Well, you said that it had a “good chance” of failing. I see your point if by “good chance” you meant probability close to 1. But if “good chance” is more like 50%, then it would still have been worth it. Let’s say MAD had a 10% chance of failing:
EU(MAD) = .1 * U(world destruction)
EU(NH) = .5 U(one city destroyed) + .05 U(world destruction)
Then EU(MAD) < EU(NH) if U(world destruction) < 10 U(one city destroyed).
Well, you said that it had a “good chance” of failing. I see your point if by “good chance” you meant probability close to 1. But if “good chance” is more like 50%, then it would still have been worth it. Let’s say MAD had a 10% chance of failing:
EU(MAD) = .1 * U(world destruction)
EU(NH) = .5 U(one city destroyed) + .05 U(world destruction)
Then EU(MAD) < EU(NH) if U(world destruction) < 10 U(one city destroyed).