Every fair die has the same simple arithmetic: each face carries a 1-in-faces chance, and the long-run average is the midpoint of its range. A d6 averages 3.5 per roll, a d20 averages 10.5. Add dice together and the distribution changes shape: one die is flat, two make a pyramid, three and more start to look like the famous bell curve. That is the central limit theorem, live at your game table.
It is also why game designers pick 2d6 when they want reliable middles with rare surprises, and a single d20 when they want drama: on one die, a critical hit is exactly as likely as a dull average roll.
Every face here comes from your browser's cryptographic generator, mapped onto the die with rejection sampling so a d20 face is 5% exactly rather than 5% roughly. How random is random covers where that entropy comes from, and the lotto draw applies the same generator to a full line of numbers.