Artefact2 / fairdice

Check for dice fairness using ECDF and chi-square tests.

Synopsis

fairdice is a very simple C program to check for dice fairness.

Usage:

fairdice <num-sides> < rolls.txt

The tests

• A ECDF test, similar to Kolmogorov-Smirnov goodness-of-fit test, but adapted to discrete dice. The ideal CDF with fair dice is randomly generated using the Monte-Carlo method. This method is more accurate for dice with lots of sides, where the goal is usually to beat a certain value.

• A regular chi-square test. Thanks to the GNU Scientific Library for doing the heavy math. This method will test against any kind of skewness but is less powerful on large dice.

• Finally, check observed frequencies and their 99% confidence interval.

Examples

fairdice 6 < examples/syg-d6-blue.txt

SmpSize:   n=180
ECDF:      p=0.7500
ChiSq:     p=0.8583
ConfInt99: OK

This dice is very likely fair. Increase the sample size if you need to be more sure.

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fairdice 20 < examples/syg-d20-blue.txt

SmpSize:   n=1000
ECDF:      p=0.6563
ChiSq:     p=0.6943
ConfInt99: OK

This dice is very likely fair.

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fairdice 20 < examples/syg-d20-green.txt

SmpSize:   n=1000
ECDF:      p=0.1407
ChiSq:     p=0.1336
ConfInt99: 9+ 18-

This dice looks problematic, two sides are not in their confidence intervals. Requires further testing.

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fairdice 20 < examples/syg-d20-black.txt

SmpSize:   n=1000
ECDF:      p=0.1875
ChiSq:     p=0.0042
ConfInt99: 12-

This dice is probably unfair according to the chi-square test, but not according to the K-S test. Requires further testing.