Difference between revisions of "Dice Reference"
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Roll20 features support for a wide array of dice mechanics. On this page we've compiled a list of all of the different types of dice rolls you can perform. Each type also has an interactive example box where you can make actual rolls using the same roll system that's built in to Roll20  a great way to experiment and check to make sure we can support your role playing game system of choice. Don't see a dice mechanic your game system needs, or think something is done incorrectly? [mailto:team@roll20.net Get in touch and let us know!]  Roll20 features support for a wide array of dice mechanics. On this page we've compiled a list of all of the different types of dice rolls you can perform. Each type also has an interactive example box where you can make actual rolls using the same roll system that's built in to Roll20  a great way to experiment and check to make sure we can support your role playing game system of choice. Don't see a dice mechanic your game system needs, or think something is done incorrectly? [mailto:team@roll20.net Get in touch and let us know!]  
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== How to Roll Dice ==  == How to Roll Dice ==  
−  Rolling  +  Dice can be rolled simply from the [[Dice Rolling GUITabletop Toolbox Dice Rolling Interface]] 
−  +  For more control over how the dice behave, or to automate processes or math, dice can be rolled in chat. Rolling dice in Roll20 is easy. Just type the <code>/roll</code> command into the text chat box, followed by a formula. In most cases, the formula is the same as the one that's printed in your game's instructions. For example, you might know that to roll an attack roll you need to roll a "D20 plus your attack modifier". In Roll20, you would just type <code>/roll d20+5</code>. If you hit and you need to roll 3d6+2 damage, you would just type <code>/roll 3d6+2</code>. Finally, you can also string multiple rolls together. If you have an attack that does two types of damage, you might do <code>/roll 2d6+5 + d8</code>.  
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<div class='diceroller'>  <div class='diceroller'>  
−  +  /roll 1d20+5  
−  +  
−  +  
</div>  </div>  
After the roll is performed, you'll see the results of the roll in the text chat area. Notice that for each group of dice that were rolled, there will be a group of numbers in parentheses, representing the result of each individual dice that was rolled. (The number sits on an outline of the dice type rolled, and this outline is in the same color as the square of color in the diceroller's player portrait in the Player Area.) You'll also see the total of all the dice values plus modifiers to the right of the equal sign.  After the roll is performed, you'll see the results of the roll in the text chat area. Notice that for each group of dice that were rolled, there will be a group of numbers in parentheses, representing the result of each individual dice that was rolled. (The number sits on an outline of the dice type rolled, and this outline is in the same color as the square of color in the diceroller's player portrait in the Player Area.) You'll also see the total of all the dice values plus modifiers to the right of the equal sign.  
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== Rolling in Secret ==  == Rolling in Secret ==  
By default, any rolls that you make are seen by everyone in the game with you (including all players). If you want to roll in secret, you can use the <code>/gmroll</code> command to perform a roll that only the GM and the original player who made the roll can see. So if you're the GM, doing a <code>/gmroll</code> will only be visible to you. It's a great way to perform skill checks in secret.  By default, any rolls that you make are seen by everyone in the game with you (including all players). If you want to roll in secret, you can use the <code>/gmroll</code> command to perform a roll that only the GM and the original player who made the roll can see. So if you're the GM, doing a <code>/gmroll</code> will only be visible to you. It's a great way to perform skill checks in secret.  
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== Including Additional Information ==  == Including Additional Information ==  
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You can also include nonformula text in your roll to indicate what that roll is for. For example, when rolling for initiative you might enter <code>/roll 1d20+5 Roll for Initiative</code>. The extra text won't affect your roll in any way, but it's included in the chat log so that others can see what you're rolling for. It's entirely optional to do this, by the way, but some GMs find it helps keep everything organized a little better.  You can also include nonformula text in your roll to indicate what that roll is for. For example, when rolling for initiative you might enter <code>/roll 1d20+5 Roll for Initiative</code>. The extra text won't affect your roll in any way, but it's included in the chat log so that others can see what you're rolling for. It's entirely optional to do this, by the way, but some GMs find it helps keep everything organized a little better.  
−  +  <div class="diceroller">  
−  <div class="diceroller">  +  /roll 1d20+5 Roll for Initiative 
−  +  </div>  
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If you want to include any numbers, parentheses, or <code>+</code>, <code></code>, <code>*</code>, <code>/</code>, or <code>%</code> in your additional text, you can preface it with a <code>\</code> to separate the formula from the text and keep the roller from getting confused. So for example you can do <code>/roll 1d20+5 \ +5 Roll for Initiative</code>.  If you want to include any numbers, parentheses, or <code>+</code>, <code></code>, <code>*</code>, <code>/</code>, or <code>%</code> in your additional text, you can preface it with a <code>\</code> to separate the formula from the text and keep the roller from getting confused. So for example you can do <code>/roll 1d20+5 \ +5 Roll for Initiative</code>.  
+  ===Inline Labels===  
If you want to include additional comments before the end of the roll (we call them "inline labels"), use square brackets. For example, <code>/roll 2d20+5[Fire Damage] + 3d6+5[Ice Damage]</code>. When these comments are applied directly after a die roll they show up as tooltips on the dice:  If you want to include additional comments before the end of the roll (we call them "inline labels"), use square brackets. For example, <code>/roll 2d20+5[Fire Damage] + 3d6+5[Ice Damage]</code>. When these comments are applied directly after a die roll they show up as tooltips on the dice:  
−  +  <div class="diceroller">  
−  <div class="diceroller">  +  /roll 2d10+2d6[crit]+5 Critical Hit! 
−  +  </div>  
−  +  
== Inline Dice Rolls ==  == Inline Dice Rolls ==  
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* They are evaluated completely before any /roll commands, so you can use them as "random variables" in your rolls.  * They are evaluated completely before any /roll commands, so you can use them as "random variables" in your rolls.  
* You will only see the result of the total roll, and you can hover over the result to see the individual dice rolls.  * You will only see the result of the total roll, and you can hover over the result to see the individual dice rolls.  
−  * If an inline roll contains a crit success, it will be highlighted with a green box  +  * If an inline roll contains a crit success, it will be highlighted with a green box. If there's a crit failure, it's highlighted in red. If it has both (because there was more than one roll), it's in blue. Also when you mouseover the inline roll to see the details of the roll, it'll show red and green highlights for the rolls themselves for crits/fumbles. 
To do an inline roll, just include two brackets in any chat message or roll, like so:  To do an inline roll, just include two brackets in any chat message or roll, like so:  
+  <pre datalanguage="javascript">  
+  /em Riley is filled with [[3d6]] points of anger!  
+  /roll [[2d6]]d5  
+  </pre>  
+  You can also nest inline rolls, one inside the other, like so:  
−  +  <pre datalanguage="javascript">  
−  <pre>/em  +  /em Steve gets slapped with [[ 3d6>[[1+3]] ]] carp! 
−  +  </pre>  
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== Roll Queries ==  == Roll Queries ==  
−  Sometimes you may have a roll (or a macro) which you want to change every time it is rolled. For example, you may want to roll a variable number of dice, or add a different modifier onto the roll each time you perform the action. Roll Queries allow you to prompt whoever is performing the roll to fill in a value when the roll is made.  +  Sometimes you may have a roll (or a macro) which you want to change every time it is rolled. For example, you may want to roll a variable number of dice, or add a different modifier onto the roll each time you perform the action. Roll Queries allow you to prompt whoever is performing the roll to fill in a value when the roll is made. The syntax for a roll query is: 
−  +  
−  +  
−  +  
−  +  <pre datalanguage="javascript">  
−  +  ?{Prompt Message}  
+  //Example:  
+  /roll ?{Number of Dice}d20  
+  //You can also include a default value:  
+  /roll ?{Number of Dice1}d20  
+  // 1 would be the default  
+  </pre>  
−  +  You can use Roll Queries in rolls, macros, abilities, emotes, whispers  pretty much anywhere in the app. Note that if you use the same exact wording for a Query, Roll20 will only ask for the value the first time it's encountered in the roll. So in this example:  
−  +  
−  +  <pre datalanguage="javascript">  
+  /roll 1d20 + ?{Bonus1} vs ?{MinToSucceed} + ?{Bonus1}  
+  </pre>  
−  +  Roll20 will ask for "Bonus1" only once and use it in both places.  
== MathOnly Rolls ==  == MathOnly Rolls ==  
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'''Compounding Exploding Dice (ShadowrunStyle Exploding Dice)'''  '''Compounding Exploding Dice (ShadowrunStyle Exploding Dice)'''  
−  Shadowrun (and some other systems) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. So for example to roll 5 d6's, you would do <code>/roll 5d6!!</code>. A common Shadowrun roll would be exploding dice compared to a target number, for example <code>/roll {5d6!!}>8</code> <em>(notice the use of the brackets to show that we don't mean "explode on anything greater than 8", but rather "explode on 6's compounding, then compare to 8 for successes)</em>. Even though the target number (8) is higher than the possible roll from a single  +  Shadowrun (and some other systems) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. So for example to roll 5 d6's, you would do <code>/roll 5d6!!</code>. A common Shadowrun roll would be exploding dice compared to a target number, for example <code>/roll {5d6!!}>8</code> <em>(notice the use of the brackets to show that we don't mean "explode on anything greater than 8", but rather "explode on 6's compounding, then compare to 8 for successes)</em>. Even though the target number (8) is higher than the possible roll from a single die, with the compounding exploding rolls a single roll can be infinitely high! 
<div class='diceroller'>  <div class='diceroller'>  
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<div class='diceroller'>  <div class='diceroller'>  
/roll 3d6>3  /roll 3d6>3  
+  </div>  
+  
+  == Critical Success and Fumble Points ==  
+  
+  You can also modify your dice rolls to allow you to specify set at which point a roll is considered to be a "Critical Success" or "Critical Failure (Fumble)".  
+  
+  To show any roll equal to 10 or greater as a critical success, just do <code>/roll 1d20cs>10</code>. To show any roll equal to or less than 3 as a critical failure, just do <code>/roll 1d20cf<3</code>. To show any roll equal to 20 or 10 exactly as a critical success, just do <code>/roll 1d20cs20cs10</code>.  
+  
+  ''Note: These values will not affect other things that by default work on max roll value (including exploding, penetrating, etc.). It only affects the display of the roll result to the player. For example, if you want dice to explode on 18 or higher, and you want to show an 18 or higher as a critical, you would need to do <code>/roll 1d20!>18cs>18</code>.''  
+  
+  <div class='diceroller'>  
+  /roll 1d20cs>10  
</div>  </div>  
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</div>  </div>  
−  == Rounding Rolls ==  +  == Rounding Rolls and Math Functions == 
−  You may want to use rounding in your roll formulas to emulate mechanics such as "half a level, rounded down to the nearest level." Roll20 provides  +  You may want to use rounding in your roll formulas to emulate mechanics such as "half a level, rounded down to the nearest level." Roll20 provides several functions to accomplish this: <code>floor()</code> which will always round the number down (e.g. 5.7 becomes 5), <code>ceil()</code> which will always round the number up (e.g. 5.1 becomes 6), and <code>round()</code> which will always round to the nearest whole number (e.g. 4.4 becomes 4 and 4.5 becomes 5). You can use these functions almost anywhere in your roll formulas (around a single math expression, groups of math expressions, or even the entire roll). For example: 
