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And, for simplicity, assume that you really have a 50—50 shot of calling the correct color. Real roulette tables have some additional green pockets on which you lose, giving the house a slight edge.

We'll also suppose that the table has no maximum bet. This pattern continues and always nets you a dollar when you win. You might object that this strategy makes money only if you eventually call the right color in roulette, whereas I promised guaranteed profit.

The chance that your color will hit at some point in the long run, however, is, well, percent. That is to say, the probability that you'll lose every bet goes to zero as the number of rounds increases.

This holds even in the more realistic setting where the house enjoys a consistent edge. If there is at least some chance that you'll win, then you will win eventually because the ball can't land in the wrong color forever.

So should we all empty our piggy banks and road-trip to Reno, Nev.? Unfortunately, no. This strategy, called the martingale betting system, was particularly popular in 18th-century Europe, and it still draws in bettors with its simplicity and promise of riches—but it is flawed.

Do you spot a flaw in the profit-promising reasoning above? It's not very likely that you will lose three in a row, though, because the probability is only one in eight. So one eighth or This effect scales up to any amount of starting capital: there is a large chance of gaining a little bit of money and a small chance of losing all your money.

As a result, many gamblers will turn a small profit playing the martingale system, but the rare gambler will suffer complete losses. As I mentioned, the idea is to keep playing until you win. The guaranteed profit depends on a willingness to keep betting more—and the inevitability of winning at some point with persistent play.

Here's the key defect: you have only so much money. The amount you wager each round grows exponentially, so it won't take long before you're betting the farm just to make up your losses.

It's a bad strategy for generating wealth when you're taking a small but nonzero chance of risking your livelihood for a puny dollar. Eventually you'll go bankrupt, and if this happens before your jackpot, then you'll be out of luck.

Finitude breaks the martingale in another way, too. Yet again the pesky practicalities of the real world meddle with our idealized fun. As we reflect back, it might seem obvious that you can't actually force an advantage in a casino game.

Yet it is surprising that we have to resort to arguments about solvency and mortality to rule it out. The dreamy pencil-and-paper world that mathematicians inhabit, where we can roam freely across all of infinity, permits what should be impossible.

For games with winning chances of 50 percent or worse, there is no betting strategy that secures an upper hand in a finite world. US airdropped aid into Gaza; groups blame Israel for deadly food line clash. Israel-Hamas War.

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