Craps Variants

Anyone who’s ever calculated the chances of winning at craps may remember being surprised by how fair the game is. (Spoiler Warning If you haven’t calculated these odds but feel you might enjoy the challenge, you should do so before reading on, because I’m about to spoil it for you rather thoroughly in the name of exploring a more general case. A full solution may also be found in the rather excellent book, Fifty Challenging Problems in Probability with Solutions.
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Semantic Code

se-man-tic (si-man’tik) adj.     1. Of or relating to meaning, especially meaning in language. Programming destroys meaning. When we program, we first replace concepts with symbols and then replace those symbols with arbitrary codes — that’s why it’s called coding. At its worst programming is write-only: the program accomplishes a task, but is incomprehensible to humans. See, for example, the story of Mel. Such a program is correct, yet at the same time meaningless.
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