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| description = Dice rolls are a central mechanic in Baldur's Gate 3 which determine the outcome of many different situations.
| description = Dice rolls are a central mechanic in Baldur's Gate 3 which determine the outcome of many different situations.
}}
}}
[[File:Deception.png|thumb|A Deception check]]
[[File:Deception.png|thumb|{{noexcerpt|A Deception check}}]]
'''Dice rolls''' are a central game mechanic in ''Baldur's Gate 3''. Dice are rolled to determine the outcome of variety of situations, such as whether or not a character will succeed at using a particular skill, or if an attack will land and how much damage it will do.
'''Dice rolls''' are a central game mechanic in ''Baldur's Gate 3''. Dice are rolled to determine the outcome of variety of situations, such as whether a character will succeed at using a particular skill, or if an attack will land and how much damage it will do.
{{TOC|limit=3}}
{{TOC|limit=3}}
== Dice notation ==
== Dice notation ==
Dice are notated with a ''d'' followed by the number of sides on that specific die: {{hlist|
Dice are notated with a ''d'' followed by the number of sides on that specific dice: {{hlist|
* {{DieIcon|d4|Force}} d4
* {{DieIcon|d4|Force}} d4
* {{DieIcon|d6|Radiant}} d6
* {{DieIcon|d6|Radiant}} d6
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* {{D20}}}}
* {{D20}}}}


The number of dice rolled is notated by with a number placed immediately before the ''d,'' and any applicable modifiers are given as an addition (if it is a bonus) or subtraction (if is a penalty) after the dice notation. When a single twenty sided die (d20) is rolled with no modifiers, it is notated as {{InfoBlob|1d20}}. When two six-sided dice (d6) are rolled with a modifier of +2, the roll is notated as {{InfoBlob|2d6+2}}.
The number of dice to be rolled is notated immediately before the ''d''. Any applicable '''[[#Modifiers|modifiers]]''' for the roll are given as an addition (if it is a '''bonus''') or subtraction (if it is a '''penalty''') after the dice notation. For example, when a single twenty sided dice (d20) is rolled with no modifiers, it is notated as {{InfoBlob|1d20}}. When two six-sided dice (d6) are rolled with a modifier of +3, the roll is notated as {{InfoBlob|2d6+3}}.


The range of potential results is usually given in parentheses. For example, a single dart from a {{SAI|Magic Missile|h=20px}} spell does 1d4+1 (2-5) Force damage, meaning it rolls 1d4 and adds 1 to the result, giving a possible total of between 2 and 5 points of damage.  
The range of potential results is often given in parentheses, especially for [[#Damage rolls|damage rolls]]. For example, a single dart from a {{SAI|Magic Missile|h=20px}} spell does {{InfoBlob|1d4+1 (2-5) Force damage}}. This means rolling 1d4 and adding 1 to the result, giving a possible total of 2 to 5 points of damage.


== Modifiers ==
== Modifiers ==
A number of modifiers are potentially added to dice rolls. These modifiers can be either bonuses which are {{em|added}} to the result or penalties, which are subtracted from the results.
A number of '''modifiers''' are potentially added to dice rolls. Modifiers are either '''bonuses''' which add to the result, or '''penalties''' which are subtracted from it. A roll may have bonuses and/or penalties from multiple sources; in such cases they are added together and expressed as a single modifier. For example, a d20 roll with a bonus of +5 and a penalty of -2 would be expressed as {{InfoBlob|1d20+3}}.


