In the eighteenth century, for example, famed mathematician and naturalist Georges-Louis Leclerc, count de Buffon, tossed a coin 4,040 times, which resulted in 2,048 heads, or very close to half the throws. In more recent eras, the coin became linked to probability, statistics, and mathematical modeling. The coin is our simplest material connection to randomness. In the late thirteenth-century, King Edward II’s own exchequer records the royal losses of “cross and pile” when the king played against domestic servants. Legend has it that Julius Caesar would settle legal disputes with a coin toss.Ī medieval variant called “cross and pile” was a favored game for children (and even young apprentices) during the Middle Ages. Known as “heads or ships,” in reference to the images that appeared on the Roman sestertii, the coin toss was a children’s game of chance as well as a gambling game among the patrician elite. Since the Roman Empire and throughout the Middle Ages of Europe, a coin toss has offered a way to decide between two alternatives. Tossing a coin to decide an outcome is nothing new. A Short History of Coin Flips Roman coin depicts the head of Emperor Caracalla (via Wikimedia Commons) Sure, Rosencrantz and Guildenstern’s epic coin tossing demonstrates that such a thing is possible, we tell ourselves-it’s just not very probable. Part of what makes Stoppard’s scene so compelling is that it plays to the audience’s skepticism that someone could win 92 tosses in a row by betting heads. In other words, Guildenstern and other flippers of coins have a profound faith that odds of a coin toss are split 50/50, between heads and tails. When an unfair coin is tossed, it conveys an unfair manipulation of the world to shift the odds in someone’s favor. It means that one side can’t be favored, whether it’s inadvertent (say, the manufacture of the coin adds weight to one side, favoring a flip to one side over the other) or intentional (a two-headed coin).

A fair coin is one where either side of the disk has an equal chance of turning up, according to the probabilities worked out by the seventeenth-century Swiss mathematician Jakob Bernoulli. So long as the coin is a fair coin, that is. A flipped coin is assumed to be an unbiased way to pick between two possible outcomes, since both parties involved in the toss have an equal chance of winning. The toss of the coin functions as cultural shorthand. What makes it so absurd? What do we “know” about the probable outcome of tossing a coin that lets us “get” Stoppard’s joke? We know that the odds of a coin toss ought to be a 50/50, split between heads and tails, so surely there must be something wrong with the universe-something unfair?-for Rosencrantz and Guildenstern’s scenario to play out. More interesting than sussing out precise odds, however, are the premises of the scene. The 92 heads in a row is, however, more likely to happen than randomly shuffling a deck of cards and discovering that they appear sorted. According to NOAA’s website, it is more likely that a person in the United States will be struck by lightning four times in one year than repeat the results of Guildenstern’s coin tossing. The likelihood of Rosencrantz and Guildenstern’s scenario actually happening is 1 in 5 octillion, a probability so small that it is practically impossible to imagine. After Rosencrantz has successfully bet heads 77 times in a row, Guildenstern proclaims that, “A weaker man might be moved to re-examine his faith, if in nothing else at least in the law of probability.” He ends up flipping heads 92 times in a row. Guildenstern spins another coin and it lands as heads again. Guildenstern flips a florin and Rosencrantz predicts that it will land as heads. In Stoppard’s scene, the bit actors Rosencrantz and Guildenstern kill time during a production of Shakespeare’s Hamlet by betting on coin tosses.

Tom Stoppard’s classic play Rosencrantz and Guildenstern Are Dead opens with two Elizabethan players, some well-stocked prop moneybags, and the flip of a coin that lands as heads.

Heads or tail coin flip