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This scheme is very old hat, and clearly very well known.
Roulette wheels don't remember their previous outcomes - hence results are independent of previous outcomes.
But, instead, the test is used to detect biased wheels.
It is probably similar to what Sir Mick's ancestor, Joseph Jagger did to clean up in Monte Carlo.
The catchy ditty however, was about another perp claiming to have broken the bank. Turned out to be a Ponzi schemer.
But if you need to be told all this, perhaps you should reconsider your gambling.