Law, Luck, and the Leningrad Elephant

The laws of chance seem similar, but have diverging implications, when applied to the questions of "when," "which," "where," or "who" as opposed to those of "whether" or "if." Casino games, by and large, involve the latter. But many solid citizens err by thinking in terms of the former.

Say that 38 people play roulette, each person betting $10 on a different number. One participant is going to win $350. That's a certainty. Luck enters the picture in determining who it will be. From the viewpoint of each player, the probability of winning is the same, 1/38. But circumstances differ. There's no certainty. Luck, here, isn't a matter of which spin will produce a winner. "If" is the operative condition. Players could continue for any arbitrary time spans and never hit, an enigma for those who chase losses believing that the law of averages says a win is due.

Slot buffs frequently compound the misconception. Instead of simply believing that a jackpot is imminent, many are convinced that machines go though cycles and are certain to hit eventually.

Gamblers aren't alone in misinterpreting the laws of chance this way. Rocket scientists, real ones, also do it. Here's an example.

In the late 1960s, the Soviet Union sent a series of instrumented probes to the planet, Venus. The Venera spacecraft were to land and transmit data back to Earth about conditions at the surface.

It was known from conventional optical and radar astronomy that the atmosphere was much denser on Venus than on Earth. But nobody was sure how much. This presented a dilemma. The laws of physics required the probes to be rugged or, like submarines going too deep in the ocean, they'd be crushed by the pressure on the way down. But rugged meant heavy, and the laws of gravity said this was undesirable for launching. So the designers had to compromise in strength and weight. They planned for a factor of 20 relative to the density of Earth's atmosphere.

Venera 4 successfully entered Venus' atmosphere on Oct 18 1967 and began relaying data. However, when transmission ceased, calculations based on the laws of motion showed the vessel to be 15.5 miles higher than expected. Some Soviets insisted that the probe achieved its objective and was destroyed on impact. They explained the 15.5-mile anomaly by saying it must have landed on a mountain. Western scientists instead concluded that atmospheric density on Venus was far greater than the designers imagined, so the unit disintegrated the indicated distance above the surface.

The noted American astronomer, Carl Sagan, in The Cosmic Connection, describes meeting shortly thereafter with a leader of the Soviet project. Sagan argued that detailed radar mapping of Venus from Earth had shown many mountains, none over a mile high. The chance, he asserted, of any peaks with elevations above 15 miles was minuscule. And, that of a probe hitting such a summit, were it even possible to exist on Venus, exceptionally unlikely. The Soviet scientist replied by asking what Sagan thought was the chance that the first German bomb dropped on Russia during World War II would kill the only elephant at the Leningrad zoo. Sagan admitted that the probably was extremely small.

Ah, the Russian exclaimed, yet this was just what happened. He left, satisfied that the fate of the Leningrad elephant answered Sagan's objection. It proved that despite the low probability, Venera 4 could have hit a 15-mile-high mountain and therefore it did. He was wrong. It didn't. (He may also have been wrong about the elephant. In conflicting anecdotes, the first allied bomb on Berlin killed only the elephant at that city's zoo, or killed all the other animals and freed the elephant to roam the streets.)

Remember the Leningrad (or is it the Berlin?) elephant next time you're depending on the law of large numbers at the casino. Say, when you're in line at a cash machine, figuring a few more bets will get you out of trouble. The poet, Sumner A Ingmark, whose elegies are elegant and never elephantine, said it like this:

I dreamed a dream of fortune, of fate that never was,
Where anything can happen, but something other does.