Newsletter Signup
Stay informed with the
NEW Casino City Times newsletter! Recent Articles
Best of Alan Krigman
|
Gaming Guru
You Can't Rely on Averages when You're Dealing with Small Chances9 December 2001
The situation is different for rare events, those with extremely low probabilities. Averages then become fickle forecasts. Progressive jackpots at Caribbean Stud offer good illustrations. The probability of a royal in Caribbean Stud is one out of every 649,740 hands. After this many hands without a grand slam, the jackpot would be around $160,000. But, it's common for jackpots to reach $250,000 or $300,000, indicating that nobody's scored in over two or three times 649,740 tries. It's also not unusual to notice totals under $20,000 or $25,000 on several successive visits to the same joint, suggesting that the jackpot's been hit and reset more than once during a relatively short interval.
These figures afford several insights about low-probability events. The most important is that averages or expected values are not necessarily good indicators of real performance when a single random event can have a large relative impact. If you're dealing with the frequency of high pairs at video poker, a few more or less than the theoretical number don't have much significance after 1,000 rounds. Getting 210 or 220 - five less or more than the numero-noodniks predict - is no big deal. But, look what happens at Caribbean Stud. Players should average one jackpot in 649,740 hands. But the table shows they indeed have the same prospect, 36.8 percent, of getting none as one. And the chance is pretty good, 18.4 percent, of getting two. Similarly, in 1,299,480 hands, two jackpots are expected; but one and two have the identical probabilities of occurring, 27.1 percent. And, there's a 13.5 percent chance of not getting any. On the flip side of the coin, the casinos might be quick to call in their fraud squads if they dished out more than five jackpots within about 2 million hands. However, this can be anticipated by chance rather than hanky panky in 8.4 percent of all 2-million hand cycles. Here's another way the bosses could view the same figure. They can be 100 minus 8.4 or 91.6 percent confident they won't have to pay jackpots to more than five solid citizens in 2 million honest hands. Enough not to stew about sacrificing their silk-suit salaries; not so much to fold the game if it happens. There's also the issue that the statistics of high and moderate probability events may bear on individuals. But the arithmetic of remote phenomena applies to whole populations - no one member of which gets near the mean value. This imbalance was implied by the improvisator, Sumner A Ingmark, in his impressive amoebaeum: Why are averages unfair? Recent Articles
Best of Alan Krigman
Alan Krigman |
Alan Krigman |