Black Swan = term for highly unusual events in finance. coined by Prof Nassim Taleb who wrote the book "Fooled by Randomness".

Hmmmm....

1) According to some who replied, the probability of a black swan occurring can be so low that it doesn't happen in a lifetime.

EXAMPLE:
30 reds in a row in Roulette = 0.000000000176. The chance of this not happening is 99.99999998%. For a trial of 2000 spins, this will probably not happen. For a trail of 10,000,000 spins however, this might happen.

2)On the other hand, some who replied says it is as likely to happen!

EXAMPLE:
30 reds in a row happening = 0.000000000176 and 30 random mixture of reds/blacks happening in a row = 0.000000000176 too! Since the random mixture happens, why not 30 reds in a row when they have the same probability? This tendency to see long strings of identical outcome as "unique" is known as Leptokurtosis i think.

3)Finally I present a paradox which might probably be the result of my lack of skill in mathematics. [img]/images/graemlins/tongue.gif[/img]

In a North America Roulette wheel the chance of hitting a Red is about 47.3%. This refers to 473 Reds out of 1000 spins IN THE LONG RUN. (100,000 spins?)

The chance of 100,000 Reds happening in 100,000 spins is a positive number still but very very very small. (0.473^100000) So this could happen.

But if 100,000 Reds occur in 100,000 spins...wouldn't the probability of Reds be 100% instead of 47.3%? The 47.3% dictates that 473 out of 1000 MUST be Red in the LONG RUN. Just like the ~5% house edge dictates that gamblers WILL lose ~5% of their bet in the long run.

Will the occurance of black swans not contradict probability theory?? [img]/images/graemlins/confused.gif[/img]