<div class='diceroller'>  <div class='diceroller'>  
/roll floor(7/2) + 2d6  /roll floor(7/2) + 2d6  
</div>  </div>  
+  
+  We also provide other Math functions:  
+  
+  * <code>abs()</code> will calculate the absolute value of the roll  
== Grouping Rolls ==  == Grouping Rolls ==  
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The &{} part is where you put your options for the roll, and the "tracker" option is what says "Show the results of this roll, but also use the result as the value in the turn tracker." If the token that you have selected doesn't already have a turn in the turn order, one will be added. If it already has at least one turn, all current turns will be updated with the new value.  The &{} part is where you put your options for the roll, and the "tracker" option is what says "Show the results of this roll, but also use the result as the value in the turn tracker." If the token that you have selected doesn't already have a turn in the turn order, one will be added. If it already has at least one turn, all current turns will be updated with the new value.  
−  =  +  == Roll Templates == 
−  == Order of Operations ==  +  [[Roll Templates]] are a special facet of the [[Character Sheets]] system which provide additional layout and styling options for the display of roll results. Using a [[Roll TemplatesRoll Template]] is very easy to use. Just include a special flag in your chat message which tells Roll20 that you want to use a [[Roll__TemplatesRoll Template]], and then provide all of the data that you want to include. 
+  
+  Here's an example that uses the 'default' template (which all games have access to, regardless of the game system or [[Character Sheets]] you are using): <code><nowiki>&{template:default} {{name= My Test Roll}} {{attack= [[1d20]]}} {{damage= [[2d6]]}}</nowiki></code>  
+  
+  ''Note: If you're interested in using Roll Templates in your own custom macros or creating your own custom templates please vist the wiki entry on [[Roll Templates]].''  
+  
+  <div class='diceroller'>  
+  <nowiki>&{template:default} {{name= My Test Roll}} {{attack= [[1d20]]}} {{damage= [[2d6]]}}</nowiki>  
+  </div>  
+  
+  == Roll20 Dice Specification ==  
+  
+  === Math Operators and Functions ===  
+  Roll20 supports the basic arithmetic operators you learned in school: <code>+</code>, <code></code>, <code>*</code> (multiply), and <code>/</code> (divide).  
+  
+  In addition to the basic four, you have access to:  
+  * <code>%</code>, for modulus division. The result of <code>a % b</code> is the ''[[wikipedia:Modulo operationremainder]]'' of <code>a / b</code>. If you think back to when you were first learning long division without getting into decimals, you were learning how to perform modulus division. Modulus is useful, for example, to test whether a value is even or odd: <code>a % 2</code> will be 0 if a is even (and positive) and 1 if a is odd (and positive). In general, the result of <code>a % b</code> when a and b are both whole numbers will be a whole number in the range <code>[0, b  1]</code> where <code>b</code> is the absolute value of b. (If a is less than 0, the result will be negative, including 0. 0 is functionally equivalent to 0.)  
+  * <code>**</code>, for exponentiation. You may be more familiar with <code>a^b</code> as the notation for "raising a to the power of b", but in Roll20 you would use <code>a**b</code> instead. Also note that finding roots is simply raising a number to a fractional exponent; square root is simply an exponent of 0.5, for example.  
+  
+  
+  You also have access to a small set of mathematical functions:  
+  * <code>floor(x)</code> rounds x towards negative infinity.  
+  * <code>round(x)</code> rounds x towards 0 if the fractional portion of x is less than 0.5, and round x towards positive infinity if the fractional portion of x is 0.5 or greater.  
+  * <code>ceil(x)</code> rounds x towards positive infinity.  
+  * <code>abs(x)</code> returns the absolute value of x.  
+  
+  
+  Operations are performed by order of precedence, just like in normal mathematics. From highest to lowest precedence:  
+  * Grouping with parentheses (<code>(</code> and <code>)</code>); just like in real math, you can modify the precedence ordering by wrapping parentheses around things  
+  * Calling floor/round/ceil/abs  
+  * Exponentiation (<code>**</code>)  
+  * Multiplication (<code>*</code>), division (<code>/</code>), and modulus (<code>%</code>), in the order they appear (lefttoright) in the formula  
+  * Addition (<code>+</code>) and subtraction (<code></code>), in the order they appear (lefttoright) in the formula  
+  
+  === Order of Operations ===  
While the Roll20 dice engine does support basic math and functions such as floor() and ceil(), it is first and foremost a dice engine, and so it has its own order of operations. This means that putting parentheses inside of your dice formula will not always affect the outcome of the roll (for example, you can't force a variable to be interpreted before a macro). Here is the general order of operations:  While the Roll20 dice engine does support basic math and functions such as floor() and ceil(), it is first and foremost a dice engine, and so it has its own order of operations. This means that putting parentheses inside of your dice formula will not always affect the outcome of the roll (for example, you can't force a variable to be interpreted before a macro). Here is the general order of operations:  
−  # Abilities are expanded (meaning the definition of the ability is placed in the formula anywhere that ability appears).  +  # Abilities are expanded (meaning the definition of the ability is placed in the formula anywhere that ability appears; e.g. %{character nameability_name} becomes /r 1d4). 
−  # Macros are expanded  +  # Macros are expanded (e.g. #macroname becomes /r 1d4). 
−  +  # Attribute calls are resolved. (e.g. @{attribute_name} becomes 4)  
−  # Roll queries are executed (the player making the roll is asked to provide a value for each query, and that value is substituted in where the roll query appears in the formula)  +  # The 3 above steps are repeated up to 99 levels deep or there are no longer any expansions required. 
−  # Inline rolls are executed,  +  # Roll queries are executed up to 99 levels deep (the player making the roll is asked to provide a value for each query, and that value is substituted in where the roll query appears in the formula). HTML entities within roll queries are parsed once after each roll query (e.g. } becomes } but &#125; becomes }) 
+  # Inline rolls are executed, starting with the most deeply nested inline roll working upward. The overall result of the inline roll is substituted in place where it appeared in the formula.  
# The remaining roll is executed: first, dice are rolled for any dice (e.g. "2d6" is rolled; including any special dice such as dropped or exploding), then the result of that roll is substituted into the formula. Next, floor() and ceil() functions are executed. Finally, the entire remaining formula is evaluated, including observing proper math order of operations (parentheses first, then multiplication/division, then addition/subtraction).  # The remaining roll is executed: first, dice are rolled for any dice (e.g. "2d6" is rolled; including any special dice such as dropped or exploding), then the result of that roll is substituted into the formula. Next, floor() and ceil() functions are executed. Finally, the entire remaining formula is evaluated, including observing proper math order of operations (parentheses first, then multiplication/division, then addition/subtraction).  
+  # Html entities are processed once more  
+  # The message is sent to chat, and the API sandbox receives the message at this point as well  
−  == Types Of Dice ==  +  
+  ''Thank you to Scott C. for additional testing in this matter!''  
+  
+  === Types Of Dice ===  
Roll20 supports more than just your standard polyhedrons when rolling dice, below are the available die types you can use in your games.  Roll20 supports more than just your standard polyhedrons when rolling dice, below are the available die types you can use in your games.  
−  === Basic Roll <code>NdX</code> ===  +  ==== Basic Roll <code>NdX</code> ==== 
Rolls '''N''' traditional (almost, you can have any number of sides that you want) dice with '''X''' sides per die. '''N''' must be greater than or equal to 0 and '''X''' must be greater than or equal to 1.  Rolls '''N''' traditional (almost, you can have any number of sides that you want) dice with '''X''' sides per die. '''N''' must be greater than or equal to 0 and '''X''' must be greater than or equal to 1.  
−  === Fate/Fudge Roll <code>NdF</code> ===  +  ==== Fate/Fudge Roll <code>NdF</code> ==== 
Rolls '''N''' Fate/Fudge dice. These dice have three sides with values of 1, 0, and 1.  Rolls '''N''' Fate/Fudge dice. These dice have three sides with values of 1, 0, and 1.  
−  === Computed Dice Roll <code>(N+Y)dX</code>/<code>Nd(X+Y)</code> ===  +  ==== Computed Dice Roll <code>(N+Y)dX</code>/<code>Nd(X+Y)</code> ==== 
Computes the number of dice to roll or the number of sides on the dice based on the mathematical expression in the parentheses. Dice computation can be used with both Basic and Fate dice.  Computes the number of dice to roll or the number of sides on the dice based on the mathematical expression in the parentheses. Dice computation can be used with both Basic and Fate dice.  
−  == Roll Modifiers ==  +  Within <code>(N+Y)dX</code>, the number of dice <code>(N+Y)</code> is rounded to the nearest whole number, just like [[Dice_Reference#Rounding_Rolls_and_Math_Functions'''round(N+Y)''']]. 
+  
+  === Roll Modifiers ===  
Modfiers that can change the behavior or outcome of dice rolls. Each modifier states which '''Types Of Dice''' it can be applied to in parentheses after the modifier name. Rolls can have multiple modifiers applied to a single roll to allow for complex dice expressions.  Modfiers that can change the behavior or outcome of dice rolls. Each modifier states which '''Types Of Dice''' it can be applied to in parentheses after the modifier name. Rolls can have multiple modifiers applied to a single roll to allow for complex dice expressions.  
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* Example Compare Points  * Example Compare Points  
−  * <code>3</code>  If the roll is equal to 3  +  * <code>=3</code>  If the roll is equal to 3 
* <code>>2</code>  If the roll is greater than or equal to 2  * <code>>2</code>  If the roll is greater than or equal to 2  
* <code><18</code>  If the roll is less than or equal to 18  * <code><18</code>  If the roll is less than or equal to 18  
−  === Target Number / Successes (B,F)  <code>CP</code> ===  +  ==== Target Number / Successes (B,F)  <code>CP</code> ==== 
Normally when you perform a roll, Roll20 reports back the total value of all the dice rolled, plus any modifiers. Some game systems, though, work by rolling a set of dice versus a target number, and then adding up the total number of successes instead.  Normally when you perform a roll, Roll20 reports back the total value of all the dice rolled, plus any modifiers. Some game systems, though, work by rolling a set of dice versus a target number, and then adding up the total number of successes instead.  
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* <code>10d6<4</code>  Roll 10 d6's and count one success for each roll of 4 or less  * <code>10d6<4</code>  Roll 10 d6's and count one success for each roll of 4 or less  
−  === Failures (B,F)  <code>fCP</code> ===  +  ==== Failures (B,F)  <code>fCP</code> ==== 
Some systems build on success checks by also including failures. Failure checks only work when a success check is already being done and each failure subtracts one from the total number of successes.  Some systems build on success checks by also including failures. Failure checks only work when a success check is already being done and each failure subtracts one from the total number of successes.  
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* <code>10d6<4f>5</code>  Roll 10 d6's and count one success for each roll of 4 or less and one failure for each roll of 5 or more  * <code>10d6<4f>5</code>  Roll 10 d6's and count one success for each roll of 4 or less and one failure for each roll of 5 or more  
−  === Exploding Dice (B,F) <code>!CP</code> ===  +  ==== Exploding Dice (B,F) <code>!CP</code> ==== 
