People often make judgments about uncertain facts and events, for example `Germany will win the world cup’. Here we present a rational analysis of these judgments: we argue that a guess functions as a compressed encoding of the speaker’s subjective probability distribution over relevant possibilities. So, a statement like `X will happen’ encodes information not only about the probability of X but also, implicitly, about the probability of other possible outcomes. We test formal computational models derived from our theory, showing in four experiments that they accurately predict how people make and interpret guesses. Our account naturally explains why people dislike vacuously-correct guesses (like `Some country will win the world cup’), and it might shed light on apparently sub-optimal patterns of judgment such as the conjunction fallacy.