This paper examines the optimal portfolio composition for a risk-preferrer who is a gambler. His indifference curves in the expected return-risk space are shown to be convex to the origin under the assumption of decreasing risk preference, and his efficient opportunity locus is in general discontinuous and convex. The optimal portfolio for such a risk-preferrer may be a diversified one, composed of several lottery and nonlottery assets. Diversification requires that there be lotteries which offer substantially higher risk than those attaching to assets with higher expected yield, making gambling an activity distinct from business investments. Risk taking and the purchase of lotteries is shown to decrease relatively with wealth.