Exploding dice, also known as "rule of 6" or "rule of 10s" depending on your gaming system, rolls an additional die if the maximum is rolled. If the additional roll is also the maximum number the additional rolls keep on going! The Compare Point can be specified to change the exploding trigger.  Exploding dice, also known as "rule of 6" or "rule of 10s" depending on your gaming system, rolls an additional die if the maximum is rolled. If the additional roll is also the maximum number the additional rolls keep on going! The Compare Point can be specified to change the exploding trigger.  
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* <code>3d6!>5</code>  Rolls 3d6 and explodes every time a 5 or 6 is rolled  * <code>3d6!>5</code>  Rolls 3d6 and explodes every time a 5 or 6 is rolled  
−  === Compounding Dice (B,F) <code>!!CP</code> ===  +  ==== Compounding Dice (B,F) <code>!!CP</code> ==== 
Shadowrun (and some other systems, such as 7th Sea and L5R) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. With the compounding exploding rolls a single roll can be infinitely high! The Compare Point can be specified to change the exploding trigger.  Shadowrun (and some other systems, such as 7th Sea and L5R) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. With the compounding exploding rolls a single roll can be infinitely high! The Compare Point can be specified to change the exploding trigger.  
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* <code>5d6!!5</code>  Rolls 5d6 and compound every time a 5 is rolled, 6's will be treated as a normal roll  * <code>5d6!!5</code>  Rolls 5d6 and compound every time a 5 is rolled, 6's will be treated as a normal roll  
−  === Penetrating Dice (B,F) <code>!pCP</code> ===  +  ==== Penetrating Dice (B,F) <code>!pCP</code> ==== 
HackMaster (and some other systems) use a special style of exploding dice where the additional rolls for each dice have 1 subtracted from the roll. To do this, add a p after the exclamation mark. A die can penetrate multiple times but the modifier is only ever 1 to each additional die.  HackMaster (and some other systems) use a special style of exploding dice where the additional rolls for each dice have 1 subtracted from the roll. To do this, add a p after the exclamation mark. A die can penetrate multiple times but the modifier is only ever 1 to each additional die.  
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* <code>5d6!p>5</code>  Rolls 5d6 and explode with a 1 modifier every time a 5 or higher is rolled.  * <code>5d6!p>5</code>  Rolls 5d6 and explode with a 1 modifier every time a 5 or higher is rolled.  
−  === Keep / Drop Dice (B,F) <code>khN</code>/<code>klN</code>/<code>dhN</code>/<code>dlN</code> ===  +  ==== Dice Matching <code>mt</code> ==== 
+  
+  It is possible to show how many of the dice rolled result in matches in the chat window. This feature works with the chat dice as well as the 3d dice, but the matches are only shown in the chat output.  
+  
+  <code>m</code> will show matches visually but not change results of the roll.  
+  <code>mt</code> will return the number of matches, regardless of the number of dice that match.  
+  
+  ===== Arguments =====  
+  
+  Both options can take 2 arguments: the number of matches required and/or the result the match needs to be.  
+  
+  As with other dice arguments, <code>!</code> will result in exploding dice. If the exploding dice cause a match, the match will display in the results as well.  
+  
+  * Rolling <code>2d6m</code> will give you the result of the 2d6 added together, while grouping the matched rolls with a colored bar.  
+  * Rolling <code>2d6mt</code> will either return 0 matches or 1 match.  
+  * Rolling <code>20d6mt</code> could return 0 to 6 matches.  
+  * Rolling <code>6d6mt3</code> will show the number of matches if there are three of any result.  
+  * Rolling <code>5d6mt3>4</code> will show the number of matches if there are three of them AND the matching numbers 4 or greater.  
+  
+  ===== How It Looks =====  
+  
+  When 2 or more dice match, the chat output displays them with a colored bar above the number in the output. Each number that matches displays with a different bar. Effort has been made to make the colors high contrast against each other.  
+  
+  Other standard visual indicators (bold, bright color) for highest and lowest numbers still work with the dice matching mechanic.  
+  
+  ==== Keep / Drop Dice (B,F) <code>khN</code>/<code>klN</code>/<code>dhN</code>/<code>dlN</code> ====  
Some game systems ask you to roll a large number of dice, and then either drop a certain number ('''N''') of the lowest rolls, or keep only a certain number ('''N''') of the highest rolls. Roll20 supports this type of roll through the <code>d</code> and <code>k</code> commands, respectively. The optional <code>h</code>/<code>l</code> parameter can either be <code>h</code> to keep or drop the highest '''N''' dice or <code>l</code> to keep or drop the lowest '''N''' dice. If not specified when keeping rolls the high rolls will be kept and when dropping rolls the low rolls will be dropped.  Some game systems ask you to roll a large number of dice, and then either drop a certain number ('''N''') of the lowest rolls, or keep only a certain number ('''N''') of the highest rolls. Roll20 supports this type of roll through the <code>d</code> and <code>k</code> commands, respectively. The optional <code>h</code>/<code>l</code> parameter can either be <code>h</code> to keep or drop the highest '''N''' dice or <code>l</code> to keep or drop the lowest '''N''' dice. If not specified when keeping rolls the high rolls will be kept and when dropping rolls the low rolls will be dropped.  
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* <code>8d100dh4</code>  Roll 8 d100's and drop the four largest rolls.  * <code>8d100dh4</code>  Roll 8 d100's and drop the four largest rolls.  
−  === Rerolling Dice (B,F) <code>rCP</code> ===  +  ==== Rerolling Dice (B,F) <code>rCP</code> ==== 
−  Several systems require that certain dice be reroll, for example brutal weapons in D&D 4e require any 1s or 2s to be rerolled and the  +  Several systems require that certain dice be reroll, for example brutal weapons in D&D 4e require any 1s or 2s to be rerolled and the original die value ignored. The reroll modifier can be specified multiple times to allow rerolling at multiple Compare Points. By default the dice will continue to reroll until the result is inside the defined parameters. Optionally you can set the results to only reroll once regardless of the outcome. 
* Example Rerolls  * Example Rerolls  
Line 327:  Line 383:  
* <code>8d6r</code>  Roll 8 d6's and reroll any time a 1 is rolled  * <code>8d6r</code>  Roll 8 d6's and reroll any time a 1 is rolled  
* <code>8d6r2r4r6</code>  Roll 8 d6's and reroll any time a 2, 4, or 6 is rolled  * <code>8d6r2r4r6</code>  Roll 8 d6's and reroll any time a 2, 4, or 6 is rolled  
+  * <code>2d6ro<2</code>  Roll 2 d6's and reroll anything less than 2 but only once  
−  === Sorting Dice (B,F) <code>sa</code>/<code>sd</code> ===  +  
+  '''Special Case: Reroll Once (B,F) <code>roCP</code>'''  
+  
+  In some systems (such as D&D 5E) you want to reroll dice below a certain value, but you only want to reroll the dice one time each. To do that, just use <code>ro</code> instead of <code>r</code>.  
+  
+  * Example Reroll Once Rolls  
+  * <code>2d10ro<2</code>  Roll 2 d10's and reroll any time a 2 or lower is rolled, but only up to one time per dice.  
+  
+  ==== Sorting Dice (B,F) <code>sa</code>/<code>sd</code> ====  
You may want to see your results in either ascending or descending order. The sorting modifier does just this. The order parameter is optional and specifies the order to sort with <code>a</code> for ascending and <code>d</code> for descending. Sorting defaults to ascending if order is not specified.  You may want to see your results in either ascending or descending order. The sorting modifier does just this. The order parameter is optional and specifies the order to sort with <code>a</code> for ascending and <code>d</code> for descending. Sorting defaults to ascending if order is not specified.  
Line 336:  Line 401:  
* <code>8d6sd</code>  Roll 8 d6's and sort the results in descending order  * <code>8d6sd</code>  Roll 8 d6's and sort the results in descending order  
−  ==== Order of Operations for Modifiers ====  +  ===== Order of Operations for Modifiers ===== 
Modifiers are applied in the following order:  Modifiers are applied in the following order:  
Line 345:  Line 410:  
* These are applied after all of the dice have "settled" and all of the result values are known.  * These are applied after all of the dice have "settled" and all of the result values are known.  
−  == Grouped Rolls ==  +  === Grouped Rolls === 
Mutliple rolls can be perfomed within a group via curly braces using a comma to seperate the subroll expressions <code>{3d6+3d4+5, 2d8+4}</code>. Grouped Rolls have their own set of Group Modifiers which perform actions across the whole group.  Mutliple rolls can be perfomed within a group via curly braces using a comma to seperate the subroll expressions <code>{3d6+3d4+5, 2d8+4}</code>. Grouped Rolls have their own set of Group Modifiers which perform actions across the whole group.  
−  == Grouped Roll Modifiers ==  +  '''Note:''' each subroll expression within a Grouped Roll must contain elements of the same type: 
+  * "Sum rolls", which can be [[Dice_Reference#Basic_Roll_NdXBasic Rolls]] or nested Group Rolls.  
+  * "[[Dice_Reference#Target_Number_.28Successes.29Success rolls]]".  
+  * ("M rolls"—which are simply numbers—may be mentioned in an error message. However, unlike the other two roll types, M rolls are not required to be present within every subroll expression.)  
+  <br>  
+  For example, <code>[[ {1d6, 5}kh1 ]]</code> will fail, but <code>[[ {1d6, 5 + 0d0}kh1 ]]</code> or <code> [[ {1d6, {5}}kh1 ]]</code> or <code> [[ {[[1d6]], 5}kh1 ]]</code> will work.  
+  
+  === Grouped Roll Modifiers ===  
Modfiers that can change the behavior or outcome of grouped rolls. Grouped Rolls can have multiple modifiers applied to a group roll to allow for complex dice expressions.  Modfiers that can change the behavior or outcome of grouped rolls. Grouped Rolls can have multiple modifiers applied to a group roll to allow for complex dice expressions.  
−  === Keep / Drop <code>khN</code>/<code>klN</code>/<code>dhN</code>/<code>dlN</code> ===  +  ==== Keep / Drop <code>khN</code>/<code>klN</code>/<code>dhN</code>/<code>dlN</code> ==== 
To apply a keep or drop modifier across multiple types of dice wrap the roll in a group. With a single SubRoll in the group the keep/drop operation is applied across all rolls. To choose the best or worse roll expression multiple subgroups can be used. In this case the keep/drop operation is applied to the final result of each subgroup.  To apply a keep or drop modifier across multiple types of dice wrap the roll in a group. With a single SubRoll in the group the keep/drop operation is applied across all rolls. To choose the best or worse roll expression multiple subgroups can be used. In this case the keep/drop operation is applied to the final result of each subgroup.  
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* <code>{4d6+2d8, 3d20+3, 5d10+1}d1</code>  Roll each of the three subroll expressions and total them up. Drop the subroll expression with the lowest total and sum the other two totals as the result.  * <code>{4d6+2d8, 3d20+3, 5d10+1}d1</code>  Roll each of the three subroll expressions and total them up. Drop the subroll expression with the lowest total and sum the other two totals as the result.  
−  === Target Number / Successes (B,F)  <code>CP</code> ===  +  ==== Target Number / Successes (B,F)  <code>CP</code> ==== 
The same concept as when using on Dice Rolls but with different behavor for a group. For a Grouped Roll with a single subroll expression the success check is done after the remaining math expressions have been totaled into each roll. Single subroll groups are also useful when doing a success check on a roll that has another Compare Point enabled modifer. For a Grouped Roll with a multiple subroll expression the success check is applied to the esult of each subroll expression.  The same concept as when using on Dice Rolls but with different behavor for a group. For a Grouped Roll with a single subroll expression the success check is done after the remaining math expressions have been totaled into each roll. Single subroll groups are also useful when doing a success check on a roll that has another Compare Point enabled modifer. For a Grouped Roll with a multiple subroll expression the success check is applied to the esult of each subroll expression.  
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* <code>{4d6+2d8, 3d20+3, 5d10+1}>40</code>  Roll each of the three subroll expression and total them up. Count one success for each subroll total of 40 or more.  * <code>{4d6+2d8, 3d20+3, 5d10+1}>40</code>  Roll each of the three subroll expression and total them up. Count one success for each subroll total of 40 or more.  
