A puzzle of roulette gambling

Standard casino games such as roulette offer (almost) symmetric 50%-50% bets in a menu with numerous positively skewed gambles (with equal expected value). It is challenging to rationalize the popularity of casino gambling with traditional risk preferences. Yet, it is even more challenging to explain a more specific point that gamblers often choose (almost) symmetric 50%-50% gambles when casino offers positively skewed gambles. In this paper, we demonstrate that many well-known theories of decision making under risk cannot explain the finding that people place (almost) symmetric 50%-50% bets in roulette gambling. An expected utility maximizer either does not gamble on roulette at all (when utility function is concave or linear) or prefers to gamble on the longest possible shot and avoids (almost) symmetric 50%-50% bets (when utility function is sufficiently convex). Similarly, in Yaari’s dual model, a decision maker either does not gamble on roulette (when probability weighting function is convex or linear) or gambles on the longest possible shot avoiding (almost) symmetric 50%-50% bets (when probability weighting function is sufficiently concave in the neighborhood of zero probability). In Viscusi’s prospective reference theory, it can be optimal to gamble on several roulette numbers (rather than on one number) but not on one half of roulette numbers. A gambler who maximizes prospect theory never places a single bet on one half of roulette numbers due to the assumption of loss aversion.