This seems similar to the Monty Hall problem, which is also quite unintuitive. Perhaps what makes it work is that the person doing the predicting sees the sequence as a whole, and hence, future events are dependent upon historical ones -- and are no longer purely random.
Consider this question, "You're somewhere in the middle of a 4 coin toss, and the last toss came up heads, what's the probability of the next one coming up heads?" I think the paper is saying it's a 40% chance -- you know you're in an finite series, and, you have partial information about that series.