−  === Failures (B,F)  <code>fCP</code> ===  +  ==== Failures (B,F)  <code>fCP</code> ==== 
Failure checks on groups work just like success checks.  Failure checks on groups work just like success checks. 
Latest revision as of 02:34, 31 March 2020
Roll20 features support for a wide array of dice mechanics. On this page we've compiled a list of all of the different types of dice rolls you can perform. Each type also has an interactive example box where you can make actual rolls using the same roll system that's built in to Roll20  a great way to experiment and check to make sure we can support your role playing game system of choice. Don't see a dice mechanic your game system needs, or think something is done incorrectly? Get in touch and let us know!
Want to skip straight to the 'nittygritty'? Check out the Dice Specification for the really advanced stuff! 
[edit] How to Roll Dice
Dice can be rolled simply from the Tabletop Toolbox Dice Rolling Interface
For more control over how the dice behave, or to automate processes or math, dice can be rolled in chat. Rolling dice in Roll20 is easy. Just type the /roll
command into the text chat box, followed by a formula. In most cases, the formula is the same as the one that's printed in your game's instructions. For example, you might know that to roll an attack roll you need to roll a "D20 plus your attack modifier". In Roll20, you would just type /roll d20+5
. If you hit and you need to roll 3d6+2 damage, you would just type /roll 3d6+2
. Finally, you can also string multiple rolls together. If you have an attack that does two types of damage, you might do /roll 2d6+5 + d8
.
/roll 1d20+5
After the roll is performed, you'll see the results of the roll in the text chat area. Notice that for each group of dice that were rolled, there will be a group of numbers in parentheses, representing the result of each individual dice that was rolled. (The number sits on an outline of the dice type rolled, and this outline is in the same color as the square of color in the diceroller's player portrait in the Player Area.) You'll also see the total of all the dice values plus modifiers to the right of the equal sign.
[edit] Rolling in Secret
By default, any rolls that you make are seen by everyone in the game with you (including all players). If you want to roll in secret, you can use the /gmroll
command to perform a roll that only the GM and the original player who made the roll can see. So if you're the GM, doing a /gmroll
will only be visible to you. It's a great way to perform skill checks in secret.
[edit] Including Additional Information
You can also include nonformula text in your roll to indicate what that roll is for. For example, when rolling for initiative you might enter /roll 1d20+5 Roll for Initiative
. The extra text won't affect your roll in any way, but it's included in the chat log so that others can see what you're rolling for. It's entirely optional to do this, by the way, but some GMs find it helps keep everything organized a little better.
/roll 1d20+5 Roll for Initiative
If you want to include any numbers, parentheses, or +
, 
, *
, /
, or %
in your additional text, you can preface it with a \
to separate the formula from the text and keep the roller from getting confused. So for example you can do /roll 1d20+5 \ +5 Roll for Initiative
.
[edit] Inline Labels
If you want to include additional comments before the end of the roll (we call them "inline labels"), use square brackets. For example, /roll 2d20+5[Fire Damage] + 3d6+5[Ice Damage]
. When these comments are applied directly after a die roll they show up as tooltips on the dice:
/roll 2d10+2d6[crit]+5 Critical Hit!
[edit] Inline Dice Rolls
If you want a more compact roll representation, you can take advantage of inline dice rolls. Inline rolls are just like regular rolls, with the following exceptions:
 You can use them in any chat message, not just a roll. For example, you can do a regular chat message, an emote, or a whisper, with an inline roll included.
 They are evaluated completely before any /roll commands, so you can use them as "random variables" in your rolls.
 You will only see the result of the total roll, and you can hover over the result to see the individual dice rolls.
 If an inline roll contains a crit success, it will be highlighted with a green box. If there's a crit failure, it's highlighted in red. If it has both (because there was more than one roll), it's in blue. Also when you mouseover the inline roll to see the details of the roll, it'll show red and green highlights for the rolls themselves for crits/fumbles.
To do an inline roll, just include two brackets in any chat message or roll, like so:
/em Riley is filled with [[3d6]] points of anger! /roll [[2d6]]d5
You can also nest inline rolls, one inside the other, like so:
/em Steve gets slapped with [[ 3d6>[[1+3]] ]] carp!
[edit] Roll Queries
Sometimes you may have a roll (or a macro) which you want to change every time it is rolled. For example, you may want to roll a variable number of dice, or add a different modifier onto the roll each time you perform the action. Roll Queries allow you to prompt whoever is performing the roll to fill in a value when the roll is made. The syntax for a roll query is:
?{Prompt Message} //Example: /roll ?{Number of Dice}d20 //You can also include a default value: /roll ?{Number of Dice1}d20 // 1 would be the default
You can use Roll Queries in rolls, macros, abilities, emotes, whispers  pretty much anywhere in the app. Note that if you use the same exact wording for a Query, Roll20 will only ask for the value the first time it's encountered in the roll. So in this example:
/roll 1d20 + ?{Bonus1} vs ?{MinToSucceed} + ?{Bonus1}
Roll20 will ask for "Bonus1" only once and use it in both places.
[edit] MathOnly Rolls
You can do mathonly rolls by adding a math expression after the roll command.
For example, if you want Roll20 to do a simple addition like 5 +
3, you'd enter the following:
/roll 5+3
Or if you want to do this in an inline roll you'd use:
[[5+3]]
[edit] Exploding Dice
Roll20 supports exploding dice  you may also know it as "rule of 6", "rule of 10s", or "acing" depending on your game system. With exploding dice, if you roll the maximum number on the dice (a 6 with a d6, a 10 with a d10, etc.) you get to reroll again and add the additional roll to your total for that roll. If the additional roll is also a maximum number, you get to keep rolling!
To perform a roll with exploding dice, just add an exclamation point after the number of sides in the formula. For example, /roll 3d6!
would roll 3 d6 dice with exploding rerolls. You can also define the exploding point for the dice using the greaterthan and lessthan symbols. For example, /roll 3d6!>4
would explode on any dice greaterthan or equalto 4. /roll 3d6!3
would explode only if a 3 is rolled.
/roll 10d6!
Compounding Exploding Dice (ShadowrunStyle Exploding Dice)
Shadowrun (and some other systems) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. So for example to roll 5 d6's, you would do /roll 5d6!!
. A common Shadowrun roll would be exploding dice compared to a target number, for example /roll {5d6!!}>8
(notice the use of the brackets to show that we don't mean "explode on anything greater than 8", but rather "explode on 6's compounding, then compare to 8 for successes). Even though the target number (8) is higher than the possible roll from a single die, with the compounding exploding rolls a single roll can be infinitely high!
/roll {5d6!!}>8
Penetrating Exploding Dice (HackmasterStyle Exploding Dice)
HackMaster (and some other systems) use a special style of exploding dice where the the additional rolls for each dice have 1 subtracted from the roll. To do this, add a p after the exclamation mark. So for example to roll 5 d6's, you would do /roll 5d6!p
.
/roll 5d6!p
[edit] Drop/Keep
Some game systems ask you to roll a large number of dice, and then either drop a certain number of the lowest rolls, or keep only a certain number of the highest rolls. Roll20 supports this type of roll through the d
and k
commands, respectively.
For example, you might roll 8 d100 dice and only be allowed to keep the top 4 rolls. In Roll20 this would be expressed with /roll 8d100k4
. When Roll20 prints the output from that roll, you'll see each individual d100's rolled value, and all but the top 4 rolls will be greyed out. Roll20 will then give you the total of the top 4 rolls. Doing a roll to drop the 3 lowest rolls would be very similar: /roll 8d100d3
. Again, the value of each dice rolled will be displayed, with the 3 lowest rolls greyed out.
/roll 8d100d3
The d
and k
commands are shortcuts for the full dl
and kh
commands. If you need to drop the highest dice use dh
and if you need to keep the lowest dice use kl
. For example /roll 8d100dh3
would drop the highest three rolls and keep the lowest 5 and /roll 8d100kl3
would keep the lowest three rolls and drop the highest 5.
[edit] Target Number (Successes)
Normally when you perform a roll, Roll20 reports back the total value of all the dice rolled, plus any modifiers. Some game systems, though, work by rolling a set of dice versus a target number, and then adding up the total number of successes instead. Roll20 uses the greaterthan symbol >
to indicate when the roll is greaterthan or equalto >=
the target number. The lessthan symbol <
is used to indicate when the roll is lessthan or equalto <=
the target number.
For example, you might be performing an action that requires a target number of 3, and you get to roll 3 d6's to see how many successes you have. In Roll20, you would do /roll 3d6>3
. Note the inclusion of the greaterthan symbol to indicate that this is a target roll versus 3. Roll20 will show you each dice that was rolled, and then tell you the number of dice with a value of 3 or greater (note that ties with the target number count as a success!). You can also roll lessthan target numbers, for example /roll 10d6<4
, which would give you a success for each dice rolled that is equal to 4 or less.
You can also add modifiers onto your target rolls, and the modifier will be added to each individual dice roll before it is compared to the target number. However, if you're going to do so, it's recommended that you use a group just to make sure the parser fully understands what you want to do. So, /roll {3d6+1}<3
would roll 3 d6 dice, and for each dice roll add on 1, then compare it versus the target number of 3.
/roll 3d6>3
[edit] Critical Success and Fumble Points
You can also modify your dice rolls to allow you to specify set at which point a roll is considered to be a "Critical Success" or "Critical Failure (Fumble)".
To show any roll equal to 10 or greater as a critical success, just do /roll 1d20cs>10
. To show any roll equal to or less than 3 as a critical failure, just do /roll 1d20cf<3
. To show any roll equal to 20 or 10 exactly as a critical success, just do /roll 1d20cs20cs10
.
Note: These values will not affect other things that by default work on max roll value (including exploding, penetrating, etc.). It only affects the display of the roll result to the player. For example, if you want dice to explode on 18 or higher, and you want to show an 18 or higher as a critical, you would need to do /roll 1d20!>18cs>18
.
/roll 1d20cs>10
[edit] Rerolling Dice
Several systems require that certain dice be reroll, for example brutal weapons in D&D 4e require any 1s or 2s to be rerolled and the orignal die value ignored.
To use reroll, just do /roll 2d8r<2
. Roll20 will roll 2 d8 and reroll any 1s or 2s, dropping the original die value. If reroll for a specific value is needed the comparison operator can be left off. /roll 2d8r8
will reroll any 8s. > and < can be used as comparisons and the r suffix can be specified multiple times. /roll 2d8r1r3r5r7
would roll 2d8 and reroll any odd number.
/roll 2d8r<2
[edit] FATE Dice
Roll20 also supports FATE dice (used for FATE, FUDGE, and other systems). Roll20 accurately simulates FATE dice as 6sided dice in which two sides are 0, two sides are +1, and two sides are 1.
To roll 4 FATE dice, just do /roll 4dF
. Roll20 will show you the result of each individual FATE dice roll, then give you the total of all the dice rolls added up together. You can also add a modifier onto the total, with /roll 4dF+1
.
/roll 4dF
[edit] Rounding Rolls and Math Functions
You may want to use rounding in your roll formulas to emulate mechanics such as "half a level, rounded down to the nearest level." Roll20 provides several functions to accomplish this: floor()
which will always round the number down (e.g. 5.7 becomes 5), ceil()
which will always round the number up (e.g. 5.1 becomes 6), and round()
which will always round to the nearest whole number (e.g. 4.4 becomes 4 and 4.5 becomes 5). You can use these functions almost anywhere in your roll formulas (around a single math expression, groups of math expressions, or even the entire roll). For example:
/roll floor(7/2) + 2d6
We also provide other Math functions:

