Tabletop RPGs often use the term "roll M N-sided dice", or "MdN" for short, to mean, "generate M high-quality random numbers between 1 and N". The dice themselves are merely an implementation detail; they could be physical dice, or some random-number generator built into a collaborative RPG software program, etc. It's common to refer to coins as "d2"s, because that's the function that they serve.
Another interesting die roll that comes up quite often is "Md3"; the 3-sided die is usually implemented by taking the more familiar 6-sided die and replacing 4,5,6 with 1,2,3 on its faces.
The percentile die, which is a golf-ball sized polyhedron with 100 faces, is also quite iconic, though rarely used in practice due to being ridiculous. Most people just roll two 10-sided dice, instead.
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OK, so after a certain point, the mugger increasing his threat will cause you to decrease your belief faster. After a certain point, the mugger increasing his threat will cause (threat badness * probability) to go decrease.
That implies that if he threatens you with a super-exponentially bad outcome, you will assign a super-exponentially small probability to his threat.
But super-exponentially small probabilities are a tricky thing. Once you've assigned a super-exponentially small probability to an event, no amount of evidence in the visible universe can make you change your mind. It doesn't matter if the mugger grows wings of fire or turns passers by into goats; no amount of evidence your eyes and ears are capable of receiving can sway a super-exponentially small probability. If the city around you melts into lava, should you believe the mugger then? How do you quantify whether you should or should not?
I don't see why this is necessarily a problem.
The claim that the mugger will torture 3^^^3 people, unless you give them $100, is so implausible that there should be no possible evidence that will convince you of it.
Any possible evidence is more plausibly explained by possibilities such as you being in a computer game, and the mugger being a player who's just being a dick because they find it funny.