; Ability score modifiers : Most rolls have an associated [[ability]], and creatures add their corresponding ability score modifier to the outcome of rolls they make.
; Ability score modifiers : Most rolls have an associated [[ability]], and creatures add their corresponding ability score modifier to the outcome of rolls they make.
:: Creatures also add an ability score modifier to the save DCs of actions they take or spells that they cast, again corresponding to an associated ability.
; Proficiency bonus : Creatures add their proficiency bonus to any attack rolls, ability checks, or saving throws that they make using weapons, skills, or saves that they are proficient in, as well as to all attack rolls made during spell attacks.
; Proficiency bonus : Creatures add their proficiency bonus to any attack rolls, ability checks, or saving throws that they make using weapons, skills, or saves that they are proficient in, as well as to all attack rolls made during spell attacks.
:: Creatures also add their proficiency bonus to the save DCs of spells they cast and class actions they take, and to the save DCs of actions they take using weapons they are proficient with.
; Additional modifiers : Some [[features]] and [[conditions]] add additional modifiers to save DCs and the results of rolls, such as [[Shillelagh]], which allows the caster to add their spellcasting ability modifier to their attack and damage rolls, instead of Strength or Dexterity.
; Additional modifiers : Some [[features]] and [[conditions]] add additional modifiers to save DCs and the results of rolls, such as [[Shillelagh]], which allows the caster to add their spellcasting ability modifier to their attack and damage rolls, instead of Strength or Dexterity.
When a creature forces an opponent to make a [[#Saving throw|saving throw]] against a spell the creature has cast or action they have taken, the applicable modifiers are added to the creature's save DC instead.


== d20 rolls ==
== d20 rolls ==
Whenever a creature attempts an action that has a chance of failure, they roll a twenty-sided die (d20) against a target number to determine whether the attempt was a success or a failure, and add any applicable modifiers. If the result is equal to or exceeds the target number, the attempt was successful. If the result was lower than the target number, or if the creature rolled a 1, the attempt failed.
Whenever a creature attempts an action that has a chance of failure, it rolls a twenty-sided die (d20) against a target number to determine whether the attempt was a success or a failure, and add any applicable modifiers. If the result is equal to or exceeds the target number, the attempt was successful. If the result was lower than the target number, or if the creature rolled a 1, the attempt failed.


These attempts are categorized either as attack rolls – which are rolled against the target's [[Armour Class]] (AC), as ability checks – which are rolled against the check's Difficulty Class (DC), or as saving throws – which are rolled against a save DC:
These attempts are categorized either as attack rolls – which are rolled against the target's [[Armour Class]] (AC), as ability checks – which are rolled against the check's Difficulty Class (DC), or as saving throws – which are rolled against a save DC:
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<center>Formula = {{InfoBlob|{{D20}} + Ability score modifier + Proficiency bonus (if proficient) + Other modifiers (if any)}}</center>
<center>Formula = {{InfoBlob|{{D20}} + Ability score modifier + Proficiency bonus (if proficient) + Other modifiers (if any)}}</center>


; Attack rolls : When a creature attacks a target, they make an attack roll against the target's AC to determine whether the attack is a hit or a miss. If the attack is a hit, it generally deals damage, and the attacker rolls for damage. Creatures generally make their attacks with their equipped [[weapon]] (including unarmed), but some [[spells]] – such as a [[Warlock]]'s [[Eldritch Blast]] – require the caster to make spell attack rolls.
; Attack rolls : When a creature attacks a target, it makes an attack roll against the target's AC to determine whether the attack is a hit or a miss. If the attack is a hit, it generally deals damage, and the attacker rolls for damage. Creatures generally make their attacks with their equipped [[weapon]] (including unarmed), but some [[spells]] – such as a [[Warlock]]'s [[Eldritch Blast]] – require the caster to make spell attack rolls.
; Saving throws : Traps, spells, conditions, and other sources of harm may allow a creature a chance to avoid or reduce their effect, known as a saving throw or ''save''. To attempt a save, a creature rolls a d20 against a target save DC.
; Saving throws : Traps, spells, conditions, and other sources of harm may allow a creature a chance to avoid or reduce their effect, known as a saving throw or ''save''. To attempt a save, a creature rolls a d20 against a target save DC.
; Ability checks : An ability check is an attempt to succeed at a specific task, and is rolled against a Difficulty Class (DC) set by the game for that task. If the final result of the roll equals or exceeds the DC, the attempt is successful.
; Ability checks : An ability check is an attempt to succeed at a specific task, and is rolled against a Difficulty Class (DC) set by the game for that task. If the final result of the roll equals or exceeds the DC, the attempt is successful.
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A Difficulty Class (or DC) is a number rolled against when making ability checks or saving throws. It represents how difficult a task is to accomplish.
A Difficulty Class (or DC) is a number rolled against when making ability checks or saving throws. It represents how difficult a task is to accomplish.


