clearstream
(He, Him)
Maybe I have this wrong, but can't probabilities of not finding be roughly described by (1-.02)^N in the first case, and chance at N * chance at last N concatenated in the second case?I really haven't come any farther along in my thoughts process, but you're right.
Let me start out by stating the "best" outcome: since the module does detail all five locations, the ideal is if they have to visit a good number of them. But of course the best thing is if they only miss out on their prize if they make a mistake, or skip something. (Rather than just making a bad roll, that is)
A) When the probability of the idol being at each site is a flat 20%, the chance of not finding it at or before site N is
Site 1 = .8^1 = 80%
Site 2 = .8^2 = 64%
Site 3 = .8^3 = 51%
Site 4 = .8^4 = 41%
Site 5 = .8^5 = 33% which is forced to be 0%
B) When the probability of the ideal being at each site cascades, the chance of not finding it at or before site N is
Site 1 = 80%
Site 2 = 60%
Site 3 = 40%
Site 4 = 20%
Site 5 = 0%
Is that correct? The first case is like drawing from a deck where initially there are unlimited cards, and the one we want appears 20/100, until we've drawn four cards and then on our fifth draw all the cards we don't want are instantly removed. The second case is different, because the distribution in the deck is gradually refined forcing the probabilities to remain exact.
Is that right, or has my maths-fu failed me utterly? Summoning @Ovinomancer?
Edit: I see that I've actually added a case, where a roll is made at 20% chance at each site (which is different from making one roll up front so we know the idol is under one of these five cups, and the odds perforce change as each cup is lifted and shown to be empty.)
@CapnZapp so your initial two cases are actually one case described in two different ways, as far as I can tell, but what about this additional one? Any value in using it?
Edit 2: Makes me think you could use the - players choose the site they will visit next, right after they choose one of the remaining sites is revealed to be empty, players can now switch to choosing a different site out of those left if they want to - conundrum. (They should switch and choose a different one, is how it plays out.)
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