We introduce lotteries - that is, randomized trading - into search-theoretic models of monetary exchange. In the model with indivisible goods and fiat money, we show that in any monetary equilibrium goods change hands with probability 1 and money changes hands with probability 7 where 7 < 1 iff the buyer has sufficient bargaining power. In the model with divisible goods, a nonrandom quantity of goods q changes hands with probability 1 and, again, money changes hands with probability 7 where 7 < 1 iff the buyer has sufficient bargaining power. Hence, the implicit assumption made in the previous literature that lotteries are ruled out is restrictive. Moreover , q may be less than but can never exceed the efficient quantity ( a result that cannot be shown without lotteries). We also consider the implications of lotteries for models with direct barter or commodity money. If commodity money has sufficient intrinsic value, we show the equilibrium quantity q is necessarily efficient ( another result that cannot be shown without lotteries).