Random flipping of coin a lot like tracking stock market

Question: How is flipping a coin a lot like tracking the volatile stock market?

Answer: Imagine a series of 1,000 coin tosses where Henry bets on heads every time, Tommy on tails, poses John Allen Paulos in "A Mathematician Plays the Stock Market."

The coin is "fair," so the two players are equally likely to be in the lead. But once one of them gets a bit of a lead, he's likely to stay in the lead over most of the 1,000 flips. People find this hard to believe, says Paulos, because they believe in the "gambler's fallacy," thinking that the coin's deviations from a 50-50 split are "governed by a probabilistic rubber band: the greater the deviation, the greater the equalizing push toward an even split."

Not so! Even if Henry were way ahead, with 525 heads to Tommy's 475 tails, his lead would be as likely to grow as to shrink. "Likewise, a stock that's fallen on a truly random trajectory is as likely to fall further as it is to rise."

True, in the long, long run the flips approach 50 percent to 50 percent, but that's as a percentage, not actual numbers. Since lead switches are relatively rare, it wouldn't be surprising if either Tommy or Henry came to be known as a "winner" or "loser." Similarly, if one professional stock picker outperformed another by a margin of 525 to 475, he might wind up interviewed on Moneyline. "Yet he might, like Henry or Tommy, owe his success to nothing more than getting 'stuck' by chance on the up side of a 50-50 split."

Also, of 1,000 stocks, roughly 500 might be expected to outperform the market next year merely by chance, like a flipped coin. Of these 500, 250 will likely do well for a second year, 125 for a third, etc., and one will do well for 10 years in a row, by chance alone. Yet "some in the business media are likely to go gaga over the performance."

Question: What's the trick to safely hand-petting a stingray in the wild?

Answer: A trip to "Stingray City" of the Cayman Islands just might do it, where for 35 years fishing crews have gathered conch and cleaned them over a certain barrier reef, says David G. Myers in "Psychology, 7th Edition." Stingrays (shark relatives) in the surrounding bay gradually became accustomed to these treats and started hanging out in numbers. Scuba divers then began feeding the increasingly friendly rays by hand. "Today, tourists can do the same, and can even pet the rays as they graze past them."