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BGonline.org Forums
A quiz to use with dice complainers
Posted By: Fabrice Liardet In Response To: A quiz to use with dice complainers (W Womack)
Date: Wednesday, 7 October 2009, at 9:01 a.m.
I don't think that your answer is perfectly fair. While even a dice whiner could be made to understand that all sequences without doublets are equally probable, that does not mean that all are equally random.
Basically you are implying the definition of randomness given by classical information theory. I am not sure it makes sense here. For example, would you say that a long sequence with exactly one doublet in it is half as random as a doublet-less sequence of the same length ?
The definition which is generally used for randomness comes from algorithmic information theory, and defines randomness as programmatic incompressibility. A sequence like "12 12 12 .... 12" (I made it longer than 4 to make the comparison clearer) is highly compressible, as it is generated by the following short program : "repeat 12 n times". By something like Occam's razor that sequence is hence more likely to have been generated by the former program than by a random number generator which happened to be stuck on 12. In that sense the dice whiner's logic is not as bad as it looks.
Those are notions that I understand only partially and I might have explained them the wrong way, for better explanations look for "Kolmogoroff complexity" and "minimum description length principle", or ask a real mathematician.
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