Guide

Dice probability, explained without the math class.

Last updated: August 15, 2026

Every die roll follows predictable odds — even though each individual roll feels random. This guide breaks down the probability behind the rolls tabletop players hit most often: 2d6, d20 checks, and advantage/disadvantage. Try any of the rolls below on the dice roller.

Single die: uniform, not "lucky" or "unlucky"

A fair d6 gives every face — 1 through 6 — exactly a 1-in-6 (16.67%) chance on every roll, regardless of what came before. Dice have no memory. If you roll three 1s in a row, the fourth roll is still 1-in-6 for a 1, not "due" for a different number. This is called the gambler's fallacy, and it trips up more tabletop players than it should.

Why 2d6 isn't uniform: the bell curve

Rolling two dice and adding them together behaves very differently from rolling one. There's only one way to roll a 2 (1+1), but six ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). That's why 2d6 systems — common in board games and some tabletop RPGs — cluster around the middle instead of spreading evenly.

Notice 7 is six times more likely than a 2 or 12. This is the same principle behind craps, Settlers of Catan, and any 2d6-based system.

d20 mechanics: flat, not curved

D&D's core resolution die, the d20, is a single die — so unlike 2d6, every result from 1 to 20 has an equal 5% chance. A DC 15 check with a +5 modifier needs a roll of 10 or higher on the die, which is a 55% success rate (11 out of 20 outcomes succeed). There's no "curve" to lean on; the swing between a great roll and a terrible one is much wider than in 2d6 systems, which is part of why d20 games feel swingier.

Advantage and disadvantage

Rolling with advantage means rolling 2d20 and keeping the higher result; disadvantage keeps the lower. This doesn't just nudge your odds — it reshapes them:

• Advantage roughly doubles the chance of rolling high (a 20 goes from 5% to 9.75% — 1 − (19/20)²), and pulls the average roll up from 10.5 to about 13.8.
• Disadvantage does the opposite: rolling a natural 1 goes from 5% to 9.75%, and the average roll drops to about 7.2.

Try it yourself: roll 2d20 a few times on the roller and manually keep the higher (or lower) value to feel how much advantage swings outcomes compared to a flat d20.

Expected value: what a roll averages out to

Expected value (EV) is the long-run average of a roll. For a single fair die with n sides, EV is (n + 1) / 2. For multiple dice, EVs add together. A few common ones:

• 1d6: EV = 3.5
• 2d6: EV = 7
• 1d20: EV = 10.5
• 4d6 (e.g. a damage roll): EV = 14
• 2d6+3: EV = 10

EV is why a fireball at 8d6 averages 28 damage even though any individual roll can land anywhere from 8 to 48 — the extremes are rare, and most rolls cluster near the average, same as the 2d6 bell curve above.

Percentile rolls (d100)

A d100, or "percentile" roll, is usually simulated by rolling two d10s — one for the tens digit, one for the ones digit — giving a flat 1% chance for each result from 1 to 100. Systems like Call of Cthulhu lean on this for skill checks expressed directly as percentages.

Try the math yourself

The dice roller supports standard notation (like 2d6+3 or 4d8) and shows the odds behind each roll, so you can check any of the numbers above against a live simulation rather than just trusting the table.