4 ms·

That average is still greater than $100, because you haven’t yet hit the Kelly point beyond which the downside catastrophe dominates. Play it out a few more rou

• bzax 3y ago
  The expected value of this distribution goes up with every iteration, there is no such Kelly point. You could try this with heads: double your money tails: lose all your money in which case the expected value is always $1, as you have a 1/2^n chance of having $2^n dollars after n rounds, and 0 otherwise. The point of discussing ergodicity here, however, is whether you can describe the behavior of the iterated distribution deterministically if you exclude a portion of that distribution which has measure zero.