Sophie's Dice has a feature that allows you to statistically test any valid expression using the supported dice notation.

To do this, right-click or long-press the 'sumbit' button besides the expression input bar, or press the 'Test' button when editing a saved expression.

• Line Graph
• Bar Charts
• Sampling

Line Graph

The line graph provides a summary of all results of the tested expression. (See here to learn how to write expressions with multiple results for comparison).
The vertical axis of the graph is the percentage of all sampled outcomes for each result (this is equivalent to the result's probabilities, with enough sampling).
The horizontal axis of the graph lists the recorded outcomes.
Each result is color-coded (the colors are enumerated beneath the graph)

The line graph has three ways to display the sampled outcomes:

• = - Shows the percentage of a result's samples that equal each outcome.
• <= - Shows the percentage of a result's samples that are below or equal to each outcome.
• >= - Shows the percentage of a result's samples that are above or equal to each outcome.

Bar Charts

Below the line graph is a bar chart for each tested result. The charts display each recorded outcome and what percentage of the result the outcome represents.
The chart can be viewed using the same options as the line graph (=, <=, and >=), and ordered either by outcome frequency or alhanumerically.
Above each chart will be its result's Mean (average/expected), Minimum, and Maximum value outcomes.

Sampling

Expression testing will not directly tell you the probabilities for given expressions (because this could become computationally... absurd), instead Monte Carlo sampling is used.
That is to say, the statistics displayed are the outcomes of many (MANY) pseudorandom simulated rolls of the dice.

The default number of samples taken is 5000 and should give a good approximation of what the probabilities are for most dice expressions, however it is worth noting the limitations of this approach:

• More samples will more accurately represent the expresion's probabilities
• Expressions with very unlikely outcomes might not be represented at all. (if an outcome has a true 1/1,000,000 liklihood, there is a good chance it won't happen with only the default 5000 samples)

The number of samples is displayed in the top-right, and the process of sampling can be paused or resumed by pressing it.
To change the maximum number of samples, see the Target Samples setting.