Bus Fare and Circumstance

I conceived the following scenario as a teenager, perhaps after having read of utility theory. A rich man has gone for a long walk carrying only 50 cents with him for he anticipated no expenditures. He tires and learns that there will soon be a bus that would take him nearly home. The bus fare is 75 cents. He rationally offers a double or nothing bet to a stranger.

The moral is that sometimes utility theory depends on current situations as well as net wealth. The rich man’s current utility function is temporarily convex instead of concave!

If the wager is flipping a fare coin and either

then we have a win-win wager—both parties have a positive expectation of utility.