The number is determined by the the task attempted – or in the case of saves – the spell, condition, or action that has to be overcome.
The number is determined by the task attempted – or in the case of saves – the spell, condition, or action that has to be overcome.


=== Natural 1s and 20s ===
=== Natural 1s and 20s ===
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[[File:Advantage Icon.png|alt=The in-game symbol for advantage.|left]]
[[File:Advantage Icon.png|alt=The in-game symbol for advantage.|left]]
[[File:Disadvantage Icon.png|alt=The in-game symbol for disadvantage|left]]
[[File:Disadvantage Icon.png|alt=The in-game symbol for disadvantage|left]]
A [[List of sources of advantage|number of situations and conditions]] give creatures advantage or disadvantage on d20 rolls. A creature that makes a roll with advantage rolls two d20 dice separately, and uses the higher of the two results. If they have disadvantage, they choose the lower of the two.
A number of situations and conditions give creatures advantage or disadvantage on d20 rolls. A creature that makes a roll with advantage rolls two d20 dice separately, and uses the higher of the two results. If they have disadvantage, they choose the lower of the two.


Creatures receive no additional benefit or penalty from having multiple sources of advantage or disadvantage on a dice roll, and still only roll twice. Likewise, creatures that have {{em|both}} advantage and disadvantage on a roll only roll a single die, even if they have multiple sources of either.
Creatures receive no additional benefit or penalty from having multiple sources of advantage or disadvantage on a dice roll, and still only roll twice. Likewise, creatures that have {{em|both}} advantage and disadvantage on a roll only roll a single die, even if they have multiple sources of either.
For an exhaustive list of sources of advantage and disadvantage, see the following pages:
* For attack rolls: [[List_of_sources_of_advantage_and_disadvantage_on_attack_rolls#Advantage_on_attack_rolls|Advantage]] and [[List_of_sources_of_advantage_and_disadvantage_on_attack_rolls#Disadvantage_on_attack_rolls|Disadvantage]]
* For saving throws: [[List_of_features_and_items_that_affect_saving_throws#Advantage_on_saving_throws|Advantage]] and [[List_of_features_and_items_that_affect_saving_throws#Disadvantage_on_saving_throws|Disadvantage]]


== Ability checks ==
== Ability checks ==
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: Ability checks are also common during dialogue, where some responses require an ability check to determine the outcome. Examples include using Charisma-based skills like [[Persuasion]], [[Deception]], or [[Intimidation]] to influence others, or Intelligence-based skills like [[Investigation]], [[History]], or [[Religion]] to determine or remember facts.
: Ability checks are also common during dialogue, where some responses require an ability check to determine the outcome. Examples include using Charisma-based skills like [[Persuasion]], [[Deception]], or [[Intimidation]] to influence others, or Intelligence-based skills like [[Investigation]], [[History]], or [[Religion]] to determine or remember facts.
; Contests
; Contests
: A contest is a special type of ability check in which two creatures both roll an ability check to oppose each other, and one wins over the other. The creatures don't necessarily roll the same type of check.
: A contest is a special type of ability check where one creature rolls an ability check against another creature's skill. Rather than rolling, the opposing creature uses a ''passive skill'' value given by {{InfoBlob|10 + skill bonus}} with {{Advantage}} on the relevant skill check adding 5 or {{Disadvantage}} subtracting 5. The passive skill value serves as the [[Difficulty Class]] (DC) of the skill check.
:: An example of this is the {{SAI|Shove}} action. The creature attempting the Shove rolls Athletics, and the defending creature rolls either Athletics or Acrobatics (the game chooses the Skill with the highest bonus) to contest the Shove. If the attacker's roll is higher than the defender's, the Shove succeeds; otherwise, it fails.
:: An example of this with {{SAI|Shove}}. The creature attempting the shove makes an [[Athletics]] check versus the target's passive Athletics {{em|or}} [[Acrobatics]], whichever is higher.
:: Another example is with {{SAI|Hide}} where the sneaking creature makes a [[Stealth]] check against an enemy's passive [[Perception]] while in their cone of vision to avoid being detected.


