We show that the supremum of the successive percentages of red balls in Pólya's urn model is almost surely rational, give the set of values that are taken with positive probability, and derive several exact distributional results for the all-time maximal percentage.
"Maximal percentages in Pólya's urn." J. Appl. Probab. 52 (1) 180 - 190, March 2015. https://doi.org/10.1239/jap/1429282614