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The Martingale system relies exclusively on the Gambler's Fallacy. I believe the record on a casino-owned roulette wheel for black was around 32. No matter how you put money into a slot machine or roulette wheel or negative ROI system, it will defeat you in the long run. As for the scientific proof, I believe it is encompassed by the Conservation of Energy, proved hundreds of years ago but easily ignored when confronted with mirages of spectacular income. Unless you have some quantum or Schrödinger model of money management, your time is best invested elsewhere.
Incidentally, if you were interested in a Schrödinger model of money management, I could probably rig something up for you. Just give me all your money and I'll bet it for you and then not tell you how it turned out. Your money will then exist in a pseudo-quantum state of both increasing and decreasing. Unfortunately, observing the reality would destroy this pseudo-quantum state, so you can never again see the money you give me. Trust me, if you're using terms like "philosopher's stone", the result is the same.
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