If the face-up card is red, the gambler wins $11 but if the face-up card is black, the gambler loses $9. The utility maximization theory will most likely predicts that most people will accept the gamble.
The term "utility maximization" was developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the problem of utility maximization tells about the problem consumers face such as "How should I spend my money in order to maximize my utility?" which is a type of optimal decision problem.
The theory's problem consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preference.
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