Dice Roller (d4 to d100)

About the Dice Roller (d4 to d100)

Pick a die — d4, d6, d8, d10, d12, d20 or d100 — and how many (1 to 20), or type dice notation such as 2d6+3, 4d6dl1 or 2d20kh1, then press Roll. Each die is drawn on screen with its face; press a die to hold it, and the next roll rerolls only the others, as in Yahtzee and many board games.

Under the dice you see the exact chance of every possible total as a chart and a table — worked out by counting outcomes, not by simulation — so you can ask "what is the chance of rolling at least 15?" before you roll. With dice held, the chances switch to the dice you are about to reroll. Every roll is kept in a history you can copy or download. The randomness comes from your browser’s cryptographically secure generator, through the same engine as the random generator.

Common uses

• Board games and party games when the dice are lost: Ludo, Monopoly, Yahtzee-style hold-and-reroll games.
• Tabletop role-playing games (Dungeons & Dragons and others): d20 checks with advantage, damage rolls such as 8d6, ability scores with 4d6 drop lowest.
• Teaching probability: compare the exact distribution of 1, 2 and 3 dice and watch the bell shape appear.
• Deciding odds before a move: the chance of reaching a target total with the dice you are about to reroll.

Dice notation

• NdM — N dice with M sides: 3d6, 1d20, d8 (one die). Dice from d2 to d1000 work; d4, d6, d8, d10, d12, d20 and d100 have their own shapes.
• + and − — add or subtract numbers or more dice: 1d20+5, 2d6+1d4-1
• d% — a percentile die (1–100); dF — a Fate/Fudge die (−1, blank or +1)
• khN / klN — keep the highest / lowest N dice: 2d20kh1 (advantage), 2d20kl1 (disadvantage)
• dlN / dhN — drop the lowest / highest N dice: 4d6dl1

Up to 20 dice can be on the table at once. The random generator reads the same notation and rolls up to 1,000 dice as text.

How the chances are worked out

Every die is fair, so every combination of faces is equally likely: three six-sided dice have 6 × 6 × 6 = 216 combinations, and 27 of them add up to 10, so the chance of a 10 is 27/216 = 12.5%. The page counts these combinations exactly for every total — for plain sums by combining the dice one at a time, and for keep/drop rules by working through the faces from best to worst and counting how many dice show each face. When there are more than 2⁵³ combinations (about 9 × 10¹⁵, for example 20d100), it does the same calculation with probabilities instead of counts, accurate to far more digits than the page shows.

The average, standard deviation, most likely total and median come from that same distribution. With dice held, the held dice are treated as fixed and only the others as random — which is what you need to decide whether a reroll is worth it.

Hold and reroll

Pressing a die holds it: its face stays when you roll again, and it is marked Held. This is how dice games such as Yahtzee and many push-your-luck games are played. Holds stay until you release them or change the dice. Keep/drop rules always look at the faces showing now, so a held low die can still be the one that is dropped. The roll counter shows how many times the current dice have been rolled.

How fair is it?

Each face is chosen with crypto.getRandomValues, the browser’s cryptographically secure random number generator, using rejection sampling, so every face of every die has exactly the same chance (no "modulo bias"). The face is decided before the tumble animation starts; the animation cannot change it. With Reduce motion turned on in your system settings the dice do not tumble at all.

Limitations

• For games, teaching and fun — not for gambling or any draw that rules say must use a certified random source.
• At most 20 dice and dice of up to 1,000 sides at a time. Exact chances for keep/drop rules on very big dice (for example 20d1000kh10) would take too long and are not shown; plain sums always are.
• The history keeps the last 100 rolls in this browser only.

Privacy

Everything runs in your browser. Your roll history and dice settings are saved in this browser only, so they are still there next time; nothing is uploaded.