The Misnah disqualifies dice gamblers from giving testimony in court. The rationale given is that they are not participating in building the world. In fact, the NET TOTAL contribution of their activity to the building of the world is negative; not in expectation, but non-randomly negative.

This might be the rationale for the modern law against playing chance games (not because the expectation is negative to one side and positive to the other side).

Therefore: poker – out, stock market – in; because playing it helps build the world, albeit capitalistically.

See the attached file (in Hebrew), copied from
http://www.daat.ac.il/daat/kitveyet/sde_chem/samuel.htm “

Let us say at any point there are w white and b black balls. The probability of picking a white ball here is:

p_w = w/(w+b).

For the next pick,

p_w+ = p_w (w+1)/(w+b+1) + (1-p_w) w/(w+b+1),

where the two terms denote whether you have a white or black ball next round. If you expand that out,

p_w+ = w/(w+b)

So the probability is constant and since we started off with 1 w and 1 b, it remains at 0.5.

Thus the chances of having 80% white balls over time is the same as the probability of having 80% heads in coin tosses over time. As N tends to infinity the probability tends to 0.

As an sporadic blog commenter i miss this kind of stuff in blogs. You have not information about your audience nor if your comments are abhored or loved (although you can imagine).

I´m surprised by how low digital flavoured subjects (computer science science related topics) as computational complexity are ranked. The hotest topic up to now seems to be algebraic geometry. We must wait and see how the ranking “evolves”.

Thanks for the pointer !

(For simplicity we can assume that t is a small constant.)