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The Odds Aren't What Gives the Casinos the Edge

6 February 1995

common misconception holds that casino gambling is a losing proposition because the odds are always with the house. It's true that casinos are favored in every game. But knowing why, and how to minimize the impact, goes beyond the odds on various bets.

Odds are numbers expressing the chances of winning a bet. But they're only half the story; payoff figures are the rest. While most individual bets are more apt to go south than come home, this isn't inherently bad as long as the poorest odds are balanced by the richest payoffs. Here are examples:

Single-zero roulette, endangered but not extinct in this great country of ours, has 37 positions -- 18 red, 18 black, one green. Red therefore wins in 18 slots and loses in 19. This sets the odds against scoring on red at a slim 19-to-18, or 1.056-to-1. The bet wins nearly half the time and every $1 wagered reaps $1 profit.

A pair of dice can land 36 different ways. Of these, two total 11 -- 6-5 and 5-6. This number therefore wins on two combinations and loses on 34, putting the odds against the bet at 34-to-2 or 17-to-1. An 11 in craps is a much greater longshot than a red at roulette, but it pays a lot more $15 rather than $1 for every $1 at risk.

A slot machine can be imagined with four reels, each having ten equally-likely stops. Such a machine would have 10 times 10 times 10 times 10 or 10,000 possible final combinations. If each reel has one flag, and four flags wins the biggie, one combination hits the jackpot and 9,999 miss. The odds against a lolla-paluzza are steep at 9,999-to-1, but a jackpot on four quarters can pay thousands of dollars.

So, you may ask, why is the house favored? If returns were in exact proportion to odds, say $1 on 11 paid $17, a bettor playing long enough could expect to break even. The casino wouldn't be favored. But two devils in the details give the house the upper hand.

Ultimately, the devil is that payoffs are less than the odds dictate. The difference constitutes the "edge" or "house advantage" on every bet. It's like a fee or commission the casino takes on the action. Insiders call it "vigorish" or "vig." Moderate fees on enough bets can grow to the point where the money can only be recovered by a fantastic stroke of luck. The effect is strongest on bets with short odds and payoffs equal or close to what's at risk, like red at roulette or banker at baccarat.

Some players think there's a second devil involving the time, money, and chutzpah to survive normal downswings. Casinos have staying power; solid citizens have limits. Over extended play, the casino makes no money from "volatility," the fancy name for bankroll swings. But it accounts for the performance players experience in sessions of reasonable length -- a few big winners and many moderate losers.

For the individual player, volatility is most portentious on longshots. Say a craps player with $80 plans to make $5 bets on 11 and quit when a hit yields a profit or breaks even. A win pays $75. So the player does well on an early hit, gets ahead if 11 appears within fifteen tries, and breaks even if it pops on the sixteenth. But there's a 40 percent probability that 11 won't roll in sixteen tries and the player will go broke. With no house edge a win would return $85 on a $5 bet, earning more for the player on a hit but not affecting the 40 percent probability of busting in sixteen tries.

Factors favoring the house are intrinsic to the games. You can't overcome them. You can minimize their impact.

Reduce the effect of vig by choosing low-edge games and bets. Baccarat has smaller house advantage than roulette, for instance, and six-deck less than eight-deck blackjack. Within baccarat, bets on Banker have lower vig than Player. And, basic strategy in blackjack trims the edge over hunches.

Protect yourself against volatility by sizing bets to your bankroll and the odds of the game. Steeper odds suggest lower bets for a given stake. Here's an illustration. At 10-to-1, you need enough bankroll to make eight tries for a 50 percent probability of at least one hit; at 20-to-1, you need enough for fifteen bets to reach the 50 percent level.

And, whether you prefer your action with short or long odds, remember that you can stop playing when you're ahead and enjoy a restaurant, lounge, show, spa, or any of the leisure attractions most casinos offer. The house can't take a hike when it has your money. As Sumner A Ingmark, Longfellow of the longshot, once waxed:

Were it just odds you've got to fight and beat,
By persevering you'd ne'er face defeat.
But skilled play also takes ability,
To master vig and volatility.

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.