How 100% correctness matters in games and security

Yesterday, I was Merlin in Avanlon Resistance, and a blissful innoccent servant was arguing how unlikely two minions would propose to be on the same boat, and therefore should be ruled out, which happened to be the truth. I was trying hard to be too fool to understand his plausible argument and reject his proposal, allegedly to my limited experience. In the end, I managed to change the vote but inevitable received the respect from the assasin.

Today, when meeting my advisor, I make a metaphor about the importance of fully verified software: Suppose there are some caves with treasure of publicly known value, or nothing at all. For each explorer, they can choose one cave and share the treaure with all the others in the same cave. Therefore, assuming an equilibria is reached and the number of explorer grows to large enough, the share of each cave with a treaure is the same. As a result, you just need to pick anyone of the non-empty cave.

How are these two senario related? As long as some strategy has some positive value, then it is always possible to be exploited, and the reward could be still considerable regarding the “unlikeness” from the perspective of the defender or “lack of profit” from the view of other competitor. If you know mixed Nash equilibrium, then probably you get it already.

Finally, it introduces the importance of fully verified software: no matter how much “confidence” you have after either the reasonning of probablity model, unit tests or history, such unsound assumption will accumulate its reward overtime to the crackers. The only way to discourage them is leaving no treasure in your cave at all.