No, the caves is a shell game. A shell game is not a game in which you have a 1-in-x chance of guessing right. It is a game that makes you think you have a 1-in-x chance of guessing right, but where you in fact have 0 chance of guessing right, because it is not a guessing game at all. Which is what "pick a door, any door" is. And Xykon fell for it hook, line and sinker, since he thought it was all about "getting lucky" when in fact it was a "do all of them before the monster regenerate" or whatever. Had he kept with his original "1-2 doors a night" he'd never have beaten the dungeon, because it is a shell game and he was never going to "get lucky".
Its a video that explains why you don't talk to the US police without a lawyer (the qualifier is kinda important, I feel. It is not a video recommending monastic vows of silence)
Grey Wolf