The Second Bet's Higher Bar

An interviewer offers you game A: a one-shot bet with an expected profit of $+\$5$ and a standard deviation of $\$20$. You take it, and you tell him it is right at the edge of what you would accept -- any less edge and you would pass.

He then offers game B, also one-shot and independent, take-it-or-leave-it at a size he sets, with a standard deviation of $\$50$.

(a) If you price risk consistently, what expected profit does B need before you take it? (b) Your friend says B needs only $+\$12.50$, "because that is the same reward per unit of risk." Who is right? (c) What is actually being tested here?