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How Casinos Measure House Advantage, and What the Values Mean24 January 2001
By Alan Krigman
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).
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.
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,