log10d10

Log10d10 is a compact, informal notation used in some mathematical and gaming contexts to denote taking the base-10 logarithm of the outcome of rolling a ten-sided die (a d10). It is not a standard mathematical operator, but a shorthand for the random variable Y = log10(X), where X is the result of a fair d10 roll with values 1 through 10.

The random variable log10d10 takes the discrete values log10(1), log10(2), ..., log10(10), i.e. {0, 0.30103, 0.47712, 0.60206, 0.69897, 0.77815, 0.84510, 0.90309, 0.95424, 1.0}. Each of these ten outcomes is equally likely in a fair die roll, giving a simple average-based analysis of its distribution.

Statistical properties for a fair d10 roll yield an expected value of log10d10 of approximately 0.656. The distribution is discrete and moderately skewed toward smaller values, reflecting the nonuniform spacing of the logarithm values across the range 1 to 10. The exact variance can be computed from the listed values and is typically around 0.09, depending on the precision used in the logarithm values.

Applications of log10d10 appear mainly in data normalization, teaching demonstrations of logarithmic scales, or game design discussions where a die outcome is analyzed on a logarithmic basis. In formal mathematics, one would simply express the variable as log10(X) with X representing the die roll.