== Saving throws ==
== Saving throws ==
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=== Save proficiency ===
=== Save proficiency ===
All classes give save proficiency with two abilities. Though when multiclassing, only the {{em|first}} class taken gives its save proficiencies. An additional save proficiency can be gained by taking the [[Resilient]] feat.
All classes give save proficiency with two abilities. Though when multiclassing, only the '''first''' class taken gives its save proficiencies. An additional save proficiency can be gained by taking the [[Resilient]] feat.
 
{{ClassSavingThrowsTable}}


=== Save DCs ===
=== Save DCs ===
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; Spell save DC : The Difficulty Class of a spell that can be saved against is determined through the following formula:
; Spell save DC : The Difficulty Class of a spell that can be saved against is determined through the following formula:
:: {{InfoBlob|8 + proficiency bonus + spellcasting ability modifier}}.
:: {{InfoBlob|8 + proficiency bonus + spellcasting ability modifier}}.
: Certain [[conditions]] and [[List of Equipment that Affect Spell DC|equipment]] worn by the caster can also affect their Spell Save DC.
: Certain [[conditions]] and [[List of equipment that affect Spell Save DC|equipment]] worn by the caster can also affect their Spell Save DC.
; Weapon save DC: Most weapons allow proficient users to perform special "weapon actions", which are typically limited to once per short rest (e.g. [[Backbreaker]]). These actions often include the chance to inflict a condition on the target, and these conditions require the target to attempt a Save to avoid them. Each weapon action can grant its own inherent bonus to DC that isn't listed anywhere, but is frequently +2. The Difficulty Class of saves allowed by weapon actions is calculated as follows:  
: This value can be checked by the shortcut key "K" and the target's saving throw can be checked by the shortcut key "T".
 
; Weapon save DC: Most weapons allow proficient users to perform special "[[Weapon_actions|weapon actions]]", which are typically limited to once per short rest (e.g. [[Backbreaker]]). These actions often include the chance to inflict a condition on the target, and these conditions require the target to attempt a Save to avoid them. Each weapon action can grant its own inherent bonus to DC that isn't listed anywhere, but is frequently +2. The Difficulty Class of saves allowed by weapon actions is calculated as follows:  
:: {{InfoBlob|1=Weapon Action DC = 8 + proficiency bonus + [[Strength]] or [[Dexterity]] modifier + inherent weapon action bonus DC}}
:: {{InfoBlob|1=Weapon Action DC = 8 + proficiency bonus + [[Strength]] or [[Dexterity]] modifier + inherent weapon action bonus DC}}
: Certain weapon actions, notably [[Concussive Smash]], instead allow the acting creature to either use their Spell Save DC or weapon action DC with a +2 bonus, whichever is higher.
: Certain weapon actions, notably [[Concussive Smash]], instead allow the acting creature to either use their Spell Save DC or weapon action DC with a +2 bonus, whichever is higher.
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=== Death saving throws ===
=== Death saving throws ===
Death saving throws are a special type of saving throw made by playable characters and companions after they have been {{cond|Downed}}. Death saves are made once per turn while the character remains Downed, and when the character takes damage while Downed. Three successful saves will let a creature stabilize, no longer needing to make death saves to survive, and three failures will lead to the creature becoming {{cond|Dead}}.  
Death saving throws are a special type of saving throw made by playable characters after they have been {{cond|Downed}}. Death saves are made once per turn while the character remains Downed. If a Downed character receives damage from any source that isn't a critical hit, they automatically fail one death saving throw. A critical hit against a Downed character results in 2 failed saves. Melee attacks against a Downed target are always classified as a critical hit.  
 
