There are also recent results about the St. Petersburg game; Gut and Martin-Lof 
give a “maxtrimmed” version of the game, while Fukker, Gyorfi and Kevei  determine
the limit distribution of the St. Petersburg sum conditioned on its maximum.
Buchmann B et al. Distributional representations and dominance of a Levy process over
its maximal jump processes. (2016) BERNOULLI 1350-7265 22 4 2325-2371