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July 14th, 2015, 01:39 PM   #1
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Simulating a coin toss with probability of heads 1/π and tails 1 - 1/π using a die

How could you simulate a biased coin that has P(Heads) = 1/π and P(Tails) = 1 - 1/π . Using a fair six sided die? thanks. Struggling with this question.
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July 21st, 2015, 04:39 AM   #2
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Look up for von Neuman's method. There is a simple equation for generating such simulations (I couldn't remember, google it).
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July 21st, 2015, 04:55 AM   #3
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Write out $1/\pi$ in base-6 and start rolling dice until the last die rolled doesn't match the relevant digit. (Either subtract 1 from each roll, or count 6s as 0s.) Since

$$1/\pi=0.152431022133341414113121401254\ldots$$

you can stop if you roll a 0 or 2-5 on the first roll, or a 1 on the first roll and 0-4 on the second roll, or 1 and 5 on the first two rolls and 0-1 or 3-5 on the third, etc. If you end up on the low side call it heads, otherwise tails.
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