Online Dice Roller

The cube is older than dice notation

The British Museum’s Naukratis record records six-sided dice from Naukratis, including limestone examples with drilled pips. Objects show that recognizable dice long predate browser animations, but they do not establish that every ancient die was balanced.

A digital d6 models six equally likely integers rather than simulating wood, bone, gravity or a table surface. The animation is an illustration of a value generated separately; it is not a physical test of a real die.

Modern tabletop notation makes the experiment portable: the number before d is the quantity and the number after it is the side count. Writing the full expression before the roll avoids silently changing a bonus or deciding afterwards which die counts.

Keeping dice changes the distribution

The official D&D Basic Rules explain advantage as rolling two d20s and using the higher, and disadvantage as using the lower. Here 2d20kh1 and 2d20kl1 express those keep rules; they do not automatically implement every rule of a game.

For a target of at least 15 on a d20, one die succeeds on 6/20 outcomes. Keeping the higher of two succeeds with probability 1 − (14/20)² = 51%; keeping the lower succeeds with (6/20)² = 9%. These are worked calculations, not measured session rates.

The midpoint of the minimum and maximum is not generally the expected value after keep or exploding modifiers. An expected average is therefore shown only for ordinary sums with fixed arithmetic. Exploding dice can add further rolls beyond the initial count; the display does not calculate an exact full probability distribution.

Build a pool without silently changing the experiment

The count before d states how many dice; the number after d states sides. 2d6+1d20 rolls two d6 and one d20, while 1d20+5 rolls one die plus a fixed bonus. Quick dice add to the current expression, and presets replace it without rolling. A custom die accepts a whole-number side count from 2 to 1,000. Check the expression after using controls, especially after an advanced modifier.

Choose the experiment before pressing Roll. Theme, sound, vibration and fullscreen affect presentation, not die sides or modifiers. Space or Enter outside editable controls can start a roll; repeated actions during a pending roll do not create overlapping results. Cancel discards an unfinished reveal, but cannot turn an already completed roll into a different one. Agree on redraw policy before play rather than rerolling selectively.

Distinguish a bonus, a keep rule and an extra roll

Keeping is not summing: 4d6kh3 rolls four dice but totals the highest three. For an invented result 6, 4, 3, 1, the kept total is 13, not 14. 2d20kl1 uses the lower. Ties among equal values can affect which graphic is marked dropped without changing the numeric total. Use the output notation to check the rule, rather than counting every visible face.

The Exploding d6 preset 1d6! adds another roll when the triggering maximum appears, retaining earlier values. A hypothetical 6 followed by 2 totals 8. This differs from a reroll that replaces an unwanted value. The dice notation reference explains modifier syntax and order; combine rules only when the game requires them. Additional rolls can exceed the initial count, and the engine’s iteration limits are not a promise of an unbounded probability model.

Separate total, bounds and expected mean

For 2d6+3, a hypothetical 3 and 4 produce 10; the fixed bonus contributes to the total but is not another die. Minimum 5 and maximum 15 describe ordinary bounds, while mean 10 is a long-run expectation. The next result is not pulled toward 10 because the previous one was high. Advanced keep or exploding expressions have a different distribution and do not receive a simple midpoint average here.

Session average is an observed average over retained results, not the expected mean of the current expression. Mixing d20 checks and d6 pools makes it unsuitable for judging either. History stores only 20 completed rolls; older entries drop out and change totals, average, high and low. CSV keeps recent records; copy the full current output as well when a reviewer needs detailed modifier notation.

Diagnose a rejected or surprising expression

Use a short ordinary expression such as 1d6 first. The page requires at least one die, at most 90 characters and 50 initial dice, with ordinary sides 2–1,000; the notation parser then checks grammar. A supported library feature is not automatically a recommended game rule. If a combined expression fails, add its components one at a time and verify brackets, modifier spelling and valid counts.

A loading or randomness error produces no completed roll. Try again after preserving the notation; do not treat a blank panel as a zero. If only clipboard access fails, CSV remains useful. Reset returns the expression to 1d6 and cancels a pending reveal; clearing history is separate. Share carries the setup for a fresh roll, not a seed, immutable receipt or reproduction of the displayed result.