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# Combination bets at roulette let you manipulate risk and reward

5 July 2010

Roulette players often mix-and-match wagers. Multiple spots straight-up; groups like three-number rows, four-number corners, and 12-number dozens; and maybe an 18-number outside bet. In all manner of combinations.

Ability to cover lots of possibilities is attractive in a game whose winners are determined by the single groove where the ball lands, out of 37 or 38 slots on single- and double-zero wheels, respectively. A surprisingly high proportion of solid citizens, however, just plop down wagers randomly – maybe believing, falsely, that they're tracking patterns scientifically or following inspired hunches. When the bets on a particular spin happen to offset one another, shaving overall loss or snatching a small victory from the jaws of defeat, well... there's the proof.

The flaw in this method of play is the missed opportunity to manipulate the odds of success and the associated amounts that can be won or lost. Here's a series of simple illustrations.

Imagine you're willing to risk \$10 per spin. Bet it all on one spot at a single-zero table; chances are one out of 37 you'll win \$10 x 35 or \$350 and 36 out of 37 you'll lose \$10. Risk the \$10 on the line between two numbers. The chance that one or the other will hit doubles, to two out of 37, but potential profits fall to \$10 x 17 or \$170; the downside is a 35 out of 37 probability you'll kiss your \$10 goodbye. A 3-number row is another option. The chance is three out of 37 of a net payout of \$10 x 11 or \$110; the likelihood \$10 will go by the boards is 34 out of 37.

More interesting combinations entail hedges, bets that complement one another. There are innumerable ways to do this, having a bevy outcomes and probabilities. A few examples will give you the idea, then you can have fun noodling out strategies that meet your own preferences for balancing risk and reward.

Pretend you want to limit your exposure on any spin to a \$10 loss. You can bet \$1 on each of five red numbers and \$5 on black. The chance of losing the whole \$10 is 14 (the 13 uncovered red numbers plus zero) out of 37. If any of the selected numbers hits, you'll win \$35, minus the \$9 on the other propositions for \$26 net profit. The likelihood of success on this is five out of 37. On black, you break even. The chance here is 18 out of 37. In all, this is five ways to win, 18 to break even, and 14 to lose.

Alternately, bet \$5 on a dozen, say 25 to 36, and five \$1 two-spot splits between 0 and 24. You lose \$10 on the 15 uncovered numbers from 0 through 24, with a probability of 15 out of 37. Hit any two-number split and grab \$17 minus \$4 minus \$5 or \$8 net, a 10 out of 37 shot. And earn \$10 minus \$5 on the dozen, with a chance of 12 out of 37. This is 10 ways to win \$8, 12 to win \$5, and 15 to lose \$10.

Such combinations are hardly secrets the bosses don't want anyone to know. The house edge on any bet at single-zero roulette is 2.7 percent. However you do it, risk \$10 on a spin and the bean counters figure it's worth \$0.27. You're changing volatility, not edge. In the short term of a session of reasonable duration, such as a couple of hours, low volatility lets you relax with a bankroll that drifts up or down at a leisurely pace, high takes you on the casino roller coaster. You pay the same for a better chance of winning less or a worse chance of winning more.

And, what about giving the devil its due? A typical roulette game gets 40 or so spins per hour. At 2.7 percent of \$10 on each round, \$0.27, the house's theoretical earnings due to edge are just over \$10 in that hour. Equivalent to the wager in one round. Not all that bad in the scheme of things. At double-zero tables, by the way, edge is 5.27 percent and the house would earn a theoretical \$20 in an hour from a \$10 bettor. Which, of course, is why you see so many more double- than single-zero tables and why the latter have higher limits than the former. The beloved bard, Sumner A Ingmark, may have had this in mind when he mused:

Monetary transactions,
Involve cash and not fractions.

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Best of Alan Krigman
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.