abs()
will calculate the absolute value of the roll
[edit] Grouping Rolls
Sometimes you may want to perform a series of rolls, and then compare each roll to a common check (like a success roll). Roll20 provides a "grouped rolls" functionality for this purpose. For example, you can roll two different pools of dice, then keep the highest dice roll across any of the pools:
/roll {4d6+3d8}kh1
If you separate the rolls inside the group with a comma, then we'll sum each individual dice expression in the group before applying any modifiers. For example, if we change the above example to use a comma, instead of keeping the highest single roll, it will instead keep the highest group total:
/roll {4d6,3d8}kh1
This is needed in games based on the Savage Worlds system, where important characters roll a "wild die" in parallel with their main die and choose the highest roll.
Grouped rolls can be a very powerful features in Roll20. See more detail about them in the full dice specification below.
Below you'll find the entire Roll20 dice engine specification. This is the "advanced" documentation. If you're looking to do something totally crazy with Roll20 dice, this is a great place to see if we can support it.
[edit] Roll To Initiative
To add a roll directly into Roll20's Turn Track (Rolling for Initiative), you'll need to incorporate a "roll option". A roll option is a special Roll20 flag that you can set anywhere in a roll to tell the roll system you'd like to do special things with the roll. For adding an initiative number to the turn track, you'll first need to select the token you wish to roll for and use this formula:
/roll 1d20 + 5 &{tracker}
The &{} part is where you put your options for the roll, and the "tracker" option is what says "Show the results of this roll, but also use the result as the value in the turn tracker." If the token that you have selected doesn't already have a turn in the turn order, one will be added. If it already has at least one turn, all current turns will be updated with the new value.
[edit] Roll Templates
Roll Templates are a special facet of the Character Sheets system which provide additional layout and styling options for the display of roll results. Using a Roll Template is very easy to use. Just include a special flag in your chat message which tells Roll20 that you want to use a Roll Template, and then provide all of the data that you want to include.
Here's an example that uses the 'default' template (which all games have access to, regardless of the game system or Character Sheets you are using): &{template:default} {{name= My Test Roll}} {{attack= [[1d20]]}} {{damage= [[2d6]]}}
Note: If you're interested in using Roll Templates in your own custom macros or creating your own custom templates please vist the wiki entry on Roll Templates.
&{template:default} {{name= My Test Roll}} {{attack= [[1d20]]}} {{damage= [[2d6]]}}
[edit] Roll20 Dice Specification
[edit] Math Operators and Functions
Roll20 supports the basic arithmetic operators you learned in school: +
, 
, *
(multiply), and /
(divide).
In addition to the basic four, you have access to:

