Risk-averse Expected Utility (EU) decision makers with wealth-dependent utility functions may find themselves indifferent between accepting and rejecting an indivisible risky prospect. Bell (1988) showed that under these circumstances it may be EU-enhancing for the decision maker to engage in an actuarially fair pre-decision side bet, accepting the indivisible risky prospect conditional upon winning the side bet. In this letter we show that decision makers restricted to actuarially unfair side bets may optimally engage in a sequence of individually EU-enhancing side bets. This contrasts with the case of actuarially fair side bets where only one such bet will be undertaken. The actuarially unfair side bet's optimal stake size can be a significant proportion of the individual's initial wealth. Nevertheless after losing the side bet wealth may still remain within the interval of interim (utility) convexity, whereupon it is optimal to place another side bet.