Quote Originally Posted by Martin Gale View Post
Assuming an infinite bankroll (yeah, never mind) and no table max limit, it's a fact that a bet progression will win. And the shorter the possible progression is, therefore, the more likely it is to lose in a shorter-run time period.
This is wrong. There is no guarantee that you will ever win a hand ever again. The amount lost on the one time this happens when considering all possible outcomes will wipe out your profit and a much much much more. It is the basic math of the situation. Your if assumes you will win at some point which is not statistically valid. You are never likely to win your next hand and the number of losses you have had prior to that never changes that fact. That is the progression math. Eventually you will lose a million or billion or googaplex hands in a row in the infinite trial. Nothing ever changes that possibility.