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Dice math: why 7 rules the table

Two dice aren’t twice one die — they’re a bell curve. The probability basics behind board games, craps, and your d20.

By Noble Erne, LLC · 5 min read · Reviewed July 2026

One die is simple: six faces, each with a 1-in-6 chance. Perfectly flat odds. The interesting thing happens the moment you add a second die — the odds stop being flat and start being a triangle.

There are 36 ways two dice can land, but only one of them makes 2 (1+1) while six of them make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So 7 shows up once every six rolls on average, and snake eyes once every 36. That single fact is the skeleton of craps, the reason the robber activates on 7 in Catan, and why the 6 and 8 hexes are the ones worth fighting over.

More dice, more bell

Add a third die and the triangle smooths toward a bell curve: middle totals common, extremes rare. This is the same statistical force (the central limit theorem) that makes so much of nature bell-shaped — dice are just the cheapest demonstration of it. Roll 3d6 on our homepage twenty times and watch the 10s and 11s pile up while 3s and 18s stay shy.

A d20, by contrast, is deliberately flat — every result 1 through 20 equally likely, exactly 5% each. That's a design choice: D&D wants gloriously swingy outcomes where a natural 20 is always one clean roll away. Flat dice for drama, summed dice for predictability. Game designers pick the curve before they pick the dice.

Two fallacies to retire

The gambler's fallacy: after five rolls without a 6, a 6 is NOT 'due' — dice have no memory, and the odds reset every throw. And the hot-hand version: five 6s in a row doesn't make the die lucky, it makes it a die (or, if it keeps up, a loaded one — real casinos use transparent dice precisely so nobody can hide weights). Every roll on this site is an independent event from a cryptographic source. The streaks you'll see are what genuine randomness looks like — streakier than intuition expects.

Published by Noble Erne, LLC. Enterprise systems consultant with a background in SAP implementation, software documentation, and instructional design. Builds the tools and writes the explainers on this site. Corrections to this guide go to the contact page and are reviewed before publication.

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