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. Getting a HHH might not look "random," but if it is a fair coin it is random.Heads. The possible outcomes are HHH, TTT, as well as HTT, HTH, HHT, THH, THT, TTH. If you flip a coin three times, its possible by random chance to get all heads or all tails. With two coin flips the possible outcomes are HH, TT, HT and TH. That means that when you flip a coin two times, each time you have a 50% chance of getting a H or T regardless of what the previous flip gave you. You can use a coin toss as a random sampling scheme to pick between two samples.Įvery time you flip a fair coin there is exactly a 50% probability of getting a heads and a 50% probability of getting a tails. Flipping a coin is a great way to randomly choose between two possible outcomes (in this case, between the two end zones).Īn unbiased coin has a 50% chance of getting heads and a 50% chance of getting tails on any given toss, so the chance of picking either of the two end zones is equal (if it wasn't, the coin would not be fair). Ever wonder why they flip a coin at the start of a football game? A coin toss of a fair (unbiased) coin is a type of random sampler.
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