Dice feel random — and each roll is — but over many rolls they follow very predictable patterns. Understanding those patterns helps you read a game’s maths, judge how risky a roll is, and know why some numbers show up far more than others. Here is the whole picture, without the heavy statistics.
One die is “flat”
A single fair die is the simplest case: every face is equally likely. On a d20, each number from 1 to 20 has exactly a 1-in-20 (5%) chance. There is no “hot” number. The only thing that changes between dice is the range and the average, which is always (sides + 1) ÷ 2.
| Die | Chance of any one number | Average roll |
|---|---|---|
| d4 | 25% | 2.5 |
| d6 | 16.7% | 3.5 |
| d8 | 12.5% | 4.5 |
| d10 | 10% | 5.5 |
| d12 | 8.3% | 6.5 |
| d20 | 5% | 10.5 |
| d100 | 1% | 50.5 |
Because every result is equally likely, a single die is a flat distribution — a straight line, not a curve.
Add dice together and the curve bends
The moment you roll two or more dice and add them, the flatness disappears. Middle totals can be made in many ways, while the extremes can only be made in one. On 2d6, a total of 7 can come from 1+6, 2+5, 3+4, 4+3, 5+2 or 6+1 — six combinations — but a 2 (snake eyes) can only be 1+1. That is why 7 is the most common roll in games like Catan and craps.
| Total on 2d6 | Ways to make it | Probability |
|---|---|---|
| 2 | 1 | 2.8% |
| 3 | 2 | 5.6% |
| 4 | 3 | 8.3% |
| 5 | 4 | 11.1% |
| 6 | 5 | 13.9% |
| 7 | 6 | 16.7% |
| 8 | 5 | 13.9% |
| 9 | 4 | 11.1% |
| 10 | 3 | 8.3% |
| 11 | 2 | 5.6% |
| 12 | 1 | 2.8% |
Plot those and you get the classic bell curve: results cluster in the middle. Add even more dice (say 8d6 for a fireball) and the curve gets tighter and more predictable — the total will almost always land near the average, rarely at the extremes.
Advantage and disadvantage
Many modern games use advantage (roll two d20 and keep the higher) and disadvantage (keep the lower). This is a bigger deal than it looks. A normal d20 averages 10.5; with advantage it averages about 13.8, and with disadvantage about 7.2 — a swing of roughly ±3.3 on average.
The effect is largest when you are on a coin-flip. If you need an 11+ to succeed (a 50% roll), advantage pushes your success chance up to about 75%, and disadvantage drops it to about 25%. Near-certain or near-impossible rolls barely change. In short: advantage helps most exactly when the outcome is in doubt.
Advantage isn’t a flat “+5”. It bends your odds most in the middle and least at the edges — which is why it feels so swingy at the table.
Dropping the lowest (rolling for stats)
Rolling ability scores in D&D usually means 4d6, drop the lowest die. Keeping the best three of four nudges the average up: plain 3d6 averages 10.5, but 4d6-drop-lowest averages about 12.2, and high scores (15+) become much more common. That is why characters rolled this way tend to be a little stronger than the “standard array”.
Modifiers just slide the curve
A flat modifier like +3 doesn’t change the shape of the odds — it slides the whole curve along by three. 2d6+3 has exactly the same spread as 2d6, just centred on 10 instead of 7. Multiplying dice (rolling more of them) changes the shape; adding a fixed number only shifts it.
The practical takeaways
- One die = flat. Every face is equally likely; there are no lucky numbers.
- Many dice = a bell curve. Totals cluster in the middle; extremes are rare.
- Advantage/disadvantage swings hardest on 50/50 rolls — about ±3.3 on average.
- 4d6 drop lowest averages ~12.2, higher than a straight 3d6.
- A +N modifier shifts the curve; it doesn’t reshape it.
See it for yourself. Roll 2d6 a few dozen times and watch how often 6, 7 and 8 turn up compared with 2 or 12 — the bell curve appears in front of you.
🎲 Roll the dice in your browserNext: which dice you actually need for D&D 5e, or how dice notation like 4d6 drop lowest works.