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# Your Best Chance to Double Your Money at Roulette

27 March 2007

A couple of weeks ago, I walked in the door at home and my wife greeted me with, "You have a package. I wonder who's trying to teach you to play poker this week."

I laughed, because the last couple of years have brought a steady stream of poker books, more than I can read, let alone review. But this was no poker book. Instead, author Ken Ross melded a couple of interests of mine in A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans (\$14, Plume Books, 187 pages, softcover).

I'll not go into this in great deal. Suffice it to say that if you're comfortable with baseball, odds and, most of all, math, you'll love this book. If your eyes glaze over at the sight of numbers, this is one you'll want to skip.

Ross' topics aren't all baseball-related. Some topics are the blend of baseball and odds promised by the title. What is the mathematical expectation that some player would have a hitting streak as long as Joe DiMaggio's 56 games? Do bigger fan bases of big-market teams affect odds enough to make it profitable to bet on small-market teams?

But Ross also delves in the world of casino games, including a roulette topic that gives me a tool to better explain something I've been telling readers for years. If you're going to play until you've either doubled your money or lost it all, do you have the best chance of doubling your money all at once? Dividing your bankroll into two equal wagers? Ten wagers? A hundred?

My standard answer has always been that your best chance is in a single wager, because it gives the house edge fewer opportunities to work against you.

Caution: I am not recommending that you bet it all at once, nor do I recommend doubling your bankroll or losing it all as a goal. Relax, have fun and skip the unrealistic expectations.

But just to explore the concept of bankroll doubling, Ross not only agrees that your best chances come with a single wager, he quantifies the problem. If you're wagering on even-money bets at double-zero roulette, such as red/black or odd/even, you have 18 ways to win and 20 ways to lose. On red/black, for example, you'd win on the 18 black numbers, lose on the 18 reds and also lose on zero and double zero. Your chances of winning are 18:20, which can be reduced to 9:10.

To express that as a percentage, divide the 9, representing your chances to win, by 19, your chances to win plus your chances to lose. That comes to 0.4737. Multiply by 100 to convert to percent, and you have a 47.37 percent chance of doubling your money with a single wager.

What if you divide your wager into two equal-sized bets, and keep re-wagering until you've doubled your money or lost it? Now, Ross explains your chances are 9 squared:10 squared, or 81:100. That's a step down from 9:10, a 44.75 percent chance of doubling your money.

What about wagering a tenth of your bankroll each time? Your chance become 910:1010 -- 9 times itself 10 times to 10 times itself 10 times. And your chances drop to about 35 percent.

For any given share of your bankroll, you raise the 9:10 to the corresponding power. Divide your bankroll into 20 parts, and you raise the 9 and the 10 to powers of 20; divide into 100 parts, and raise the 9 and 10 to powers of 100, and so on.

The smaller the share of your bankroll you wager, the smaller your chances of doubling up.

Just the opposite is true for games in which the player has an edge. A blackjack card counter, for example, increases the chance of doubling his or her bankroll by dividing it into smaller units and giving the mathematical edge more chances to work against the house.

Note that I still recommend that you stay within your bankroll, not bet too large a share of your gambling money at once, and give yourself a chance to enjoy your casino visit. After all, for most players, a day at the casino is about having fun and maybe winning a little, not about doubling your money or blowing it all.

As for A Mathematician at the Ballpark, I enjoyed it, and recommend it highly if you're into odds and probability. If you prefer your bets and baseball without the numbers, then this isn't the one for you.

Listen to John Grochowski's "Beat the Odds" tips Saturdays at 6:20 a.m., 2:50 p.m. and 7:41 p.m. and Sundays at 8:20 a.m., 2:50 p.m. and 10:42 p.m. on WBBM-AM, News Radio 780 in Chicago, streaming online at www.wbbm780.com, and to his casino talk show from 7 to 8 p.m. Saturday on WCKG-FM (105.9), streaming at http://1059freefm.com.

Recent Articles
Best of John Grochowski
John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

#### Books by John Grochowski:

The Craps Answer Book
John Grochowski
John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.