From Gamble Expectation and the Ergodicity Conundrum by Michael Harris

… Peters’ example with 50% gain for heads and 40% loss for tails, variance V is relatively large and although the mean arithmetic return is positive, the geometric return is less than 1, resulting in decaying equity over time. This is nothing new and it also has nothing to do with ergodicity or any other fancy terminology.

From Gamble Expectation and the Ergodicity Conundrum by Michael Harris

…oken a tautology in probability theory. This would be a major breakthrough, but actually it is not. The whole argument is based on conflating the mean arithmetic return factor with the expectation of the gamble. What do I mean by that?

From Gamble Expectation and the Ergodicity Conundrum by Michael Harris

… is a statement about a positive value of a random variable on the average for a sufficient sample. Therefore, wealth increases necessarily, again assuming there is enough starting wealth to absorb intermittent ruin conditions before averages converge to expectation. It should be clear that CM’s statement is the definition of expectation and nothing more than that.…