Chances Are . . .: Adventures in Probability - Softcover

Ellen Kaplan trained as a classical archaeologist and has taught math, biology, Greek, Latin, and history.She and her husband, Robert, run the Math Circle, a nonprofit foundation dedicated to joyous participatory learning, and are the authors of The Art of the Infinite.

Discovering

Even chance, which seems to hurtle on, unreined, Submits to the bridle and government of law. – Boethius (Anicius Manlius Severinus, last of the classical minds, whose desperate attempt to summarize all ancient knowledge was cut short by imprisonment, torture and death at the hands of Theodoric the Ostrogoth.)

Anyone can talk to God; it’s getting an answer that’s difficult. Few of us can regularly count on divine guidance, and experience shows that going to an intermediary is not always satisfactory. The Lydian ruler Croesus planned to invade Persia, so he prudently checked with the oracle at Delphi. "If Croesus crosses the Halys, he will destroy a great empire," said the crone in the fume-filled cavern. A true prediction – but the empire was Croesus’ own. Pressed by his enemies, Saul went to the witch of Endor and had her call up the ghost of Samuel. Samuel was hardly helpful: "The Lord hath rent the kingdom out of thine hand, and given it to thy neighbor." The king must have left feeling like a stressed executive told by his doctor to exercise more and eat less. It’s easy to see the appeal of a mechanism that would restrict Destiny to simpler, less irritating answers.

Many things happen unpredictably, on the larger scale (defeats, disasters) and on the smaller (things dropped, things flipped). It is almost a given of human nature to posit a connection between the two scales: between local accident and universal doom. Sortilege – telling fortunes by casting lots or throwing dice – is a tradition that dates back almost without change to before the dawn of writing. Fine cubic ivory dice (with opposite sides adding up to seven, just as in Monte Carlo or Las Vegas) accompanied pharaohs into their tombs. Even then, dice must have been a form of amusement as well as a tool of divination . What, after all, would a pharaoh need to predict in the afterlife? Pausanias, the Baedeker of the ancient world, nicely captures this double role of dice. He describes the great hippodromos at Elis, where, in the jumble of memorials and victory tributes, stood the Three Graces, resplendent in giltwood and ivory, holding a rose, a sprig of myrtle – and a die, "because it is the plaything of youths and maidens, who have nothing of the ugliness of old age." Perhaps that is the secret of this shift of dice from oracle to game: the young are too busy living to be interested in fate; the old know the answer all too well.

Dicing became the universal vice of the Roman aristocracy: the emperor Augustus, otherwise the pattern of self-restraint, spent whole days gambling with his cronies. Claudius wrote a book on dice and had his sedan chair rigged for playing on the move. Caligula, of course, cheated.

Meanwhile, in the dense, whispering forests across the Rhine, the Germans gave themselves completely to gambling – with savage literalness. Tacitus said: "So bold are they about winning or losing, that, when they have gambled away all else, they stake their own freedom on the final throw."

The pure gambling games played in Roman times all seem to have been variants of hazard, the progenitor of modern craps, played with either dice or the knucklebones of sheep. Wherever the Roman armies camped you find hundreds of dice – a fair proportion loaded. In Augustus’s favorite version of hazard the highest throw (all dice showing different faces) was called Venus, appropriately for a pastime that was also a conversation with the gods. But even with the gods, humans seek an edge: Venus was the highest throw, but also the most likely. After all, we don’t go to the temple to add to our bad luck: all divination retains its popularity only as long as it gives a high proportion of favorable answers. And once you know that daisies usually have an odd number of petals, you can get anyone to love you.