betterbias

betterbias - Achieving Better Bias - - - The Better Bias...

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Sheet1 Page 1 Achieving Better Bias --------- ------ ---- The Better Bias Bureau takes M faced biased dice with known biases and makes from them N faced biased dice with desired biases. More specifically, if you have an M faced biased die with probability pm[j] of throwing face j, for j from 1 though M, but you really want instead an N faced biased die with probability pn[i] of throwing face i, for i from 1 through N, then good old B3 will give you a method of achieving your desires. The method is this. You are to consider throwing your M faced die an infinite number of times and writing out the resulting faces, f1, f2, f3, . .., as an infinite fraction .f1f2f3. .. base M. The fraction will be a number, call it F, in the range from 0 through 1. For any number r, 0 <= r <= 1, we can compute the probabil- ity that F <= r. Let rn[i] be defined so that probability F <= rn[i] = probability that an N faced die throw is k for some k <= i = sum of pn[k] for k from 1 through i Then when you throw a value F with your M faced die, you
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This note was uploaded on 04/29/2011 for the course IT 201 taught by Professor K.v.arya during the Spring '11 term at IIT Kanpur.

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betterbias - Achieving Better Bias - - - The Better Bias...

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