 Continuity implies that no outcome \(A\) is so bad that you would not be willing to take some gamble that might result in you ending up with that outcome, but might otherwise result in you ending up with an outcome (\(C\)) that you find to be a marginal improvement on your status quo (\(B\)), provided that the chance of \(A\) is small enough. Intuitively, Continuity guarantees that an agent’s evaluations of lotteries are appropriately sensitive to the probabilities of the lotteries’ prizes.