In terms of odds-to-lose?
So, for example, the odds of losing 10 consecutive 50% in a row is the same as the odds of losing one 99.90234375%?
I guess I need ask about more than just raw probabilities, otherwise it is trivial as you've just demonstrated.
So, I'd like to know:
I place a martingale doubling series bet, starting at size X. It takes Y number of doublings before a win is generated. What single bet size and odds is that equivalent to?
There ought to be a nice graph in there somewhere
The problem is, it's a non-definitive answer. If you are betting at 50%, for example, it's 50% that you'll generate a win after one roll, 75% that you'll generate a win within two rolls, ect, but technically you could go on forever without winning a roll (thus then the gamblers fallacy).