If you bet on a single number in roulette, your odds of winning are 37:1. Meanwhile, your potential payout is only 35:1. Any idiot can see, the house has an edge here. No matter what, they will compensate you less than your risk. Over time, they’ll end up ahead, not you.
But 35:1! That’s a lot of money. If only we can all sneak in a few lucky wins before the great equalizer of probability catches up…
Jay Jacobs, an information security specialist focusing on risk and data analysis, wanted to flesh out this house edge in real wins and losses. So he created a simulation of 20,000 people playing 250 spins of roulette. Each put down a reasonable $5 bet on a number for each spin. And we can see who won big and lost big over time.
“Rather than simply stating, “the house edge for roulette is 5.26%,” (which has almost no meaning to anyone but statisticians), I decided to focus on the question, ‘what am I going to walk out with,’” Jacobs writes Co.Design. “Because everyone can understand money in (or missing from) their pocket.”
On this chart, every gambler was followed by a continuous line. The color changes by whether they won or lost each night over 2-4 nights of gambling. The green means money. The yellow is a slight loss. The red means tears. And the whole thing is sinking to the right, like the Titanic.
That said (and maybe we shouldn’t point this out), there are winners! Someone walked away with about $2,000. And a large chunk of people made out with anywhere from a few bucks to a few hundred bucks.
“We can see that it’s entirely possible and even highly probable that a gambler would have a few really good nights or that they’d be able to rationalize, ‘if only I stopped when…,’” writes Jacobs. “But we can also see that more times than not, the gambler walks out with less money than they went in with. That makes for much more accurate advice to gamblers.”
To add salt to the wound, Jacobs visualized many other roulette strategies, like betting on red and black, high and low, four number squares, and even mixing up the bets. Over time, the results all have “about the same mean” loss. No matter what the strategy, the average gambler will lose about 5%. (And what do you know, the house odds on roulette are 5.26%.)
“I’d like to say the best strategy to follow in roulette is to not play at all, but that’s just my strategy and it hasn’t yielded me any winnings yet. What this work does show is that statistically, there is no best or even good strategy for roulette,” Jacobs writes. “One of the most descriptive quotes I came across while researching this was this: ‘The only thing casinos love more than roulette players are roulette players who use a ‘system.’”
[Hat tip: Flowing Data]