Three successful saves will let a creature stabilize, no longer needing to make death saves to survive, and three failures will lead to the creature becoming {{cond|Dead}}.  


Death saving throws are not associated with an ability score and so don't get any modifiers, nor do they benefit from the proficiency bonus. They only benefit from bonuses that apply to all saving throws (such as {{SAI|Bless}}) or specifically to death saves (such as [[Family Ring]]). Death saves are always DC 10. A character dies when three failures are accumulated, or stabilizes when three successes are accumulated, whichever happens first.
Death saving throws are not associated with an ability score and so don't get any modifiers, nor do they benefit from the proficiency bonus. They only benefit from bonuses that apply to all saving throws (such as {{SAI|Bless}}) or specifically to death saves (such as [[Family Ring]]). Death saves are always DC 10. A character dies when three failures are accumulated, or stabilizes when three successes are accumulated, whichever happens first.
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=== Critical hits ===
=== Critical hits ===
{{main|Critical hit}}
[[File:critical hit.png|right|thumb|Example of a critical hit with a 1d6 shortsword.]]
[[File:critical hit.png|right|thumb|Example of a critical hit with a 1d6 shortsword.]]
When a creature rolls a natural 20 on an attack roll, the attack is a ''critical hit.'' Critical hits automatically land regardless of the target's AC, and the attacker also rolls twice the normal number of dice to determine damage dealt, including additional dice such as those from smites or combat maneuvers. Modifiers and bonuses – including the creature's relevant ability score modifier and proficiency bonus – are not doubled.
When a creature rolls a natural 20 on an attack roll, the attack is a [[critical hit]]''.'' Critical hits automatically land regardless of the target's AC, and the attacker also rolls twice the normal number of dice to determine damage dealt, including additional dice such as those from smites or combat maneuvers. Modifiers and bonuses – including the creature's relevant ability score modifier and proficiency bonus – are not doubled.
 
Some [[feats]], [[Classes|class features]], and [[items]] [[Critical Hit threshold reduction|reduce]] the critical hit threshold by 1, allowing the creature to land critical hits by rolling either 19 or 20 on attack rolls. Multiple sources of this effect stack, allowing the critical hit threshold to go even lower than 19. See [[list of sources of critical hit threshold reduction]].


Some conditions, such as {{cond|Sleeping}} and {{cond|Paralysed}}, automatically turn all incoming attacks into critical hits.
Some [[feats]], [[Classes|class features]], and [[items]] [[Critical Hit threshold reduction|reduce]] the critical hit threshold by 1, allowing the creature to land critical hits by rolling either 19 or 20 on attack rolls. Multiple sources of this effect stack, allowing the critical hit threshold to go even lower than 19.


=== Armour Class ===
=== Armour Class ===
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The formula that determines AC when wearing Armour in the torso slot is:
The formula that determines AC when wearing Armour in the torso slot is:
: {{InfoBlob|Torso armor AC + [[Dexterity|Dexterity modifier]] + shield bonus + other bonuses and penalties}}
: {{InfoBlob|Torso armor AC + [[Dexterity|Dexterity modifier]] + shield bonus + other bonuses and penalties}}
The AC bonus from Dexterity is typically capped at +2 when wearing [[Armour#Medium armour|medium armour {{note|The [[Medium Armour Master]] feat increases the cap from +2 to +3.}}{{note|A few rare armours have an "Exotic Material" trait that allow the wearer to get the full Dexterity bonus to AC. These include [[Yuan-Ti Scale Mail]], [[Unwanted Masterwork Scalemail]], [[Sharpened Snare Cuirass]], and [[Armour of Agility]].}}]], and is reduced to zero when wearing [[Armour#Heavy armour|heavy armour]].
The AC bonus from Dexterity is typically capped at +2 when wearing [[Armour#Medium armour|medium armour]]{{note|The [[Medium Armour Master]] feat increases the cap from +2 to +3.}}{{note|A few rare armours have an "Exotic Material" trait that allow the wearer to get the full Dexterity bonus to AC. These include [[Yuan-Ti Scale Mail]], [[Unwanted Masterwork Scalemail]], [[Sharpened Snare Cuirass]], and [[Armour of Agility]].}}, and is reduced to zero when wearing [[Armour#Heavy armour|heavy armour]].


