  It seems reasonable to prefer \(A\) (which offers a sure $100 million) to \(B\) (where the added 10% chance at $500 million is more than offset by the risk of getting nothing). It also seems reasonable to prefer \(D\) (an 10% chance at a $500 million prize) to \(C\) (a slightly larger 11% chance at a much smaller $100 million prize). But together, these preferences (call them the Allais preferences) violate Independence. Lotteries \(A\) and \(C\) yield the same $100 million prize for tickets 12–100. They can be converted into lotteries \(B\) and \(D\) by replacing this $100 million prize with $0.