The Arithmetic of Life and Death (17 page)

Women, it seems, intuitively understand the inevitability of streaks. Cecilia Sharpe, who won ten consecutive hands of blackjack at the annual Snohomish County Law Enforcement fund-raiser several years ago, then promptly quit, is an excellent example.

Men, on the other hand, seem to be more inclined toward the Law of Averages. Reginald DeNiall is a good example. He manages to lose money at craps, a dice game, at the Snohomish fund-raiser each and every year without fail. Last year, he asked Cecilia, whom he has known for many years and who seems to win at the annual Law Enforcement fund-raiser more often than she loses, to help him out.

After some gentle cajoling, Cecilia agreed. Then she looked Reginald right in the eye and said that she could show him how to win 70 percent of the time.

Every experienced gambler knows that there is no such thing as a system that can reverse unfavorable odds, much less produce a winning percentage of as much as 70 percent. That knowledge, and the inescapable reality of his own gambling career, caused Reginald to be skeptical in the extreme. Nevertheless, he asked Cecilia to explain her system.

Rather than explain it, Cecilia offered to prove it. She then removed her Sharp (no relation) calculator from her purse, along with a pencil and paper, and went to work. Reginald did his part by agreeing that any experienced craps player should win at least 48 percent of the time by avoiding long-shot bets.

With that figure in mind, and assuming a population of 1,000 craps bettors and an even bet of $10 per player per roll of the dice, Cecilia modeled the following result:

1. On the first roll of the dice, 480 players win $10 each. All of them immediately retire from the game as winners.
   
2. The other 520 lose the first bet. However, 120 of them win the next two bets in a row (520 X .48 X .48), leaving them ahead $10. They also retire from the game.
   
3. After three rolls, four hundred players remain in the game. Of that number, approximately 259 have lost two of three. But the other 141 have lost all three rolls and they are also asked to retire from the game.
   
4. Sixty of the remaining 259 (approximately 23 percent) win the next two rolls, after which they retire ahead. Of the remaining 199, seventy (approximately 27 percent) have lost three of four and they are asked
   to retire from the game. The remaining 129 (slightly less than 50 percent) have won two and lost three of the first five rolls and they are allowed to play on.
   
5. Thirty of the remaining 129 win both rolls six and seven, after which they retire ahead. Thirty-five lose both rolls and retire as losers, leaving sixty-four players to continue, all of whom have won three rolls and lost four.
   
6. Of the sixty-four players who continue, fifteen win the next two rolls and retire ahead and seventeen lose both rolls and retire after winning three rolls and losing six.
   
7. After nine rolls, 705 players have quit the game ahead $10. Another 263 have quit the game after falling behind by exactly $30. The remaining thirty-two players have won four rolls and lost five, so there are a total of 295 losers.
   
8. Although there are 705 winners and only 295 losers, and no loser has lost more than $30, the house is still ahead by more than $1,100, as follows:
   

   Number of Losers	Total Losses
   263	$7,890
   32	$320
   Total Losses	$8,210
   Less Winnings	$7,050
   House Advantage	$1,160

    
   

Thus, Cecilia proved that it is possible for there to be more than 700 winners out of 1,000 players, even though the house holds a clear advantage.

As a former CEO and a sitting congressman, however, Reginald featured himself as a high-profile player. He did not, therefore, see the point of quitting after only a few rolls of the dice. So he asked Cecilia what his bottom line was likely to be after 100 bets of $100 each. Cecilia quickly informed him that, according to the Law of Averages, he would be $400 in the red after winning forty-eight bets and losing fifty-two. However, depending on his streaks, he could either be ahead—or much farther behind. As was his nature, Reginald chose the Law of Averages and probable loss.

In the short run, streaks are indigenous to the Nature of numbers. Over the long run, however, the sum of all streaks normalizes into the Law of Averages. Whether you watch or whether you play, expect the streak. But don’t expect it to last because, sooner or later, the Law of Averages will have its day.

I
f coincidences are so rare, how can they be so common? The answer, it turns out, can be found in the simple aggregation of daily experience.

Given the tremendous power of our senses, it is not much of a stretch to estimate that we see an average of at least one new thing per second, especially if we include all of the people we see, all of the buildings and trees and shrubs, all of the cars, all of the parts of cars like license plates, and so on and so on and so on. Likewise, unless impaired, we ought to hear or touch or smell at least one new something per second.

The average sentient American adult is awake an average of about 16.5 hours per day, which is 990 minutes or 59,400 seconds. That adds up to a conservative estimate of
around 118,800 (2 × 59,400) observations or experiences per day. Out of so many, some are certain to be rare.

