When I hear from Paul, I expect a video poker question. I’ve mentioned him before, as student at a seminar in the 1990s who has contacted me from time to time ever since.

Imagine my surprise when I opened an email from Paul, and it was about roulette.

“You know me,” he said. “I don’t play roulette. But my neighbor just had a big win. He’s been crowing about winning more than \$12,000 for \$10.

“He decided that just for a change, he wasn’t going to spread his chips. He was going to bet \$10 on a single number. Win big or go home.

“He bet No. 6, his wife’s birthday. He lost a couple of times, but then it came up real quick.

“Here’s the weird bit. Instead of taking his \$350 in winnings, he let it ride. With that and his original \$10, he had a \$360 bet.

“Then the 6 came up again. That was a 35-1 payoff on \$360, so that’s \$12,600 in winnings, and he still had the \$360 bet, so he’d turned his \$10 original bet into \$12,960.

“He asked if I wanted to try, and I told him congratulations, but I’ll stick to video poker. I wasn’t going to rain on his parade, but it seems like he just got very lucky.”

I’m sure Paul knew full well how lucky his neighbor had been, but let’s break it down.

There are 38 numbers, including 0 and 00 on standard American roulette wheels. The chances of winning two consecutive single number bets are 1 in (3838), or 1 in 1,444. That Paul’s neighbor was able to win two in a row within a few spins was fortuitous, to say the least.

Paul’s neighbor looked at it as if he was risking \$10 per trial, since the winnings he reinvested were “house money” that didn’t come out of his pocket. I look at it differently. Money is yours after you’ve won it, and the decision to immediately bet back \$350 wins means you’re risking money you could use for other purposes.

But even looking at it the neighbor’s way, an average outcome in which every possibility happens once would mean putting \$14,440 of his original bankroll at risk. And at the end of the trial he’d have \$12,960, or \$1,480 less than his starting point.

That’s not even the downside. One win per 1,444 trials is the average, but there’s nothing that says your number HAS to come up twice in a row in that time. It would be well within normal probability to go twice that long or more without winning two in row. It’s also possible to win more than once within 1,444 trials, but the cost can get very steep very quickly when the ball isn’t landing in your number’s slot.

Single number bets are volatile. You can win big or go broke fast. That’s exponentially true if you’re going to double down on wins. Most players seek to decrease volatility by covering several numbers per spin.

So I’m glad this little experiment worked out well for Paul’s neighbor, but I hope he doesn’t get it into his head that this is THE WAY and start overbetting on high-risk wagers.

“I’m not worried about him,” Paul said. “He’s usually a \$100 max loss guy. If he lost 10 or 12 bets in a row, he’d go off his system real fast. He’s been bragging about how he won his daughter’s tuition for next semester. He won’t risk that.”