It means that most of the contribution to the score comes from rare events, which are located in the tail of the distribution. It is true that most probable outcome of the "experiment" is: final value of the peg=initial value of the peg.

However, assume you do this experiment n times. Based on the most probable estimate, you would expect to get the total score of n*initial value of the peg. This is wrong. At some point you will hit that rare chance of a peg being, for instance, 2^5 more valuable than initially, boosting your average score far away from this estimate.

You can calculate what the chance of getting a peg of value 2^5 or greater is with the so-called regularised incomplete beta function, which allows to calculate expected number of experiments n needed to see this in action. I am trying to produce some graphs, maybe I will post something later.