On the way to work last week, Cecilia Sharpe saw two Porsche 911s in a row on the Interstate. A fan of the famous German marque, Cecilia pulled closer to look them both over. One was a white, turbocharged model from the mid-eighties; the other a red, late-nineties convertible. There were no Porsche dealerships in the immediate area. The license plates were from different states. The drivers left the interstate at different exits so they weren’t traveling together.

Fifteen to sixteen million new vehicles are purchased in the United States every year. In 1998, however, Porsche sold only about 8,000 911s. Porsche sales have been even lower in the past, but they tend to be driven much longer than the average automobile. So Porsche 911s can be approximated to be about one in every two thousand cars on the road in the United States. Therefore, Cecilia’s odds of seeing two in a row at any one time were about one in four million (1 in 2,000 × 1 in 2,000), which she thought to be an extraordinary coincidence.

Being numerically inclined, however, she began to think it over during the rest of her trip to work in downtown Seattle. That evening, on her one-hour commute home in stop-and-go traffic, she counted more than six thousand cars traveling either with her or in the opposite direction. Since she faced the same quantity of traffic twice each day, she concluded that she saw a million cars every eighty-three to eighty-four workdays, or about every 3.6 months. Approximately every fourteen and a half months, therefore, and a total of perhaps thirty-three times over the course of her career, Cecilia would be likely to see two consecutive
Porsches on the road. From that perspective, the extraordinary coincidence of the consecutive Porsche 911s seemed a bit more ordinary.

Surprised by the ease of the explanation, Cecilia decided to apply the same logic to those mysterious airport encounters with old friends and acquaintances. First, she estimated that she knew at least one thousand people in the United States. She also estimated that she traveled by air twenty times per year, passing through an average of six airports per trip, three each way. At each airport, Cecilia estimated that she saw an average of two thousand travelers, even if she was just changing planes on the same concourse at a hub like Chicago, San Francisco, or Denver.

Therefore, every year Cecilia saw approximately 240,000 people at airports, about one in every 1,100 people living in the United States. In the aggregate of her life’s experience, however, Cecilia estimated that she had known more than 1,000 Americans well enough to recognize them. So, all things being equal, she concluded that she would unexpectedly encounter an acquaintance at an airport once every twelve or thirteen months.

By the same logic, if you see, hear, smell, or touch 118,800 things every day, then something you experience every eight or nine days will be, on average, a one in a million coincidence. It may be something very small, so you may not notice it. On occasion, it will be worthy of note. In a rare moment, it may truly be something extraordinary. If you experience or observe 118,800 events per day, then you are likely to encounter a one in a billion coincidence every twenty-three years or so.

Coincidences are common in life. Their frequency is a function of the thousands of things that we experience
every waking hour of the day. Thus, they are a product of our senses, which are Nature’s gift to us. Even though coincidences are not rare, it behooves us to observe each one and to be thankful to Nature for what each coincidence represents: one sensational experience in a lifetime of billions!

D
espite the famous weather, the Northwest is not a perfect place to live. One of the reasons is rapidly increasing traffic congestion. As usual, local politicians are steadfastly ignoring the situation. But the problem, especially during rush hours, is often complicated by drivers who insist on driving in the passing lane regardless of their slow speed.

This is no coincidence; there are just too many of them. Therefore, we must conclude that this phenomenon is directly attributable to the emergence of a covert road conspiracy called the PLLO, which stands for Permanent Left Lane Occupants. Thought to have been founded in the Seattle area in the late 1980s, the PLLO movement has since spread to almost every state in the nation, possibly with the financial backing of a secret, right wing, government agency.

These days, you can observe the PLLO in action on any
stretch of Washington highway at almost any time of the day or night. Members are immediately recognizable by their modus operandi, which is so consistent that it must certainly require in-depth training:

When traveling in pairs, committed PLLO members have even been known to leave the High Occupancy Vehicle lane to slow traffic in the passing lane. And they can sometimes be observed driving the exact same speed as the driver to their immediate right for miles.

The result is always the same. Lines of cars begin to form behind them. Clumps of traffic appear on otherwise uncongested highways. If there are enough PLLO on the road, as there frequently are in the Puget Sound area, then the clumps begin to congeal into PLLO-induced traffic jams. Faster drivers, who have been denied the passing lane by the PLLO, become impatient and then angry. Dangerous driving tactics, such as tailgating and passing on the right, inevitably ensue.