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Best of Alan Krigman

Gaming Guru

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Casinos Let You Pick Your Own Odds, Even in Your Own Favor

24 July 1995

at if casinos allowed you to pick the odds you'd win? Wouldn't they quickly go belly-up? Surprise! They already let you do it, even to the point where you have greater than 50-50 chance to win any or all bets. Still, they'll be open when next you visit.

This apparent paradox isn't exploited in some super system sold to unsuspecting solid citizens as an "insider's secret casino bosses don't want you to know." It's no paradox at all. Casinos don't make money on odds, but on "edge." Sure, odds figure into this factor, but only along with payoffs and bankroll, not to mention sophistication, luck, and human nature.

Roulette offers particular flexibility to select your own odds. Picture the wheel with thirty-eight grooves, numbered 00, 0, 1, 2, ... 35, 36. One number wins on any spin; the other thirty-seven lose. So, odds against a hit are 37-to-1. Wins pay 35-to-1.

Say you risk $30 per spin. You've chosen to make "inside" bets directly on individual numbers. You're avoiding "outside" bets on predetermined groups like red/black or odd/even, and aren't betting on rows, columns, edges, or corners, either. Here are some options.

Bet the whole $30 on a single number. The odds against you are 37-to-1. Hit, and the profit is 35 times $30 or $1050.

Bet $15 each on two numbers. Now you have two ways to win and thirty-six to lose, so the odds against you fall to 36-to-2 (18-to-1). If one of your numbers hits, you collect 35 times $15 or $525 but lose the other $15, for a net of $510.

Bet $2 on each of fifteen numbers. You have fifteen ways to win and twenty-three to lose, so you're fighting odds of 23-to-15 (1.53-to-1). Hitting returns $2 times 35 or $70 but takes away $28 on the other fourteen so net profit is $42.

Bet $1 on each of thirty numbers. You have thirty ways to win versus eight to lose. You're favored 30-to-8 (3.75-to-1). A hit gets you $35 minus $29, leaving you $6 ahead.

These examples show how you can set your own odds. They also indicate how profits for winning decline as you shift odds in your favor. The 37-to-1 longshot returns a rare $1050 for the $30 you risk. Bucking mild 1.53-to-1 odds, you put up $30 to win fairly frequent $42 payoffs. As a 3.75-to-1 favorite, you risk a few $30 wipe-outs against relatively steady $6 gains.

Where does the casino stand in all of this? And how does ability to manipulate odds affect your chances of a profitable session?

The edge when you bet on individual numbers in roulette is the same, regardless of odds, so players pay and casinos earn an identical theoretical "commission" no matter how bets are made. Consider some of the $30 total wagers for 3800 statistically-distributed spins each number getting 100 hits.

$30 always bet on a single number: the house wins $30 times 3700 or $111,000 and loses $1050 times 100 or $105,000; the casino earns players lose $6,000.

$30 always bet as $5 on each of six numbers: the house wins $30 times 3200 or $96,000 and loses $150 times 600 or $90,000; the casino earns players lose $6,000.

$30 always bet as $1 on each of thirty numbers: the house wins $30 times 800 or 24,000 and loses $6 times 3000 or $18,000; the casino earns players lose $6,000.

To overcome house edge with uniformly-sized bets, players must win more often than predicted by the laws of probability. To overcome normal downswings caused by volatility, players should match their bets to their bankrolls and exercise the savoir-faire to outride cold streaks. Luck helps. So do knowledge and discipline to recognize and quit with a profit or comeback commensurate with the dynamics of whatever they're playing. As Sumner A Ingmark, the Coleridge of the casinos, cleverly counseled:

I made a bet and won it,
Then told myself I'd done it.
That's when I tried to run it,
And wished I'd not begun it.
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.