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July 14th, 2015, 01:39 PM  #1 
Newbie Joined: Jul 2015 From: Ontario Posts: 1 Thanks: 0  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.

July 21st, 2015, 04:39 AM  #2 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 122 Thanks: 43 Math Focus: Area of Circle 
Look up for von Neuman's method. There is a simple equation for generating such simulations (I couldn't remember, google it).

July 21st, 2015, 04:55 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Write out $1/\pi$ in base6 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 25 on the first roll, or a 1 on the first roll and 04 on the second roll, or 1 and 5 on the first two rolls and 01 or 35 on the third, etc. If you end up on the low side call it heads, otherwise tails. 

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1 or π, coin, die, heads, probability, simulating, tails, toss 
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