The Martingale System
Is what you're describing. It only works if you have unlimited funds, which sadly nobody has.

en.wikipedia.org/wiki/Martingale_(betting_system)
(Vice Admiral Sir Charles Cockbrush KCB MBE DSO, who is finding it increasingly difficult to log into b3ta.com wants to duck your aunt and kick your puppy, Fri 8 May 2009, 16:38, 2 replies)

and if you did
then why would you be gambling
(TheManWithThePlan cussed your mum on, Fri 8 May 2009, 16:55, closed)

Yes
I didn't factor in the 0/00 slots which would, of course, devalue the odds somewhat. It's an interesting run of arguments here - the gambler's fallacy mentioned below and the arguments about the different types of probability above come down to the notions of conditional and non-conditional probability scoring, i.e. the bingo example mentioned elsewhere on this QOTW (or maybe above?) is an example of conditional probability, where one result influences another, and roulette is of course non-conditional probability. Well, it least it would be if WH and the likes didn't build in strategies to influence the probabilities! I'd never heard of the Martingale system before but I knew this couldn't be unique - sounds too good to be true!
(hangableautobulb is an anagram of the best album ever, on, Fri 8 May 2009, 17:31, closed)

Even with unlimited funds it wouldn't work for roulette
Because of the 0 (and 00) as mentioned above. Also, of course, the whole switching colours thing is a red/black herring - it makes no difference whether you keep betting the same colour or switch colours.

I've mentioned before in another qotw that I've always had a problem with the whole 'every run is equally improbable' argument about statistical aberrations, by the way. It isn't true that ten reds in a row is as likely as any other combination, in the sense that ten reds in a row is 'interesting', whereas most sequences are interchangeable. That means that yes, a run of reds genuinely is improbable and worthy of surprise in just the way that common sense says it is. What it isn't is any less probable than any other *particular* run, but of course that's not what people mean at all. Arguing against that is just smug pedantry (and I speak as a fully paid-up smug pedant)

I think people confuse this with the Gambler's Fallacy, which is to say that *after* a run of reds, a black is more likely. That's a genuine error.
( flatfrog Staring vacantly into space, Fri 8 May 2009, 17:04, closed)

yes. you have a point
but the a 1 in 30,000 event isn't statistically particularly rare or significant. Particularly because, as is pointed out below, you can't regard that probability in isolation.

you've got a 1 in 30,000 probability off 15 spins. How many times does a roulette wheel spin in a day? I'll get the maths wrong here, as I'm doing it off the top of my head, but I think that you only need the wheel to spin something like 2000 times for the chances of a 1 in 30,000 sequence coming up to be more or less evens.
( the mighty badger Aphrodite, on a bar stool, by your side, Fri 8 May 2009, 17:29, closed)