The coins that Rosencrantz and Guildenstern flip at the beginning of the play symbolize both the randomness of the world and the play’s exploration of oppositional forces. The pattern of coin after coin landing heads up defies the expectation that the laws of probability actually do work and that the world makes clear sense. Instead, the coins suggest that the world is ruled by randomness and the occurrence of highly improbable events. The point made by the coins is reiterated by the way that Rosencrantz and Guildenstern get caught up in a string of improbable situations that, from their perspective at least, occur entirely at random and make no sense whatsoever. Randomness is often contrasted to determinism, the notion that events happen according to some unbreakable plan. Rosencrantz and Guildenstern Are Dead combines randomness with determinism to suggest that chance seems deterministic. Rosencrantz and Guildenstern feel that they can do nothing to counteract the chance’s determinist force, just as they can do nothing to stop the coins from landing heads up.
The coins also stand in for the play’s exploration of oppositional forces. Although the coins land heads up so many times that they may seem one-sided, coins are actually two-sided, a fact the audience is reminded of when a coin lands tails up. This two-sidedness reflects the many sets of opposites in the play, from the division between Guildenstern’s philosophical pessimism and Rosencrantz’s pragmatic optimism to the dual nature of language, which is a source of both pleasurable wit and painful confusion. Imagining the world as a set of opposites is somewhat at odds with the coins’ symbolism of a world dominated by chance, since oppositions impose order on the world. Stoppard resolves this tension by having the oppositions in the play break down. Rosencrantz and Guildenstern reveal themselves to be more complex and less oppositional than they initially seem, for instance. This breakdown of oppositional forces is reflected in the coins in that the laws of probability suggest that flipped coins should split evenly between heads and tails, but Stoppard shows that such a simple model does not account for the sheer randomness of the world.
Almost the entirety of Act III takes place onboard a boat to England, and Stoppard uses the boat to reflect the experience of living in a universe that is beyond our control. Guildenstern initially responds quite positively to being on the boat, noting that it is pleasurable to give up responsibility and allow oneself to simply be carried along through life. This resignation to life’s randomness is freeing, Guildenstern believes, because it means that we no longer have to worry about whether we are making the right decisions—we can just relax and see where life takes us. The play suggests that this is a naïve and dangerous attitude, however, as Rosencrantz and Guildenstern’s refusal to take any action for themselves will end up getting them killed. Guildenstern realizes that getting on the boat was a mistake, since giving up their freedom meant that they lost all control over their lives. Simply giving in to the randomness of the world, as well as believing that giving in leads to freedom, are self-destructive gestures. These gestures make us like men on a boat they cannot steer, unable to do anything about our experiences.