>>13890657Actually I think this is way more complicated than I realized, since there are two ways the being can be lying.
He can be lying about his ability to predict the future (!A), and he can also be lying about his behavior (!B). If we assume that both have a 50% probability then your options are:
1. Take just the $1k box. Easy $1k, no chance involved.
2. Take just the $1m box.
E(A & B) = 0.25 * $1m = $250k
E(!A) = 0.5 * (0.5 * $1m + 0.5 * $0) = $250k
E(A & !B) = 0.25 * $0 = $0
E = $500k
3. Take both boxes.
E(A & B) = 0.25 * $1k = $250
E(!A) = 0.5 * (0.5 * $1m + 0.5 * $0) = $250k
E(A & !B) = 0.25 * $1.001m = $250.25k
E = $500.5k
So still best option is still to take both.
