 The point made by Cramér in this passage can be generalized. Suppose that the upper boundary of an outcome’s value is \(2^m.\) If so, that outcome will be obtained if the coin lands heads on the mth flip. This means that the expected value of all the infinitely many possible outcomes in which the coin is flipped more than m times will be finite: It is \(2^m\) times the probability that this happens, so it cannot exceed \(2^m\). To this we have to add the aggregated value of the first m possible outcomes, which is obviously finite. Because the sum of any two finite numbers is finite, the expected value of Cramér’s version of the St. Petersburg game is finite.