Most [[Shields]] grant +2 AC.
Most [[Shields]] grant +2 AC.


Other bonuses include things like the [[Fighting style|Defense]] fighting style, which grants +1 AC while wearing armor, and the [[Cloak of Protection]].
Other bonuses include things like the [[Fighting style|Defense]] fighting style, which grants +1 AC while wearing armor, and the [[Cloak of Protection]], which grants +1 AC at all times. Bonuses to AC stack with each other.


==== Other formulas ====
==== Other formulas ====
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{{SAI|Unarmoured Defence (Barbarian)}}:
{{SAI|Unarmoured Defence (Barbarian)}}:
: {{InfoBlob|10 + Constitution modifier† + Dexterity modifier + shield bonus + other bonuses and penalties}}
: {{InfoBlob|10 + Constitution modifier + Dexterity modifier + shield bonus + other bonuses and penalties}}


{{SAI|Unarmoured Defence (Monk)}}:
{{SAI|Unarmoured Defence (Monk)}}:
: {{InfoBlob|10 + Wisdom modifier† + Dexterity modifier + other bonuses and penalties}}
: {{InfoBlob|10 + Wisdom modifier + Dexterity modifier + other bonuses and penalties}}


== Damage rolls ==
== Damage rolls ==
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Which ability score modifier is added to a damage roll depends on the attack:
Which ability score modifier is added to a damage roll depends on the attack:
* When making weapon attacks, the attacking creature usually adds the ability score modifier that they added to the attack roll.
* When making weapon attacks, the attacking creature usually adds their ability score modifier to the attack roll.
* Ability score modifiers are not normally added to damage rolls dealt by spells or spell attacks, unless specifically stated otherwise in the spell's description, or if enabled by some feature, such as {{SAI|Agonising Blast|h=20px}}.
* Ability score modifiers are not normally added to damage rolls dealt by spells or spell attacks, unless specifically stated otherwise in the spell's description, or if enabled by some feature, such as {{SAI|Agonising Blast|h=20px}}.


Proficiency bonuses are {{em|not}} added to damage rolls unless the attack being used (e.g. [[Shadowsoaked Blow]]) says so.
Proficiency bonuses are ''not'' added to damage rolls unless the attack being used (e.g. [[Shadowsoaked Blow]]) says so.


== Other rolls ==
== Other rolls ==
; Healing : [[Healing]] restores a target's [[hit points]] in a similar manner to damage rolls. Healing rolls may also add modifiers, but there's no general rule for this; any bonuses are determined by the source of the healing. For example, a [[Potion of Healing]] restores {{DamageText|2d4+2|Healing}}. There are many magic items, class features, and other effects which also provide bonuses to healing, for example the {{Class|Life Domain}}'s {{SAI|Disciple of Life}} feature.
; Healing : [[Healing]] restores a target's [[hit points]] similarly to damage rolls. Healing rolls may also add modifiers, but there's no general rule for this; any bonuses are determined by the source of the healing. For example, a [[Potion of Healing]] restores {{DamageText|2d4+2|Healing}}. There are many magic items, class features, and other effects which also provide bonuses to healing, for example the [[Life Domain]] [[Cleric]]'s {{SAI|Disciple of Life}} feature.
; Wild Magic : When a Wild Magic sorcerer casts a leveled spell, a d20 is rolled to determine if they will trigger a Wild Magic Surge. A surge is triggered only when the outcome is 20. The resulting effect, and Wild Magic Barbarian surge effects for Rage: Wild Magic, are also determined with dice rolls.
; Wild Magic : When a Wild Magic sorcerer casts a leveled spell, a d20 is rolled to determine if they will trigger a Wild Magic Surge. A surge is triggered only when the outcome is 20. The resulting effect, and Wild Magic Barbarian surge effects for Rage: Wild Magic, are also determined with dice rolls.


