The improvement in guessing accuracy over 50% is a measure of the overlap of the density functions used by the two players (specifically, I believe it is the ar

The improvement in guessing accuracy over 50% is a measure of the overlap of the density functions used by the two players (specifically, I believe it is the area under both curves). The result notes that if Player 2 uses a density function +/-inf, they can guarantee at least epsilon overlap. However, it's interesting to note that, practically speaking, if you played this game in a pub, Player 1's density function would likely be highly predictable -especially if they came up with the numbers mentally. As long as Player 2 chooses a reasonably similar density function they can likely do quite significantly better than 50%. It would take some patter, and you might lose a friend, but I could see it being possible to win "real" money this way.