%
, for modulus division. The result ofa % b
is the remainder ofa / b
. If you think back to when you were first learning long division without getting into decimals, you were learning how to perform modulus division. Modulus is useful, for example, to test whether a value is even or odd:a % 2
will be 0 if a is even (and positive) and 1 if a is odd (and positive). In general, the result ofa % b
when a and b are both whole numbers will be a whole number in the range[0, b  1]
whereb
is the absolute value of b. (If a is less than 0, the result will be negative, including 0. 0 is functionally equivalent to 0.) 
**
, for exponentiation. You may be more familiar witha^b
as the notation for "raising a to the power of b", but in Roll20 you would usea**b
instead. Also note that finding roots is simply raising a number to a fractional exponent; square root is simply an exponent of 0.5, for example.
You also have access to a small set of mathematical functions:

floor(x)
rounds x towards negative infinity. 
round(x)
rounds x towards 0 if the fractional portion of x is less than 0.5, and round x towards positive infinity if the fractional portion of x is 0.5 or greater. 
ceil(x)
rounds x towards positive infinity. 
abs(x)
returns the absolute value of x.
Operations are performed by order of precedence, just like in normal mathematics. From highest to lowest precedence:
 Grouping with parentheses (
(
and)
); just like in real math, you can modify the precedence ordering by wrapping parentheses around things  Calling floor/round/ceil/abs
 Exponentiation (
**
)  Multiplication (
*
), division (/
), and modulus (%
), in the order they appear (lefttoright) in the formula  Addition (
+
) and subtraction (
), in the order they appear (lefttoright) in the formula
[edit] Order of Operations
While the Roll20 dice engine does support basic math and functions such as floor() and ceil(), it is first and foremost a dice engine, and so it has its own order of operations. This means that putting parentheses inside of your dice formula will not always affect the outcome of the roll (for example, you can't force a variable to be interpreted before a macro). Here is the general order of operations:
 Abilities are expanded (meaning the definition of the ability is placed in the formula anywhere that ability appears; e.g. %{character nameability_name} becomes /r 1d4).
 Macros are expanded (e.g. #macroname becomes /r 1d4).
 Attribute calls are resolved. (e.g. @{attribute_name} becomes 4)
 The 3 above steps are repeated up to 99 levels deep or there are no longer any expansions required.
 Roll queries are executed up to 99 levels deep (the player making the roll is asked to provide a value for each query, and that value is substituted in where the roll query appears in the formula). HTML entities within roll queries are parsed once after each roll query (e.g. } becomes } but } becomes })
 Inline rolls are executed, starting with the most deeply nested inline roll working upward. The overall result of the inline roll is substituted in place where it appeared in the formula.
 The remaining roll is executed: first, dice are rolled for any dice (e.g. "2d6" is rolled; including any special dice such as dropped or exploding), then the result of that roll is substituted into the formula. Next, floor() and ceil() functions are executed. Finally, the entire remaining formula is evaluated, including observing proper math order of operations (parentheses first, then multiplication/division, then addition/subtraction).
 Html entities are processed once more
 The message is sent to chat, and the API sandbox receives the message at this point as well
Thank you to Scott C. for additional testing in this matter!
[edit] Types Of Dice
Roll20 supports more than just your standard polyhedrons when rolling dice, below are the available die types you can use in your games.
[edit] Basic Roll NdX
Rolls N traditional (almost, you can have any number of sides that you want) dice with X sides per die. N must be greater than or equal to 0 and X must be greater than or equal to 1.
[edit] Fate/Fudge Roll NdF
Rolls N Fate/Fudge dice. These dice have three sides with values of 1, 0, and 1.
[edit] Computed Dice Roll (N+Y)dX
/Nd(X+Y)
Computes the number of dice to roll or the number of sides on the dice based on the mathematical expression in the parentheses. Dice computation can be used with both Basic and Fate dice.
Within (N+Y)dX
, the number of dice (N+Y)
is rounded to the nearest whole number, just like round(N+Y).
[edit] Roll Modifiers
Modfiers that can change the behavior or outcome of dice rolls. Each modifier states which Types Of Dice it can be applied to in parentheses after the modifier name. Rolls can have multiple modifiers applied to a single roll to allow for complex dice expressions.
 B  Basic Roll
 F  Fate/Fudge Roll
Many modifiers compare each die to a target number to decided if the modifier action should be applied. We'll call this a Compare Point or CP for short in the roll modifiers below. A Compare Point consists of an optional compare operation <
,=
,>
and a target number. If the operation is not specified =
is assumed and for most modifiers the entire Compare Point can be left off for the default behavior.
 Example Compare Points

