Casino Math Isn't Always What You Learned in School

ere I writing science fiction, I might depict a Class-M planet where a cosmic anomaly reversed certain familiar laws of math or physics. Maybe, no way to create light but methods of beaming out darkness. Or machines that speed up, not stop, when unplugged because energy accumulates rather than dissipates. The plot would require Earthlings to adjust their behavior accordingly, or die.

Come to think of it, Earth has places where ordinary math doesn't apply. Casinos. And not just because solid citizens believe laws of probability are suspended there. Rather because money has nowhere to go but into and out of player pockets and casino coffers. Still, what's won or lost at machines and tables doesn't balance what a house thinks it earns on the action. The anomaly, by the way, is that casinos are governed by a logic under which they don't consider what they do as gambling with their patrons.

Say Izzie and Lizzie each hit the floor with $100. They each find slot machines "set" to return 90 percent to players and hold 10 percent for the house. This means if $1 million passes through the slot over an extended period, $900,000 will be disgorged into the tray and $100,000 diverted into a bucket behind the panel.

Izzie's machine is a hundred-dollar wheeler-dealer. He inserts one token and never sees it again. Lizzie's takes $1 at a time. She plays for hours then finally goes broke. They each lose $100. But the casino bean counters think they earned $110, not $200.

Why? Casinos rate slot players by volume and hold percentage. So they peg Izzie at $10 -- 10 percent of the $100 he dropped into the slot. They have Lizzie for roughly $100 -- because by recycling intermediate winnings, she fed about $1000 into the slot. The machine can't tell it's seeing the same money over and over again. And 10 percent of $1000 is the $100 the casino earned.

Now imagine that Izzie put in his $100 token and "won" one coin. He actually "pushed" and got his own $100 back. And pretend that Lizzie was down to her last dollar, dropped it into the slot, and hit for $100. She'd be at break-even. Neither player won or lost a cent, but the casino thinks it earned the same $110 as before.

Here's another. Arthur and Martha each belly-up to craps with $100. Arthur drops $25 on the pass line and takes $75 triple odds when the point becomes four. Martha bets her whole stake flat on the line. The shooter passes. Arthur wins $175; Martha wins $100.

Regular arithmetic would have the house losing $275 on these two bets. Casino actuaries disagree. They don't think they've lost at all; they figure they've earned $1.76.

Why? As on the machines, the casino calculates earnings at table games based on the edge inherent in the bets, regardless of outcome. The edge on flat pass line bets is 1.41 percent; it's zero on money taken as odds. So Arthur's action earned the casino 1.41 percent of $25 -- $0.35, and Martha's bet earned the house 1.41 percent of $100 -- $1.41. These earnings sum to $1.76.

What if the shooter had sevened-out? Arthur and Martha would each lose $100. But the back room bookkeepers wouldn't chalk up $200 on the action. They'd credit themselves $1.76, just as they did when the shooter passed and the couple won a combined $275.

If normal math doesn't hold in a casino, how do you adjust your behavior to survive, even prosper? By remembering you're not in a joint that gauges civilians by what they leave in the cash box. Under governing casino logic, your customer "rating" has much less to do with what's in your wallet before and after your visit than with the extent of your action and the edge built into the game you play. So don't expect to be pampered because the house has your $100 after you lose one flat craps line bet. The accountants think they made only $1.41 on this wager.

As Sumner A Ingmark, to whose verse the normal rules of poetry often don't apply, once wrote:

From straight paths of arithmetic,
the casinos have meandered,
You're measured not by win or loss;