Before the die roll, there’s a 1⁄3 chance that you’ll get the reward ($20), and a 2⁄3 chance that you’ll be asked to pay the penalty. For the expected utility to be 0, (2/3)*|penalty| = (1/3)*$20. Multiply both sides by 3, and 2*|penalty| = $20, so |penalty| = $10.
Before the die roll, there’s a 1⁄3 chance that you’ll get the reward ($20), and a 2⁄3 chance that you’ll be asked to pay the penalty. For the expected utility to be 0, (2/3)*|penalty| = (1/3)*$20. Multiply both sides by 3, and 2*|penalty| = $20, so |penalty| = $10.
How’s that for minor reputational damage?
Crap. Never mind. You know, this happens when I’m sufficiently tired, and it’s scary. I am a poopy head.
I’ll take that as a successful mugging. ;)