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Kingreaper comments on Open Thread: July 2010 - Less Wrong
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EDIT: I am an eejit. Dangit, need to remember to stop and think before posting.
Umm, not quite. The die being biased towards 2 and 5 gives the same probability of 3.5 as the die being 3,4 biased.
As does 1,6 bias.
So, given these three possibilities, an equal distribution is once again shown to be correct. By picking one of the three, and ignoring the other two, you can (accidentally) trick some people, but you cannot trick probability.
This is before even looking at the maths, and/or asking about the precision to which the mean is given (ie. is it 2 SF, 13 SF, 1 billion sf? Rounded to the nearest .5?)
EDIT: this appears to be incorrect, sorry.
Intuitively, I'd say that a die biased towards 1 and 6 makes hitting the mean (with some given precision) less likely than a die biased towards 3 and 4, because it spreads out the distribution wider. But you don't have to take my word for it, see the linked paper for calculations.
Ahk, brainfart, it DOES depend on accuracy. I was thinking of it as so heavily biased that the other results don't come up, and having perfect accuracy (rather than rounded to: what?)
Sorry, please vote down my previous post slightly (negative reinforcement for reacting too fast)
Hopefully I'll find information about the rounding in the paper.