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Best of Alan Krigman

Gaming Guru

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How Much Should You Bet at Roulette?

26 July 1999

What you bet per round at a table, relative to the stake you're willing to risk during a session of reasonable length, determines how much you can expect to win as well as the chance you won't go prematurely broke. Solid citizens and roulette tables, however, are like the blind men and the elephant -- each individual has a unique perspective. Unlike other serious table games, roulette allows players to choose among anything from a high probability of a small win, to nearly 50-50 chance at even money, to a longshot at a substantial return. These differences dictate disparate answers to questions about what's wise to wager.

To get an idea of bet sizes suited to your playing proclivities, consider strategies with low, medium, and high volatility for the same total wager per spin. The first might involve apportioning the bet equally on each of 30 numbers, the second dropping it all on red or black, and the third risking everything on a single number. Actual play is usually somewhere betwixt and between.

Assume your primary criterion is to avoid depleting your bankroll during five hours of play. You might average 40 spins per hour on a norrmal table, so this session represents 200 bets. Putting out 1/200 -- half a percent of your nest egg -- or less per spin, for example $5 on an $1,000 stake, you'd be sure of surviving the session. This, even without winning a single hand, regardless of how the money was wagered. But few folks would be happy with the returns their $1,000 stakes could earn making bets this small.

It's more practical to use the survival criterion by setting a level of confidence in not going belly-up during a stint. Then "risk of ruin" principles give the highest corresponding fraction of a bankroll to bet. A sensible guideline is 85 percent chance of surviving four hours. Here are the maximum proportions of a stake the math says can be bet per spin: 6 percent spread over 30 numbers, 5 percent on either color, and 1 percent on a single spot. Starting with $500, this is $30, $25, and $5 respectively.

The profit potentials corresponding to these betting levels can be determined using the win goal criterion. Chances of reaching win goals at various percentages of the starting bankroll for the indicated bets are shown in the following list.

 percentage  1/30 of total  total  total
 of bankroll  bet  bet  bet
 set as  on 30  on  on one
 win goal  numbers  red or black  number

 20%

 23%

 73%

 81%

 50%

 3%

 48%

 61%

 100%

 0%

 25%

 42%

If your win goal for a particular style of play is such that the indicated chances of attainment are too small, you have to bet more to obtain the necessary upswings. With a specified stake, one that seemed prudent when you left home (not when you're at a cash or credit card terminal in the casino), this raises the risk of bottoming out during a normal downswing.

For instance, say you start with $500 and always bet on red or black. You won't quit unless you double your money -- earn a $500 profit -- or lose your stake. At $25 a shot, the list shows you have 25 percent chance reaching your win goal before going bust. If, instead, you bet $50 per spin, the chance you'll hit your goal before tapping out jumps to 45 percent. But the probability you'll survive a four hour session drops from 85 to 34 percent.

Similar logic applies to bets on single numbers. Consider how the likelihood of doubling your money changes if you raise the wager from 1 to 2 percent of a bankroll -- for example $5 on a $250 rather than a $500 stake. Now, you're up from 42 to 46 percent chance of earning $250 profit before going broke, but your chance of surviving for four hours is down from 85 to 43 percent.

Conversely, you can raise the likelihood you won't crater before your time if you bet less than the guidelines suggest. However, you'll have to be content with a smaller win when the wheel is spinning on your wavelength. The beloved bard, Sumner A Ingmark, had it right on the ball after all when he wrote:

With laws of chance though you may fiddle,
You balance ends against the middle.
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.