You have not proven the key really is on the server. From a game-theory point of view I have no reason to believe it is there, and thus no reason to attack.
Shouldn’t the expected value of attempting this somehow include the likelihood of the key actually being on the machine? Surely the probability is much higher than 0? I would guess the expected value for actually being the first one is around $300, not 0
You may need to brush up on your game theory. It's worth it to spend $1 for a 1% chance to win a million dollars. You don't need to be certain the key is there for it to be worth it to do a supposedly trivial exploit.
what a pedantic way to look at the world
Not sure that logic really holds up. If the cost of trying is low, why wouldn't you?