We investigate the ability of expected utility theory to account for simultaneous gambling and insurance. Contrary to a previous claim that borrowing and lending in perfect capital markets removes the demand for gambles, we show expected utility theory with nonconcave utility functions can explain gambling. When the rates of interest and time preference are equal, agents seek to gamble unless income falls in a finite set of values. When they differ, there is a range of incomes where gambles are desired. Different borrowing and lending rates can account for persistent gambling provided the rates span the rate of time preference.