For those who are interested in my question about backgammon terminating,
let me say something about the phrase "probability = 0".

The existence of outcomes which give an event
does not imply that the event has probability > 0.
For example consider the experiment "toss a fair coin infinitely often".
Getting Heads on every toss is in the sample space but the
Probability of this event is 0. In fact, Pr(asymptotic proportion
of heads does not =.5) = 0.

Thus examples such as "suppose both players are on bar and each has
at least one home board point. they can then both fan infinitely often"
does not show that bg can last forever with probability > 0.

Bob Koca
bobk on FIBS