=3
 If the roll is equal to 3 
>2
 If the roll is greater than or equal to 2 
<18
 If the roll is less than or equal to 18
[edit] Target Number / Successes (B,F)  CP
Normally when you perform a roll, Roll20 reports back the total value of all the dice rolled, plus any modifiers. Some game systems, though, work by rolling a set of dice versus a target number, and then adding up the total number of successes instead.
 Example Success Checks

3d6>3
 Roll 3 d6's and count one success for each roll of 3 or higher 
10d6<4
 Roll 10 d6's and count one success for each roll of 4 or less
[edit] Failures (B,F)  fCP
Some systems build on success checks by also including failures. Failure checks only work when a success check is already being done and each failure subtracts one from the total number of successes.
 Example Failure Checks

3d6>3f1
 Roll 3 d6's and count one success for each roll of 3 or higher and one failure for each 1 
10d6<4f>5
 Roll 10 d6's and count one success for each roll of 4 or less and one failure for each roll of 5 or more
[edit] Exploding Dice (B,F) !CP
Exploding dice, also known as "rule of 6" or "rule of 10s" depending on your gaming system, rolls an additional die if the maximum is rolled. If the additional roll is also the maximum number the additional rolls keep on going! The Compare Point can be specified to change the exploding trigger.
 Example Exploding Dice

3d6!
 Rolls 3d6 and explodes every time a 6 is rolled 
3d6!>5
 Rolls 3d6 and explodes every time a 5 or 6 is rolled
[edit] Compounding Dice (B,F) !!CP
Shadowrun (and some other systems, such as 7th Sea and L5R) use a special style of exploding dice where the the additional rolls for each dice are added together as a single "roll". To do this, just use two exclamation marks instead of one. With the compounding exploding rolls a single roll can be infinitely high! The Compare Point can be specified to change the exploding trigger.
 Example Compounding Dice

