D20 Probability Explained: Hits, Crits and Advantage

Every tabletop player has felt it: you need a 15, the whole table leans in, and the die clatters across the table. But how likely was that roll, really? The twenty-sided die is beautifully simple to reason about, and a little probability makes you a sharper player and a fairer game master. Here is the math behind hits, critical rolls and advantage, with no formulas you cannot do in your head.

The Basic Rule: Five Percent per Face

A fair d20 has twenty faces, so each number has a 1 in 20 chance — exactly 5%. That makes quick estimates easy: every point you need on the die is worth 5% in either direction.

To find the chance of rolling at least a target number T, count the faces from T up to 20 and multiply by 5%:

• Need 11 or higher: 10 faces, so 50%.
• Need 15 or higher: 6 faces, so 30%.
• Need 20: 1 face, so 5%.

How Modifiers Change Your Odds

In d20 systems you add a modifier to the roll and compare the total to a target, such as a Difficulty Class (DC) or an Armor Class. A modifier simply lowers the number you need on the die.

Example: you attack a monster with Armor Class 15 and your attack bonus is +5. You need 10 or more on the die, which is 11 faces — a 55% chance. Each extra +1 adds another 5%. That is why a small bonus from a spell or a magic item feels so significant: +2 turns 55% into 65%.

Most games also have special rules for natural 1s and 20s. In Dungeons & Dragons fifth edition, a natural 20 on an attack roll always hits and scores a critical hit, and a natural 1 always misses, no matter the modifier.

Advantage and Disadvantage Math

With advantage you roll two d20s and keep the higher; with disadvantage you keep the lower. The effect is bigger than most players expect:

• Natural 20 with advantage: 1 − (19/20)² = 9.75%, almost double the normal 5%.
• Natural 1 with disadvantage: also 9.75%.
• Average roll: about 13.8 with advantage and about 7.2 with disadvantage, compared with 10.5 for a single die.

The boost is largest for middle targets. Needing 11 or more rises from 50% to 75% with advantage, which is why many players describe advantage as roughly worth +5 on mid-range rolls. For very easy or very hard targets it is worth less.

Rolling With the D20 Tool

The tool opens ready for the most common roll in tabletop gaming:

1. Press Generate for one d20: a number from 1 to 20, each with an equal 5% chance.
2. For advantage or disadvantage, set Number of dice to 2 and keep the higher or lower result.
3. Use Sides per die to switch to d4, d6, d8, d10, d12 or d100 for damage and other rolls; you can roll up to 20 dice at once.
4. Read every individual roll plus the total in dice notation, such as “Total: 27 (3d20)”.
5. Share a link with your settings so the whole group uses the same roller.

Using the Math at the Table

For game masters, the 5% rule makes difficulty easy to set. A DC 10 check is routine for a trained character, DC 15 is a real challenge and DC 20 is a heroic feat. If a player needs a 19 to succeed, they know it is a long shot — and it is fair to tell them.

For players, knowing the odds helps with decisions. Should you spend a resource for advantage, or take a +2 bonus? On a roll where you need around 11, advantage is usually better; when you already need only a 4, the extra die barely matters.

Why the Distribution Feels Swingy

A single d20 has a flat distribution: a 1 is exactly as likely as a 10. Rolling several dice and adding them, such as 3d6, creates a bell curve where middle totals are much more common. That is why a d20 game feels unpredictable — a skilled hero can fail an easy roll, and a novice can succeed brilliantly. Many groups love that drama; others prefer house rules that soften it, such as letting a failed roll still make partial progress.

Pro tips

• Count faces and multiply by 5% to estimate any d20 roll.
• Treat each +1 bonus as an extra 5% chance.
• Advantage matters most when you need around 11 on the die.
• Announce DCs as easy, medium or hard if your table prefers mystery.

Frequently asked questions