You Won't Get Rich by Confusing Chance and Skill

13 April 1998

By Alan Krigman

My neighbors, Nick and Nora, knew how to beat the casino. They'd met Doug, a 'talented' roulette dealer. Nick schmoozed the guy, 'took care' of him. Doug, finding a kindred spirit, said something like: "I'm gonna let you in on a secret. Watch number 33."

Nora chimed in, "three or four spins later, he hit it. This kept happening all day. And when he didn't make 33, he came close."

Lots of dealers think they have special skill. Predicting cards, calling the dice, 'spotting' the ball. And many players are eager believers. "Humbug," I growled. Nick retorted, "You'll be there Saturday. Doug'll be working. We'll show you."

I watched Doug on and off all afternoon. Charisma, he had; skill, well... His table was crowded and he was raking in tips. Sure enough, he told everyone what good people they were and divulged his secret. Number 33. I heard him sing this song a dozen times that day. And I caught the routine. He'd say "I'm warmed up for 33" or some such. Players would bet, and he'd spin the wheel.

If 33 hit, he was a hero. If the spin came up 32 or 34, he was mum but some solid citizen would notice he'd bracketed his call. And all the clued-in players were on those points to catch 'near misses.' If the ball landed in 16 or 21, Doug would explain that numbers weren't in sequence around the wheel, but these were the positions on either side of 33, so he was only a squeak away. And all the clued-in players had bet these points, too.

When none of the five numbers hit, Doug lamented being rusty but asserted he'd keep trying. If he hit within half a dozen or so spins, Doug took the credit and the players chortled over their inside information. If nothing came through, Doug let the matter slide. When an apostate was arrogant enough to allude to it, Doug apologized for failing folks with faith in him, but vowed to work on it. And if 33 hit on some arbitrary spin, Doug claimed he'd been "pretty sure" but didn't want anyone to take the risk yet.

Ultimately, 33 or one of the four 'adjacent' numbers hit often enough to sway Nick, Nora, and Doug's other doting disciples. But, did Doug have any special ability? What do the laws of probability predict? Can money be made from the situation?

Pick any five numbers on a double-zero roulette wheel. The odds favor at least one hit in six tries by almost 57-to-43. So, chance alone makes Doug more likely than not to look good.

Sadly, this doesn't enrich players. Assume you bet $1 on each of five numbers, six times. Losing all six spins costs you $30. Win one out of six; you collect $35 minus $4 or $31 on that spin but lose $25 on the other five for $6 net profit. Win two out of six; you pick up $62 but lose $20 for $42 net profit. And so on, up to six wins for $186 net profit. It's all random. Here's what probability theory says will happen if a million players do this.

So, 428,926 players lose all six spins and wonder what went wrong. (Was Doug just having a bad day?) The other 571,074 make from $6 to $186 and are sure they're on the road to riches. The overall grosses, though, are $12,867,780 lost and $11,288,844 won. This is a $1,578,936 net loss. And, guess what. The million players bet $30 million. They lost 1,578,936/30,000,000 or 5.26 percent of the action. What a coincidence! The house edge in double-zero roulette for all but even-money bets is 5.26 percent.

Here's how Sumner A Ingmark, whose skill in spotting involves rhyme and meter, advises those who seek fame:

Reputations most terrific,
Build on claims not too specific.