== Karmic Dice ==
== Karmic Dice ==
[[File:karmic dice setting.png|upright=0.7|thumb|The optional Karmic Dice setting, located in Gameplay Options]]
[[File:karmic dice setting.png|upright=0.7|thumb|The optional Karmic Dice setting, located in Gameplay Options]]
When the Karmic Dice option is enabled (it is by default), the game will avoid streaks of very low or very high rolls.
When the Karmic Dice option is enabled (it is by default), the game will avoid streaks of low rolls.  


However, Karmic Dice influences all rolls – including those of enemies – and the results always skew toward a positive result for the dice roller. In short, '''the Karmic Dice setting makes combat encounters quicker and deadlier''' for both you and your enemies, as attacks are more likely to hit and do higher damage.  
However, Karmic Dice influences all rolls – including those of enemies – and the results always skew toward a positive result for the dice roller. In short, '''the Karmic Dice setting makes combat encounters quicker and deadlier''' for both you and your enemies, as attacks are more likely to hit and do higher damage.  
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|}
|}


Notice how often the 5 appears in the possibilities for the '''total value''' (4 out of 16 possibilities) vs. how often the 8 appears (1 out of 16).  This means a 2d4 roll has a 25% chance of resulting in 5 points of damage, but only a 6.125% chance of resulting in 8 points of damage.  Meanwhile, the 1d8 roll actually has a higher chance of resulting in the maximum damage value of 8, since 1 out of 8 possibilities (12.5%) result in an 8. However, the average roll of 2d4 is 5 damage, while the average roll of 1d8 is only 4.5. Therefore, 2d4 is generally more consistent in damage output and will result in higher rolls in the long run.  
Notice how often the 5 appears in the possibilities for the '''total value''' (4 out of 16 possibilities) vs. how often the 8 appears (1 out of 16).  This means a 2d4 roll has a 25% chance of resulting in 5 points of damage, but only a 6.25% chance of resulting in 8 points of damage.  Meanwhile, the 1d8 roll actually has a higher chance of resulting in the maximum damage value of 8, since 1 out of 8 possibilities (12.5%) result in an 8. However, the average roll of 2d4 is 5 damage, while the average roll of 1d8 is only 4.5. Therefore, 2d4 is generally more consistent in damage output and will result in higher rolls in the long run.  


=== Advantage mathematics ===
=== Advantage mathematics ===
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|8||65% ||87.75%||42.25%
|8||65% ||87.75%||42.25%
|-
|-
|9||60% ||84%|| 42.25%
|9||60% ||84%|| 36%
|-
|-
|10||55%||79.75%||30.25%
|10||55%||79.75%||30.25%
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|}
|}


==== Effects of advantange on the average of dice rolls ====
==== Effects of advantage on the average of dice rolls ====
A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll.
A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll.


