Re: Dice Game
Can the general solution even be expressed mathematically? It seems like it requires a conditional ("if current roll is < EV of replacing, replace. Lather, rinse, repeat."). It could be easily done as a recursive function, though.
FWIW, According to my calculations, for n=20 rolls you should replace anything lower than a six for the first 15 rolls, then take a 5 or 6 for rolls 16-18, then 4, 5, or 6 on roll 19, and of course whatever you can get on roll 20.
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