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How Casinos Measure House Advantage, and What the Values Mean

24 January 2001

By Alan Krigman

Everybody knows why casinos get rich. They have an advantage on every bet in games of independent trials. But only a handful of hopefuls understands how the handicap is achieved. Many solid citizens think it's just that the bosses have more chance of winning every round than the players... that "the odds are always with the house." While this is true for bets paying at least even money, it isn't universal. For instance, bet on two columns simultaneously at roulette; the odds are 24-to-14 you'll win.

Odds alone don't fill casino coffers. Payoffs are also factors. The house advantage arises because the payoff for winning a bet is a bit below the odds overcome to do so. Take the two-column roulette example. Bet $12 per column, $24 total. A win nets you $12. But the odds were 24-to-14, so a bet with no house advantage would pay $14. The casino's profit comes by grabbing the $24 when you lose but forking over $12 instead of $14 when you win.

Confusing the issue even further is the fact that house advantage is evaluated in four different ways, and you may encounter one or another of the figures interchangeably. The measures are edge, return percentage, vigorish -- often called vig, and hold -- sometimes called hold percentage or PC (for percentage).

Edge is a theoretical quantity. It's the fraction of the overall amount bet that the casino would earn if every set of decisions fell precisely into statistical line. Consider the two-column roulette bet again. In 38 spins, the house expects to win 14 rounds at $24 each for $336 in all, and to lose 24 rounds at $12 each for a total of $288. The total bet would be $24 x 38 or $912 while theoretical "take" is $336 - $288 or $48. The edge is $48 divided by $912 or 5.26 percent. A particular series of 38 rounds may not give the casino 24 wins and 14 losses. But, 38,000,000 such decisions will be close enough to 24,000,000 and 14,000,000 that the moguls can haul their 5.26 percent to the bank.

Return percentage, another theoretical quantity, is the fraction of the overall bet that would go back to players if results were on the statistical button. Return percentage, most often used to characterize slot machines, is the complement of edge. That is, a 94 percent return implies 100 minus 94 or 6 percent edge.

Vigorish is an actual fee the casino collects from bettors. In some instances, the casino assesses the vig when it books the wager so players pay it whether they win or lose. On buy bets at craps, for example, the vig is 5 percent of the wager, usually rounded down to the nearest whole dollar. So, if you buy a four for $100, you give the dealer $105 -- $100 for the bet and $5 for the vig. If you win, you get back your $100 plus a $200 payoff; the casino keeps the $5. If you lose, you're out the whole $105.

On some propositions, most notably Banker at baccarat, the casino charges a vigorish only on winnings. Pretend you bet $20 on Banker. If you lose, your $20 goes south. If you win, you collect $20 minus the 5 percent -- or $1 -- vig. So you only net $19.

Hold or PC has two distinct meanings, different when referring to slots or tables. Both are tangible, however, not theoretical.

On the slots, hold is the fraction of the money actually cycled through the machine that the casino keeps. It's the real counterpart of edge -- or the flip side of return percentage -- based on tallies rather than probabilities.

At the tables, hold is the fraction of the drop -- the cash crammed into the box when players buy into the game -- that the casino keeps. It's counted rather than predicted. It's influenced by edge but is not analogous to it, because hold also depends on how long players continue to bet from their original buy-ins and how they size their wagers relative to their bankrolls.

Sumner A Ingmark, poet laureate of the casino scene, agreed that knowing the various ways house advantage is measured and quoted can aid in understanding and sometimes in minimizing the effect. But he cautioned against believing it can be eliminated.

No matter how much you dilute it,
Discuss, calculate, or dispute it,
Renaming the edge won't confute 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 were focused on those interested in gambling probability and statistics. He passed away in October, 2013.