Why the casinos shouldn't want to wipe you out

Flo and Moe each go to a casino with $100 and play roulette for $5 per spin. All the bets they make are "inside" – on spots, lines, corners, rows, columns, and so forth such that the house edge is 5.26 percent. By coincidence, they bet the same way on every round, although not on the same numbers. For instance, when Flo bets $5 on the 7-8-9 row, Moe puts his nickel on 19-20-21. Or, when Flo takes the 1-2-4-5 corner, Moe is on 11-12-14-15.

Flo turns out to make some lucky guesses, and after 40 spins – about an hour – she's up $100 and quits. Moe can't get out of the path of traffic; after the same 40 spins, he's gone broke.

Which of them do sophisticated casino bosses like better? A no-brainer of a question? Flo took their $100 while Moe donated his. They must hate Flo and love Moe. Right? Sorry, wrong!

If they each bet $5 on 40 spins, gross wagers of $200, their business is worth 5.26 percent of $200, or $10.52. This, regardless of what they took out or left behind.

The reason is that the casino makes its money on the edge applied to every bet. The swings, which are driven by the volatility of the game, can go up or down and are a wash for the house over an extended period with a lot of action. Since Flo and Moe made comparable bets in terms of amounts at risk, payoffs, and chances or success or failure, the games they played had the same volatilities. Flo's wagers, in this admittedly contrived example, happened to increase her bankroll; Moe's decreased his, pretty much at rates equal in magnitude but down and not up.

Pat yourself on the back if you see a small flaw in the previous logic. In Flo's case, volatility had to overcome the $10.52 edge-induced loss and send her bankroll up by $110.52 to earn $100. In Moe's the volatility only had to add $89.48 to the $10.52 edge-induced loss to cost $100. But, the general idea is valid.

Of course, if you only know about Moe, you might think the casino liked him better because he bit the dust. Give him a comp worth $3.78 for a buffet priced at $15.95 to make him happy, so he'll return and lose another $100 next week. Knowing about both Flo and Moe or, more precisely, understanding that their performance in the fictitious small is what occurs on the average in the true large, a different picture emerges.

Consider bets – like "dozens" – with lower volatility. Flo hits a profit of $50 and prances away, while Moe loses $50 and slinks off, both in the same number of spins. Maybe they each bet $1 on five rows. Because of the lower volatility, the bankroll swings are smaller. Pretend it takes them 80 spins to reach these levels. The gross wager is $5 x 80 or $400. And the casino's earnings due to edge are 5.26 percent of $400 or $21.04.

If you only watches Moe, you might think the house did better in the higher-volatility game than this. Here, he left $50 and took the rest home. In fact, the house earned more because he played more rounds. The joint also made more from Flo, but not because she won $50 rather than $100. In both instances, the reason is that edge accounted for $21.04 instead of $10.52.

The point is that bankroll fluctuations resulting from volatility are bidirectional. And, on the average – which is all the casino should care about – a game and mode of play that is conducive to one bettor busting out in short order is also instrumental in quickly sending another punter over the top. And the joint doesn't make its money by knocking some solid citizens for a loop then clearing the space for fresh blood. It derives its profits from folks making lots of bets on their bankrolls.

This apparent anomaly is not easy to grasp. Most players, and some bosses, don't get it at all. But who ever said that what you see in a casino is what's there? The counterintuitive coupleteer, Sumner A Ingmark, wrote this rhapsodic rhyme about such results:

Too often the apparent, Conceals the aberrant.