Martingale seems really a fascinating topic for a lot of gamblers
But don't worry @deisik, I like your approach and thinking out of the box, although you know my opinion about something that might work to a certain extent in reality (with small gains, if you play it safe), but not in theory
You know what they say?
Right, there is nothing so practical as a good theory (the emphasis on good, obviously). And the theory says that on finite timeframes (dealer's choice), it is not something which "might work to a certain extent in reality" but rather something which would work most of the time given enough sample size (to make the theory fully applicable)
As I see it, the house edge would make for more revenue flow, but it will still be making profits with a zero house edge simply because it will be able to stay in the game longer than any other player. Put differently, the sheer size of its bankroll will be the house edge on its own.
Imagine all those players putting all their funds in one pot and going all-in a few times - and getting lucky. Then this "syndicate" would suddenly have the house edge over the casino
This would be sheer luck, indeed. However, you don't need luck for that at all. A bunch of wily and artful gamblers can slowly but surely drain a casino's bankroll empty, and drive it out of business without any luck involved. Ironically, it would turn to be a matter of extreme luck for the casino to stay afloat in that case
In general, this is of course a zero sum game, which is maybe good for money laundering, but else then that ? Your theory of a "bankroll house edge" makes sense, as far as I see it, but only, if you make Martingale mandatory for all players and no syndicates allowed. But all in all this is so far from reality
It can't possibly be a zero sum game for the simple reason someone is set to bust at the end of the day
And I'm not sure what martingale has to do with that unless you actually mean the opposite of what you have written above. A thought-out martingale strategy takes away from the house edge, in whatever form it may exist. It is hard to beat a mighty bankroll, but if your goal is limited only to taking something from it, a small piece of the pie, the more the merrier