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I was speaking with a good friend and mathematician at MIT. We discovered that we each admire Tom Stoppard’s play Rosencrantz and Guildenstern are Dead, which presents Hamlet from the point of view of two minor players, the comically indistinguishable students from Wittenberg.

In Shakespeare’s play, Rosencrantz and Guildenstern are unwittingly used in a plot to kill Hamlet. But Hamlet revises the plot and instead these characters unwittingly travel to meet their own deaths.

Stoppard’s play is told from the befuddled perspective of these bit players—the prototypes, perhaps, of such comic innocents as Laurel and Hardy, Lloyd Christmas and Harry Dunne, and Pozzo and Lucky. The audience is rooted in the saga of these minor characters, and when the Hamlet play breaks out on stage from time to time, it evokes the saying, “I went to the fights and a hockey game broke out.”

The Stoppard play actually begins before his heroes have even joined the Shakespeare play. They have been “sent for” and they are killing time by flipping coins. Guildenstern flips a coin 104 times by my count and 103 times in a row it comes up heads. There are two streaks actually. While they are alone with each other, heads comes up 92 times in a row. When the troupe of actors appears the game continues with a streak of 11. This is the most famous streak in literature.

The MIT professor’s pleasure in Rosencrantz and Guildenstern are Dead was mathematical. He knows that people underestimate the likelihood of streaks, expecting the mythical “law of averages” to smooth things out. That a famous play depicts a rare but perfectly possible event is a “teachable moment” to a probability professor. Indeed, the ruminative Guildenstern offers among other explanations the one a mathematician would favor —“a spectacular vindication of the principle that each individual coin spin individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does” (Rosencrantz and Guildenstern are Dead, Act One).

How unlikely then is a streak of this length? It can happen, so it’s not impossible. But how many times would one have to flip 103 coins to expect to get a streak of all heads or all tails? If every person who ever lived (around 110 billion) flipped 103 coins simultaneously every second since the beginning of the universe (around 14 billion years), we could expect just two such streaks to occur. Rare, but even a streak of this prodigious length is expected to occur.

What about the streak of 11? Well, Hamlet was probably first staged around the year 1600, since the first quarto (1603) identifies the play as having been “diuvers time acted…in the Cittie of London…and elsewhere” (Thank you Professor Paula Berggren). Let us imagine that the play has been put on daily from January 1, 1600 to January 1, 2010 (ignoring the Plague, the Roundheads banning of theatre and any other inconvenient facts of history). Imagine, furthermore, that during each staging, Rosencrantz and Guildenstern play the coin flipping game, tossing a fair coin 103 times every day. They would play this game 149,752 times. Since we can expect streaks of 11 heads or tails to occur about 4.6% of the time in a trial of 103 tosses, we would expect, therefore, over 6,888 streaks of 11. Streaks happen.

The source of my delight in this streak is different. The subject of Book of Odds in its broadest sense is the relationship between the past and the future. If we have an accurate count of past events such as incidents of arson, how much can we infer about the likelihood of arson in the future? When actuarial data can be applied to cancer statistics, the historical data proves very helpful in prediction for a period of time, barring a major change in diagnostic or treatment regimens.

The past history of coin flips tells you nothing, however, about the next toss. But what if one lived in a world in which the rules of past, present, and future were systematically different from ours?

That is one way of reading Stoppard’s play and one which delights me.

Consider that the rules of tense in plays are different than, say, in newspapers. Events in plays are always expressed in the present tense. Hamlet the son speaks to the ghost of Hamlet the father. Ophelia commits suicide. Polonius stands behind the arras.

Tense conventions, consistently applied, can establish whatever vantage point seems most interesting. Hamlet is in the eternal present because it is always occurring, always immutably, and yet always surprisingly, not because it has changed but because we have.

This time perspective is similar to the tense conventions of the Odds Statements. These place the reader at a moment of maximum dramatic irony: after the facts have been collected but before they have been revealed. Whether the past reveals anything at all about the future is the question users of Book of Odds are invited to ask at every moment. How and when is induction helpful?

In my reading of Stoppard’s play, the 103 heads come up identically because the bit players, while offstage, operate in a time peculiar to their status as not yet having materialized in the play, which is their reason for being. They are in time’s “green room” and what happens in this limbo state once happens over and over again. There is no randomness here, there are no distributions, but instead the Groundhog Day state of eternal recurrence. The play’s coin streak is not meant to reveal the possibility of streakiness, but rather the opposite—to imagine a dreary state in which the streakiness which makes life fascinating cannot occur.

But what about the 104th toss? The one that came up tails?

Take the mathematician’s view and it is no surprise at all. The odds were 1 in 2. Coming up tails is no more surprising than the heads before it and its appearance is fully independent of the streak which preceded it.

Here, however, is an alternate interpretation. The discovery that it is tails occurs just as Ophelia and Hamlet run across the stage. Guildenstern has his foot on the coin and none of us knows whether it is heads or tails. The stage lighting changes as Ophelia and Hamlet cross the stage. It is Shakespeare time now, not Stoppard time. Whether the coin is heads or tails is unknown. Perhaps in Stoppard time the coin could not have been anything but heads, and in Shakespeare time nothing but tails. Or vice versa.