# Roulette win

There’s a well-known way to win in Vegas, and famously some people have done it systematically. Maybe it works for startups too?

Suppose you’re betting on “red” in a game of Roulette.

There are 41 places a Roulette ball can land — numbers 1 through 40, plus a “double-zero” and sometimes a “zero.” (So it’s a CHAR(2) not an INT(2)). The numbers also alternate red and black — twenty of each plus that special double-zero which is considered neither color. (For the ensuing math we’ll assume a wheels with 00 and without a 0.)

When you gamble on “red, ” say, you double your money if you guess right and lose your money if you guess wrong. If it weren’t for that pesky double-zero, this would be perfectly even odds, but there’s 20 ways to win and 21 ways to lose, so the house always gains in the long run.

Still, it’s close enough to even-odds (is that an oxymoron?) that an interesting algorithm presents itself — an algorithm that guarantees you’ll make money.

You start by betting \$1 on red. If you win, you take your winnings and leave with an extra \$1.

If you lose, next time you bet \$2. If you win, you earn \$2 and, even though you previously lost \$1, you’re still \$1 ahead, so you’ve made money.

If you lose, next time bet \$4. If you win, you earn \$4, you previously lost \$3, so you still made \$1.

And so on, doubling the amount of money wagered each time. If you play enough times you have to win at some point, in which case you’ll walk away \$1 richer. It might be a boring, inefficient way to earn \$1, but you always win. Multiply all these numbers by 1000 and it becomes interesting.

But this is even more interesting: You can perform a similar process by betting on a number instead of a color. Betting on number 12 pays 40:1, so if you hit that you win big. Of course there’s just a 1/41 chance you’ll hit, so the process of re-betting has to be done longer — much longer. It could easily require 50 bets.

But when you win, you really win, because the payoff is 40x, not 2x your last bid. So if you won on the \$16 bet, you would have lost \$15 so far but won \$16 x 40 = \$640.

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