Re: roulette double bet
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the only problem i can see with this is the bet limit.
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Congratulations. There's your answer.
This fails for exactly the same reason the doubling strategy fails. The number of spins it takes for you reach the betting limit and suffer a catastrophic loss is fewer than when you only double up - but (probability of hitting the maximum bet and losing)x(maximum bet) is still larger than (probability of winning before the progression ends)x(minimum bet). The house gets a fixed percentage of your action in the long run, regardless of what distribution of bet sizes you choose.
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