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in reply to @tati's post:

in reply to @belarius's post:

Thanks for indulging my little guessing game! I figure I should come clean before leaving it too long.

If you roll all four dice, the sum of the resulting values are a very close approximation to samples from a standard normal distribution. In other words, these are collectively a z-score generator. This is accomplished by having the distribution generated by each die be approximately normal with a mean of 0.0 and a standard deviation of 0.5. Since variances are additive, the sum of four such random values results in a standard deviation of (0.5^2 + 0.5^2 + 0.5^2 + 0.5^2) = 1.0. And since there are thousands of possible unique combinations across the four dice, the resulting Gaussian distribution is quite smooth, despite each individual die yielding a pretty chunky discretization.