Short-term deviations from the norm

Casino gambling is a numbers game, and if you've played for very long, you're likely to have some of the numbers committed to memory:

An average of 1 in every 6 rolls of two dice will total 7. When you make a single-number bet in double-zero roulette, you have a 1 in 38 chance of winning. If you play 9/6 Jacks or Better video poker at expert level, your average return will be 99.5%.

For the casino, those numbers will hold up day after day, year after year. And if you play often and keep track of your results, they'll hold up for you, too.

But on one visit to the casino, one session at a table or machine, there's room for a lot of deviation from the norm. There has to be. If you were guaranteed that, in a half hour at the craps table, the numbers would roll in precisely the proportions they should, you'd never play. The casino would win every time, and that's no fun.

We play because sometimes the shooter will get on a long streak without rolling a 7, because our roulette number comes up two or three times in a row, or because a royal flush or a few fours of a kind temporarily give us a video poker payback percentage in the hundreds or thousands.

What happens then? Celebration time. Those short-term deviations from the norm mark our best times the casinos. The times for high fives all around, to tip the dealer a little extra, to try the steak house instead of the buffet. The times we win.

But although such times are special, they're also part of the normal odds of the game.

That two six-sided dice will total 7 an average of once per six rolls doesn't mean that every set of six rolls will yield a 7. If you watch 36 rolls of the dice, there don't have to be six 7s, nor do there have to be 36 7s in 216 rolls. Shooters can and do go six and more rolls in a row without a single 7. It works the other way, too. It's also common to see two sevens in a row, and I've seen four 7s within six rolls.

What those 1-in-6 odds mean is that on every roll, there is 1 chance in 6 that the shooter will roll a 7. It doesn't matter if the last roll was a 7. It doesn't matter if the last three rolls were 7s. It doesn't matter if there hasn't been a 7 in a couple of dozen rolls. When the shooter picks up the dice each time, there is 1 chance in 6 that the roll will be a 7.

It's the same kind of deal in roulette. The ball might have landed in No. 17 on the last couple of spins, and it might not have come up at all in 50 or more trials. But on the next spin, there is a 1 in 38 chance that the ball will land on 17. That's a 1 in 38 chance on this spin, the next spin, the spin after that — it never changes.

And in video poker, where royal flushes turn up about once per 40,000 hands — the exact number depends on your playing strategy — the chances if you've just hit a royal on the last hand are still 1 in 40,000, and they're still 1 in 40,000 even if you have the stamina and bankroll to have persisted through 100,000 hands without a royal.

When we win, have we defied the odds? Overcome the law of averages? Not at all. Winning streaks are part of the normal expectations designed into any casino game. Given enough trials, anything that can happen eventually will, and there are plenty of trials in casinos every day.

For one hand when you draw a royal, or for one hot streak at a craps table where no 7s turn up for 20 rolls, or for one shining moment at the roulette wheel where the ball lands on your birthday number two spins in a row, it looks like the law of averages has been suspended. The improbable is happening.

With the millions of trials going on in any casino on any day, the improbable is a certainty. Big wins and winning streaks will happen. Still, the casino makes its money. Losing streaks, when the winners show up less often than you expect, also are a certainty.

The numbers that are in effect on every play — 1 in 6 chance of rolling a 7, 1 in 38 chance of your number in roulette, 1 in 40,000 chance of a royal flush in video poker — will make sure the house gets its edge. Over millions of plays, the results will come up in something very close to those proportions.

In one visit for one person, though, streaks where the results vary wildly from the norm can and do happen. They have to, or else we'd never win.

Listen to John Grochowski's "Beat the Odds" tips Saturdays at 6:20 a.m., 2:50 p.m. and 7:41 p.m. and Sundays at 8:20 a.m., 2:50 p.m. and 10:42 p.m. on WBBM-AM, News Radio 780 in Chicago, streaming online at www.wbbm780.com.