Dice Roller: dice notation with exact odds

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Exact odds

Exactly At least At most

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Mean
Standard deviation
Median
Range

Table of every total

Total	Exactly	At least	At most

Notation

Write	Meaning	Try
`NdX`	N dice with X sides. Leave out N for one die.
`d%`	A percentile die, 1 to 100.
`dF`	Plus-minus dice: each shows +1, 0 or −1, all equally likely.
`khN` `klN`	Keep the N highest or lowest dice. `kN` means `khN`.
`dhN` `dlN`	Drop the N highest or lowest dice. `dN` right after the sides means `dlN`.
`!`	Explode: a die showing its top face adds another roll of that die.
`!!`	Compound: the added rolls join the die that exploded, as one total.
`rC`	Reroll dice that match C until they don’t.
`roC`	Reroll dice that match C once.
`>=N` `<=N` `>N` `<N` `=N`	Count the dice that meet the condition (successes) in place of adding them up.
`fC`	With a success count, subtract one for each die that matches C.
`+ - * / ( )`	Arithmetic. Division is not rounded.
`floor` `ceil` `round` `abs`	Round down, round up, round to the nearest whole number (halves go up), or drop the sign.
`,` `;`	Several rolls at once.
`Name:`	Name a roll.
`[text]`	Label one term.
`Nx`	Repeat a roll N times.

Conditions

C is a face, like 1, or a comparison, like <3 or >=5. Explode takes one too: 5d10!>=9 explodes on 9 and 10. Without one, a die explodes on its top face.

A comparison right after ! or !! belongs to the explode. For both, write the explode condition first: 5d10!=10>=8.

Conventions used here

A die explodes at most 20 times in a row, in rolls and in the odds.
Rerolls apply to every roll of a die, including rolls added by exploding.
Keep and drop rank whole dice: a die that exploded counts as one die, by the sum of its rolls. When dice tie, the earlier one is kept.
Successes and failures count every kept roll, including added rolls. A compounded die counts once, by its total.
Every dice group rolls separately: 1d6-1d6 rolls two dice.

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