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# Why do so many players lose at the casino, and who gets the dough?

5 April 2010

A common article of faith among civilians who scoff at casinos is that gambling victimizes or at least imposes a regressive de facto tax on the very solid citizens least able to afford the hits. The presumption is, since the operators have an edge in the games, players as a whole lose their lunch money to the fat cat owners. The occasional winners? Hah! Bait to seduce the suckers.

Far more gamblers do lose than win. But why? And how much of the lost lucre flows to the greedy bosses and how much elsewhere?

The chief elements in this determination are the establishment's mathematical advantage or edge and the amount bet over a period of time. Not that edge and aggregate wager forecast how a particular punter will fare in a stipulated session of reasonable duration. The calculations are valid only as averages across huge numbers of bets made by many patrons over long time spans.

Pretend a person with a \$100 poke plays the 25-cent, three-coin-maximum slots. At a moderate pace, a spin every 10 seconds, such a bettor will get 1,080 rounds in three hours. The handle is \$0.75 times 1,080, or \$810. If the machine has a low 93 percent player return; edge is the remaining high 100 - 93 or 7 percent.

The average casino gross from gamblers who bet \$810 total with 7 percent edge is \$56.70. This, regardless of their initial stakes. Not all the \$56.70 goes into the casino coffers. Policies vary, but a (pre-recession) rule of thumb is that players receive about a third of their theoretical losses from edge back in comps. A third of \$56.70, almost \$19, is on target for the buffet meals coveted by 25-cent slot buffs with \$100 stakes. Deducting the \$19 allowance, the house's gross drops from roughly \$57 to \$38. Even this isn't pure profit. These joints are expensive to run.

After accounting for loss due to edge in this example, players still expect, statistically, to have around \$43 of their original \$100. Casino aficionados know from experience this isn't the way it works. A few people may luck out but everyone else who enters enthusiastically with \$100 departs despondently without it.

What happens to the \$43 left after the edge takes its toll on the \$100 stake? The casino collects it. But the bigwigs have already been paid by the losers from the edge; the rest goes to the winners. Simplistically, how many who begin with \$100 and give up \$57 to edge must lose the other \$43 for every \$1,000 or \$10,000 winner? A lot. Divide \$1,000 or \$10,000 by \$43 to get 23 or 232.

Suppose edge was less usurious. For instance, 2 percent. The bosses would hold an average of \$16.20 on a cumulative wager of \$810, leaving about \$84 rather than \$43 from \$100 for winners. Kiss the comps good-bye, of course. However, more bettors starting with \$100 would finish as winners and the hauls would be larger. But the majority of players would lose their \$100 anyway.

One reason they'd lose is volatility, the characteristic ups and downs of the games. This overwhelms edge in the short run of most specific sessions. But volatility can go in either direction.

A second cause of defeat is that gamblers are rarely satisfied winning less than, the same as, or even a mere two or three times their bankrolls. This isn't avarice. It's the utility principle. Casino visitors with \$100 budgets can readily put together this much cash. (See, here it is!) They're gambling for amounts they know they can't amass otherwise, so they tend to go for broke.

A third factor in poor performance is "risk of ruin," the chance players will tap out on down-swings and lack the wherewithal to continue and try to recover. Mathematically, the larger the win goal relative to a loss limit, the greater the risk of ruin.

The ultimate lessons here are that routs are more apt to result from player choice than house advantage, and that losers pay the winners as well as the bosses. Here's how the punter's poet, Sumner A Ingmark, put the predicament:

Losers pay for winners, it's an undisputed matter,
Changing house advantage only biases the data.

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Best of Alan Krigman
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 focused on gambling probability and statistics. He passed away in October, 2013.
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 focused on gambling probability and statistics. He passed away in October, 2013.