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A sum defined by count and face range

For n dice with s numbered faces, the smallest total is n and the largest is n × s. The expected total is n(s + 1)/2. With three fourteen-sided dice, the range is 3 through 42 and the average is 3 × 15/2 = 22.5. The formula assumes each die is independent and every face from 1 through s is equally likely.

Three d14 values in practice

Suppose the three displayed faces are 4, 11, and 13. Their total is 28. A total of 28 can be reached by many different triples, whereas 3 requires 1, 1, 1 and 42 requires 14, 14, 14. That is why totals near 22 or 23 occur more often than endpoints even though every individual d14 face has the same chance.

Changing either input changes the shape

Adding a die broadens the possible total and concentrates probability relatively more around the middle. Increasing sides broadens each die's contribution. These are different design choices: 2d20 ranges from 2 to 40 with a middle near 21, while 1d39 has nearly the same range but a flat distribution. Matching only the minimum and maximum is not enough.

Rules this configuration cannot infer

The fields describe ordinary positive integer dice summed together. They do not express labelled faces, weighted faces, subtraction, success counting, exploding dice, or a reroll condition. Use a purpose-built rule or calculate the special operation separately when the desired game mechanic is more than an independent uniform sum.

A quick plausibility audit

For three d14, any total below 3 or above 42 is impossible. The expected 22.5 is not an allowed integer result, but totals around 22 and 23 have many combinations. Check both the hard endpoints and the intended distribution when adapting this configuration; a plausible-looking total can still come from the wrong dice model. A written notation such as 3d14 makes the count and face range auditable.

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