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To know what bonus having advantage gives to our roll, we calculate
To know what bonus having advantage gives to our roll, we calculate
{{math_block|1= \mathbb{E}[\text{D}n \text{ with advantage}] - \mathbb{E}[\text{D}n] = \frac{2n}{3} + \frac{1}{2} - \frac{1}{6n} - \frac{n + 1}{2} = \frac{1}{6}\left(n - \frac{1}{n}\right) }}
{{math_block|1= \mathbb{E}[\text{D}n \text{ with advantage}] - \mathbb{E}[\text{D}n] = \frac{2n}{3} + \frac{1}{2} - \frac{1}{6n} - \frac{n + 1}{2} = \frac{1}{6}\left(n - \frac{1}{n}\right) }}
When we apply this expression to a d20, the results is that having advantage is equivalent to an average bonus of +3.325.
When we apply this expression to a d20, the result is that having advantage is equivalent to an average bonus of +3.325.


Because of symmetry, having disadvantage instead of advantage means we can simply make the permutation of {{math|\{1, \dots, n\} \to \{n, \dots, 1\} }} for the values of dice rolls and all the calculations will remain the same. Therefore the size of the bonus of advantage is equal to the size of the penalty of disadvantage.
Because of symmetry, having disadvantage instead of advantage means we can simply make the permutation of {{math|\{1, \dots, n\} \to \{n, \dots, 1\} }} for the values of dice rolls and all the calculations will remain the same. Therefore, the size of the bonus of advantage is equal to the size of the penalty of disadvantage.


==== Effects of advantage on criticals ====
==== Effects of advantage on critical rolls ====
When making an ability check, attack roll, or saving throw, a 1 or a 20 will {{em|always}} be treated as a critical failure or success, respectively, regardless of the results after any potential modifiers are added. On a dice roll without advantage or disadvantage, this effectively means there is a {{math|1/20}} (or 5%) chance of either a critical success or failure.
When making an ability check, attack roll, or saving throw, a 1 or a 20 will {{em|always}} be treated as a critical failure or success, respectively, regardless of the results after any potential modifiers are added. On a dice roll without advantage or disadvantage, this effectively means there is a {{math|1/20}} (or 5%) chance of either a critical success or failure.


Having advantage or disadvantage can drastically increase or reduce the chance of critical successes and Failures. For example, when rolling with advantage, the only way to get a Critical Failure is to roll {{em|two}} 1s at the same time. The odds of this result is {{math|1=1/20 \cdot 1/20 = 1/400}} (or 0.25%). Conversely, rolling a Critical Success is far more likely - out of the 400 possible dice roll outcomes,  39 will result in a 20 (rolling 20 on the first die and 1, 2, 3, ... 20 on the second die, plus rolling 20 on the second die and 1, 2, 3, ... 20 on the first die, minus one so that the result of two 20s is not doubly-counted). The odds of this result is {{math|39/400}} (or 9.75%). The opposite is true for rolling with Disadvantage: a Critical Success has a 0.25% chance and a Critical Failure has a 9.75% chance.
Having advantage or disadvantage can drastically increase or reduce the chance of critical successes and Failures. For example, when rolling with advantage, the only way to get a Critical Failure is to roll {{em|two}} 1s at the same time. The odds of this result are {{math|1=1/20 \cdot 1/20 = 1/400}} (or 0.25%). Conversely, rolling a Critical Success is far more likely - out of the 400 possible dice roll outcomes,  39 will result in a 20 (rolling 20 on the first die and 1, 2, 3, ... 20 on the second die, plus rolling 20 on the second die and 1, 2, 3, ... 20 on the first die, minus one so that the result of two 20s is not doubly-counted). The odds of this result are {{math|39/400}} (or 9.75%). The opposite is true for rolling with Disadvantage: a Critical Success has a 0.25% chance and a Critical Failure has a 9.75% chance.


Effectively, rolling with advantage means that critical failures are ''20 times {{em|less}} likely'', and critical successes are almost {{em|twice}} as likely, while the inverse is true for disadvantage.
Effectively, rolling with advantage means that critical failures are ''20 times {{em|less}} likely'', and critical successes are almost {{em|twice}} as likely, while the inverse is true for disadvantage.
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== Footnotes ==
== Footnotes ==
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[[Category:Gameplay mechanics]]
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