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It seems obvious that a gambler is motivated to take risks by expectation of gain. In the development of a theory of gambling behavior the need has been recognized of determining the gambler's “utility function” with respect to money, that is, the relative worth to him of various amounts of money. But more than money may be involved in the gambler's expected gain. Gambling itself may have a “utility” for him. Here a theory of gambling decisions takes into account both utilities.
Royden et al. (Wed,) studied this question.