PLAYING IT SMART by ALAN KRIGMAN

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.

More, in a situation like that for blackjacks, you'd have cause for concern were you to get only half the expected naturals in 10,000 hands. The table shows, though, that while three royals are expected in 1,949,220 Caribbean Stud hands, players are as apt to get only two -- 22.4 percent, and wouldn't ask the Supreme Court to order a recount were they to get only one, or none at all, the chances there being 14.9 and 5.0 percent respectively.

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? Take a million paupers and a trillionaire. With what should I them compare? To a million people with an equal share.

(c) 2000, ICON/Information Concepts Inc

English Harbour is one of the finest casinos online. They offer you your own personalized start page, $35 free with a minimum first purchase of $35 and first rate software.The software must be downloaded, but the wait is well worth it.The largest slot machine jackpots on the internet.