What Do You Want from the Casino Experience, and at what Price?

19 July 2004

By Alan Krigman

Gamblers are often admonished to set loss limits and win goals, then quit accordingly. Few do. Queues at casino cash and credit card terminals attest to solid citizens who exhaust what they'd planned to risk and try to recover by digging a bit deeper into the cookie jar. And everyone remembers at least once when their fortunes peaked before they gave it all back. And maybe more.

An old margarine commercial on TV concludes "It's not nice to fool Mother Nature." Similarly, it's not wise to fight human nature. So this won't be a lecture on setting and sticking to limits and goals you'll ignore in the heat of the action. But you may appreciate mileposts suggesting how you affect your chance of success by settling for less or insisting on earning more with the same investment, and how you influence your shot at reaching some profit point by sizing your bankroll.

The precise figures depend on the game you play and how you bet. The trends are similar regardless of the details, however, so an illustration based on flat bets at double-zero roulette will give you the general idea. Say you bet $1 on each of 15 spots. You're risking $15 to win $21. Probability of success on any spin is 15/38 or 39.5 percent. House advantage is 5.26 percent. Typical bankroll fluctuation per spin -- the standard deviation -- is $17.60. Skewness is +0.43, implying that you'll need only a moderate degree of luck to come out ahead in the short term.

As a baseline, assume you have a $200 drop-dead stake and wish to double your money. The probability you'll earn $200 profit before losing $200 is about 27 percent. The first of the accompanying tables shows how your chance of reaching a win goal on your $200 loss limit changes with lower or higher objectives. The figures show that aiming for lower earnings with the same stake improves your chances of success dramatically, while insisting on greater profits gradually drops your prospects toward zero.

Chance of reaching various win goals with $1 on each of 15 spots at double-zero roulette starting with a $200 bankroll.

win goal	probability of success
$50	69%
$100	49%
$150	36%
$200	27%
$250	20%
$300	15%
$350	11%
$400	9%

You can also think about how your likelihood of earning $200 varies as your buy-in shrinks or grows. This effect is indicated in the second table. Here, wagering with a wad that's too small for your aspirations sharply reduces your chances of success. However, adding to your stash yields only marginal improvements.

Chance of earning $200 betting $1 on each of 15 spots at double-zero roulette starting with various bankrolls.

bankroll	probability of success
$50	11%
$100	18%
$150	23%
$200	27%
$250	29%
$300	31%
$350	32%
$400	33%

Note that the two scenarios are not symmetrical. For the same size bet and bankroll, chances of reaching various earnings levels before going bust span the range from very high to almost nil. For the same bet size and win goal, chances of success with alternate bankrolls go from close to zero to some level typically far shy of 100 percent. The reason for the limit is that as you seek higher profits with constant bets, using a richer reserve to recover from possible downswings, larger numbers of rounds are implied -- corresponding to more action and greater erosion of your fortune as a result of the house advantage.

Maybe this won't convince you that gambling is anything but a way to grab as much money as you can lay your paws on, and use it to a shot at getting rich. But it may prompt you to at least think what you want from the casino experience, and what it's worth to you. The irascible inkslinger, Sumner A Ingmark, put it thusly:

Between a triumph and defeat,
Lies ample room for self-deceit.