A Less Obvious Martingale Fallacy

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The thing is that I can choose to stop after I win my series

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No you can't. In this game the Martingaler plays forever,

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Ok, but isn't the whole point of the theory that it is broken into series and you can stop after a win? I'm not sure it is supposed to be valid if you aren't given that ability.

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Even if you plan to stop, you must realize that you are gambling that you will eventually win a bet. You aren't absolutely 100% sure you will, though. And the penalty for not winning a bet increases geometrically after each losing spin.

Even if you have lost 15 bets in a row, or 15,000 bets in a row, the odds of your winning the *next* spin are still less than 50%. So while you may look into the future, saying "I have to win a bet *eventually*", the wheel doesn't know that, and each new spin is a new chance because the wheel has no memory. Meanwhile your losses are multiplying geometrically.

It may seem like it is too farfetched to imagine that you might NEVER win another spin. But if you had essentially unlimited players each playing on independent wheels, there could be one player who just loses every single bet he makes. This is parallel to the chances of your sitting down and just losing every bet--it's an infinitesimally small chance, but given unlimited time, you could fall into that slot. And the finacial penalty would be unlimited, too.

For every winning player or winning sequence, there is a theoretical counterpart which is losing the same amount or more. So theoretically the system isn't going to produce a profit even with no restrictions on table limits or bankroll.