How Do the Casinos Make Money from Million Dollar Players? - Friday 26th of May 2006

"Casino insider" shows on television seem to portray wealthy gamblers as idiots. Folks pursued because of the big bucks they're sure to lose. And who don't mind as long as their new best friends on the casino staff pander to them brashly enough.

High-limit players do represent good profit potential for the casinos. But not, as the shows imply, because the house advantage its edge dooms them to leave their bundles with the bosses. That's not how house advantage works. Even individuals who play foolishly can win substantial sums.

On one recent program, a host remarked that it didn't matter he didn't actually care whether his million dollar player won or lost. As long as this person gave the casino enough action so the joint had a shot at his bankroll.

True. True. And false. True, the casino shouldn't care whether a particular patron prevails or fails. True, the criterion should be the amount of play. And false, "enough" action isn't meant for the casino to get a shot at taking a bettor's whole stake; it's to expose a large gross wager, or "handle," to the erosive effect of the edge on all the money placed at risk.

Imagine a gambler with a million dollar reserve who likes to play blackjack head-to-head against the dealer. Who past experience suggests will put in 10 hours at the tables during a weekend, betting one spot half the rounds and two or three spots a quarter of the rounds each. Who'll wager $5,000 to $10,000 per spot with an average of $7,500. This works out to a handle of roughly $20 million on that $1 million wad during the expected 10 hours.

With perfect Basic strategy and liberal rules, the house has 0.4 percent advantage. Its theoretical "take" from the $20 million is $80,000. This, not a shot at the $1 million pocketbook is the value of the player to the casino. And it's the monetary basis for deciding how much to spend to attract and hold this customer.

The casino has a chance to grab the whole pie, of course. The probability the player will exhaust the $1 million before completing 10 hours is 9 or so percent. Conversely, at the end of 10 hours, the patron's chances are 14 percent of being ahead by $500,000 and something like 2 percent of winning $1 million. Were time not a factor, a player determined to go double or nothing with the bosses would have 65 percent chance of busting out and 35 percent of withdrawing $1 million from the casino's coffers.

The casino's prospects improve if the bettor plays poorly and gives up 1 percent edge. The theoretical take rises to $200,000 and the likelihood of the house having the whole $1 million before the end of 10 hours is 10 or 11 percent. The player's chances of serious gain drop under 10 percent for $500,000 and 1 percent for $1 million. The $1 million double-or-nothing figures are 81 percent for the house and 19 percent for the player.

The key is the role of the edge. It drives the theoretical take $80,000 with the hypothetical good player and $300,000 with the poor. Not the $1 million in the bettor's designer fanny pack, but still a decent gross profit. It also biases the swings in fortunes associated with the volatility, making it more likely for the player to lose than win any given amount.

Oh yes, that bit about the host not caring whether a particular high roller wins or loses. It presupposes the casino getting enough action at a certain level, not necessarily all from one person or all in one day, that the upswings and downswings caused by volatility will average themselves out and edge will prevail. Those television shows don't bring this out. They simplistically caricature high rollers as heading for a fall and imply that house advantage is pushing them inexorably toward it. Maybe this is what appeals to the solid citizens on their couches who tune in, simultaneously fantasizing about being in the shoes of the rich and famous while hoping they get their comeuppance. Here's how the poet, Sumner A Ingmark, nailed this side of human nature:

The rich getting richer brings throes of resentment,
To those who won't work for their own self-contentment.

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