5d6!!
 Rolls 5d6 and compound every time a 6 is rolled 
5d6!!5
 Rolls 5d6 and compound every time a 5 is rolled, 6's will be treated as a normal roll
[edit] Penetrating Dice (B,F) !pCP
HackMaster (and some other systems) use a special style of exploding dice where the additional rolls for each dice have 1 subtracted from the roll. To do this, add a p after the exclamation mark. A die can penetrate multiple times but the modifier is only ever 1 to each additional die.
 Example Compounding Dice

5d6!p
 Rolls 5d6 and explode with a 1 modifier every time a 6 is rolled 
5d6!p>5
 Rolls 5d6 and explode with a 1 modifier every time a 5 or higher is rolled.
[edit] Dice Matching mt
It is possible to show how many of the dice rolled result in matches in the chat window. This feature works with the chat dice as well as the 3d dice, but the matches are only shown in the chat output.
m
will show matches visually but not change results of the roll.
mt
will return the number of matches, regardless of the number of dice that match.
[edit] Arguments
Both options can take 2 arguments: the number of matches required and/or the result the match needs to be.
As with other dice arguments, !
will result in exploding dice. If the exploding dice cause a match, the match will display in the results as well.
 Rolling
2d6m
will give you the result of the 2d6 added together, while grouping the matched rolls with a colored bar.  Rolling
2d6mt
will either return 0 matches or 1 match.  Rolling
20d6mt
could return 0 to 6 matches.  Rolling
6d6mt3
will show the number of matches if there are three of any result.  Rolling
5d6mt3>4
will show the number of matches if there are three of them AND the matching numbers 4 or greater.
[edit] How It Looks
When 2 or more dice match, the chat output displays them with a colored bar above the number in the output. Each number that matches displays with a different bar. Effort has been made to make the colors high contrast against each other.
Other standard visual indicators (bold, bright color) for highest and lowest numbers still work with the dice matching mechanic.
[edit] Keep / Drop Dice (B,F) khN
/klN
/dhN
/dlN
Some game systems ask you to roll a large number of dice, and then either drop a certain number (N) of the lowest rolls, or keep only a certain number (N) of the highest rolls. Roll20 supports this type of roll through the d
and k
commands, respectively. The optional h
/l
parameter can either be h
to keep or drop the highest N dice or l
to keep or drop the lowest N dice. If not specified when keeping rolls the high rolls will be kept and when dropping rolls the low rolls will be dropped.
 Example Keep Rolls

8d100k4
 Roll 8 d100's and keep the four largest rolls. 
8d100kl4
 Roll 8 d100's and keep the four smallest rolls.  Example Drop Rolls

8d100d4
 Roll 8 d100's and drop the four smallest rolls. 
8d100dh4
 Roll 8 d100's and drop the four largest rolls.
[edit] Rerolling Dice (B,F) rCP
Several systems require that certain dice be reroll, for example brutal weapons in D&D 4e require any 1s or 2s to be rerolled and the original die value ignored. The reroll modifier can be specified multiple times to allow rerolling at multiple Compare Points. By default the dice will continue to reroll until the result is inside the defined parameters. Optionally you can set the results to only reroll once regardless of the outcome.
 Example Rerolls

2d10r<2
 Roll 2 d10's and reroll any time a 2 or lower is rolled 
8d6r
 Roll 8 d6's and reroll any time a 1 is rolled 
8d6r2r4r6
 Roll 8 d6's and reroll any time a 2, 4, or 6 is rolled 
2d6ro<2
 Roll 2 d6's and reroll anything less than 2 but only once
Special Case: Reroll Once (B,F) roCP
In some systems (such as D&D 5E) you want to reroll dice below a certain value, but you only want to reroll the dice one time each. To do that, just use ro
instead of r
.
 Example Reroll Once Rolls

2d10ro<2
 Roll 2 d10's and reroll any time a 2 or lower is rolled, but only up to one time per dice.
[edit] Sorting Dice (B,F) sa
/sd
You may want to see your results in either ascending or descending order. The sorting modifier does just this. The order parameter is optional and specifies the order to sort with a
for ascending and d
for descending. Sorting defaults to ascending if order is not specified.
 Example Rerolls

8d6s
 Roll 8 d6's and sort the results in ascending order 
8d6sd
 Roll 8 d6's and sort the results in descending order
[edit] Order of Operations for Modifiers
Modifiers are applied in the following order:
 Exploding, Compounding, Penetrating, Rerolls
 These are applied while the dice are still rolling. imagine that you roll some exploding 6d6 on your table and the instant one of them settles as a 6 another die is rolled
 Keep, Drop, Success, Failure, Sorting
 These are applied after all of the dice have "settled" and all of the result values are known.
[edit] Grouped Rolls
Mutliple rolls can be perfomed within a group via curly braces using a comma to seperate the subroll expressions {3d6+3d4+5, 2d8+4}
. Grouped Rolls have their own set of Group Modifiers which perform actions across the whole group.
Note: each subroll expression within a Grouped Roll must contain elements of the same type:
 "Sum rolls", which can be Basic Rolls or nested Group Rolls.
 "Success rolls".
 ("M rolls"—which are simply numbers—may be mentioned in an error message. However, unlike the other two roll types, M rolls are not required to be present within every subroll expression.)
For example, [[ {1d6, 5}kh1 ]]
will fail, but [[ {1d6, 5 + 0d0}kh1 ]]
or [[ {1d6, {5}}kh1 ]]
or [[ {[[1d6]], 5}kh1 ]]
will work.
[edit] Grouped Roll Modifiers
Modfiers that can change the behavior or outcome of grouped rolls. Grouped Rolls can have multiple modifiers applied to a group roll to allow for complex dice expressions.
[edit] Keep / Drop khN
/klN
/dhN
/dlN
To apply a keep or drop modifier across multiple types of dice wrap the roll in a group. With a single SubRoll in the group the keep/drop operation is applied across all rolls. To choose the best or worse roll expression multiple subgroups can be used. In this case the keep/drop operation is applied to the final result of each subgroup.
 Single SubRoll Keep Example

{4d6+3d8}k4
 Roll 4 d6's and 3 d8's, out of those 7 dice the highest 4 are kept and summed up.  Multiple SubRoll Drop Example

{4d6+2d8, 3d20+3, 5d10+1}d1
 Roll each of the three subroll expressions and total them up. Drop the subroll expression with the lowest total and sum the other two totals as the result.
[edit] Target Number / Successes (B,F)  CP
The same concept as when using on Dice Rolls but with different behavor for a group. For a Grouped Roll with a single subroll expression the success check is done after the remaining math expressions have been totaled into each roll. Single subroll groups are also useful when doing a success check on a roll that has another Compare Point enabled modifer. For a Grouped Roll with a multiple subroll expression the success check is applied to the esult of each subroll expression.
 Single SubRoll Success Example

{3d20+5}>21
 Roll 3 d20's, for each roll add 5 and then count a success for each result of 21 or more. 
{2d6!}>4
 Roll 2d6 exploding and count a success for each roll of 4 or greater.  Multiple SubRoll Success Example

{4d6+2d8, 3d20+3, 5d10+1}>40
 Roll each of the three subroll expression and total them up. Count one success for each subroll total of 40 or more.
[edit] Failures (B,F)  fCP
Failure checks on groups work just like success checks.
 Single SubRoll Failure Example

{3d20+5}>21f<10
 Roll 3 d20's, for each roll add 5 and then count a success for each result of 21 or more and count a failure for each result of 10 or less. 
{2d6!}>4f1
 Roll 2d6 exploding and count a success for each roll of 4 or greater and a failure for each roll of 1.  Multiple SubRoll Failure Example

{4d6+2d8, 3d20+3, 5d10+1}>40f<10
 Roll each of the three subroll expression and total them up. Count one success for each subroll total of 40 or more and one failure for each subroll total of 10 or less.