I disagree with your answer about using the Martingale with an infinite bankroll ( column). If, like I did, it is assumed that an unlimited bankroll is at our fingertips and there is no table limit - meaning doubling to infinity is possible, can/does the system still fail because the 'theory assumed win' is not a guarantee?
Granted, losing 1,000 or 1,000,000 times in a row at something is very unlikely, but it is possible.
Albeit the house edge is small on certain types of wagers in a casino, there is no guarantee that the win will ever occur. However, I went one step deeper by saying that the system will fail because Martingale assumes that on an unlimited bankroll you will win one time to make the 1 unit profit sought after. I conceded that point, that, yes, the table limits will stop this system. My discussion mates used an unlimited bankroll to make the theory work to their advantage by saying the ONLY thing wrong with the theory is the table limits set by the casinos.
I just left a discussion in which we all agreed the Martingale System is not good use.