Roulette odds

Until I received a phone call from my old friend Greg a couple of weeks ago, I didn't know he played roulette. For that matter, I didn't know he gambled — he was never part of our late-night college poker games.

"I've loosened up a lot since then," said Greg, who was more into grades than games all those years ago. "It's my wife's fault. About three years ago, she got us on a park district bus trip to a boat in Iowa, and I hit a slot jackpot for $1,034. We've been going every couple of months ever since."

It wasn't a three-year-old slot jackpot that prompted the call. Greg had roulette on his mind.

"Last time we were out," he said, "It was my wife's birthday. We went to the roulette table together. Minimum bets were $5, and minimum chip value was $1. She just plays red or black, or sometimes odd or even, but I decided to spread a few bucks in the middle."

In roulette, on the outside bets that rim the perimeter of the layout, you must bet the table minimum on each proposition you choose. So when Greg's wife bet on black, she had to plunk down the full $5, and if she added a bet on even, she had to put down another $5.

On the inside bets — the individual numbers and combinations of numbers such as the two-number split, three-number street and four-number corner — you can spread chips around, as long as they add up to the minimum bet. If Greg wanted to make single-number bets on 14 and 25, a two-number split that would win on 2 or 3, three-number streets on 4-5-6 and 34-35-36, and a four-number corner that would pay on 28, 29, 31 and 31, he could do it by placing $1 chips on each of the five propositions for a total of $5.

"What I actually did was to add an extra dollar and bet $2 each on three numbers," he explained. "I wanted my wife's birthday, Oct. 26, so I bet $2 on 10 and $2 on 26. Then I took the third $2 and put it on our anniversary, the 18th.

"Quite a system, huh?"

It's as good as any other. Any number is as likely as any other to turn up on a given spin of the wheel. I don't play roulette often, but when I do, I'm in the family birthdays and special days brigade.

"Hah! I'd have figured you for something more scientific. But wait till you hear what happened.

"The first spin was 26, so I won right away. The second spin was 18, so now I'd won on both a birthday number and the anniversary. And this is what floored me. The third spin was 10. I'd won single-number bets on the first three spins we were playing, with three different numbers.

"What are the odds of that?"

Since Greg was making three single number bets, and there are 38 numbers on the wheel including 0 and 00, he had a 3 in 38 chance of winning on each spin — 1 in 12.67. His chances of winning on three consecutive spins were 1 in (12.6667 times 12.6667 times 12.6667), or about 1 in 2,032.

The odds are much higher against winning in that particular sequence — 26, followed by 18, followed by 10. Then the chance of winning with 26 on the first spin is 1 in 38, the chance of winning with 18 on the second spin is 1 in 38 and the chance of winning with 10 on the third is 1 in 38. The chance of all three coming through is 1 in (38 x 38 x 38), or 1 in 54,872.

"Wow!" Greg said, after I'd tapped it all out on the calculator. "Seems like I should have made more money, with odds like that. I figure I came out $198 ahead for those three spins. Could I have made more?"

Sure, or he could have lost it all. After the first winning spin, Greg had turned his $6 into $72. If he'd then divided that in three for the second spin and wagered $24 on each of his three numbers, a winner would have given him $864. Dividing that in three would have left him with wagers of $288 on each number for the third spin, and a winner would have been worth $11,232.

"Would you have played it that way?"

No. There was no way to tell that streak was coming, and a loss on the second or third spin would have wiped out previous winnings.

"So I did good?"

Yep. I hope you didn't give too much back.

"We left the table with a $150 profit, and had a nice dinner in the casino's steak house. A special little birthday treat."