Having read all the comments in this thread I have written a piece of software to demonstrate exactly how this works.
The software is free and is available from
Toxic Drums Doubling Simulator. There is an article explaining exactly how it works in theory and exactly why it doesn't work in practice at
Doubling System Explained. It is worth noting that all lengths of lose sequences are about as likely as the volume of money bet so far. So if you are in the region of hundreds of bets you are likely to be getting 6 to 10 losing sequences (2^6=64 & 2^10=1024) and by the time you are in for millions you are in the region that millions can be lost. But there is a way to get a good chance of small wins but the casinos will not allow doubling. And, of course, they always put limits which kill your chances too. But all the maths and the explanations are not as convincing or as impressive as seeing those graphs of the betting sequences behaving the same in character every time. Play with the software and you'll never be tempted to try the doubling system for real.
Wishing you all well, Sam.
P.S. By the way - your best ever chance of winning the most in your life is to take all the dosh you will ever bet and to put it on one 50/50 bet. That is it! But gambling for fun can still be a very cost effective form of entertainment.

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