Pretty sure the variables the author picked are not the most interesting ones.<p>Urn models are engineered to have a rich get richer bias which is best seen by varying the initial populations.<p>Instead of offering trial count and pick counts which are (invariates in the actual model) he could have picked initial ball count and initial white/red ratio.
The proof seems to concentrate on the marginal distribution as n goes to infinity. But the simulation hints at something more interesting: each sample of the random process seems to converge to a value, where the value itself is U(0,1).<p>Is it true that a sample of the random process is convergent with probability 1?
> After a large number of picks, what is the behavior of the proportion of red balls in the urn<p>Isn’t the more enticing question how strong the bias towards the first picked Color is?