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[[File:Deception.png|thumb|A Deception check]] | [[File:Deception.png|thumb|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 | '''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 or not 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 | Dice are notated with a ''d'' followed by the number of sides on that specific die: {{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 | The number of dice rolled is notated by with a number placed immediately before the ''d'' and any applicable modifiers are given in addition (if it is a bonus) or substraction (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 range of | A number of modifiers are potentially added to dice rolls. These modifiers can be either bonuses {{subst:}} which are {{em|added}} to the result – or penalties, which are subtracted from the results. These are notated | ||
The range of 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. | |||
Dice rolls are expressed in the game using both dice notation: {{math|xdN + y}}, where ''x'' is the number of dice rolled, and ''N'' is the number of sides of those dice. ''y'' is the sum of all modifiers added to the dice roll. | |||
The game also expresses damage using a range: {{math|a \sim b}}, where ''a'' is the minimum damage possible and ''b'' is the maximum damage possible. | |||
== Modifiers == | == Modifiers == | ||
A number of | A number of modifiers are potentially added to dice rolls. These modifiers can be either bonuses {{subst:}} which are {{em|added}} to the result – or penalties, which are subtracted from the results. | ||
; Ability score modifiers : Most rolls have an associated [[ability]] | ; Ability score modifiers : Most rolls have an associated [[ability]] and creatures add their corresponding ability score modifier to the outcome of rolls they make. | ||
; Proficiency bonus : Creatures add their proficiency bonus to any attack rolls, ability checks | :: 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. | ||
; Additional modifiers : Some [[features]] and [[conditions]] add additional modifiers to save DCs and the | ; 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 proficiency with. | |||
; Additional modifiers : Some [[features]] and [[conditions]] add additional modifiers to save DCs and the result 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. | |||
== d20 rolls == | == d20 rolls == | ||
Whenever a creature attempts an action that has a chance of failure, | 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. | ||
These attempts are | These attempts are categorised 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: | ||
<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 | ; Attack rolls : When a creature attacks a target they make an attack roll against the target's DC 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 attacks. | ||
; Saving throws : Traps, spells, conditions | ; 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. | ||
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 | 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. | ||
=== Natural 1s and 20s === | === Natural 1s and 20s === | ||
Rolling a 1 or 20 on a d20 roll is referred to as a ''natural 1'' or ''natural 20''. When making an attack roll or ability check, rolling a natural 1 is always an automatic failure, while a natural 20 is always an automatic success, regardless of the final result after modifiers are applied. Saving throws attempted during dialogue | Rolling a 1 or 20 on a d20 roll is referred to as a ''natural 1'' or ''natural 20''. When making an attack roll or ability check, rolling a natural 1 is always an automatic failure, while a natural 20 is always an automatic success, regardless of the the final result after modifiers are applied. Saving throws attempted during dialogue and death saving throws can also roll roll natural 1s and 20s. | ||
Unlike attack rolls and ability checks, saving throws are not guaranteed to fail or succeed when the d20 result is either a natural 1 or 20 respectively, | Unlike attack rolls and ability checks, saving throws are not guaranteed to fail or succeed when the d20 result is either a natural 1 or 20 respectively, however when saving throws are used during dialogue they will guarantee failure or success when a 1 or 20 is rolled. | ||
=== Advantage and disadvantage === | === Advantage and disadvantage === | ||
[[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 | A [[List of sources of advantage|number of situations and conditions]] give creatures advantage or disadvantage on d20 rolls. A creatur that makes a roll with advantage rolls two d20 dice separately, and use the higher of the two results. If they instead 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. | Creatures receive no additional benefit or penalty from having multiple sources of advantage or disadvantage on a dice roll, and still only roll twice. Likesise, creatures that have {{em|both}} advantage and disadvantage on a roll only roll a single die, even if they have multiple sources of either. | ||
== Ability checks == | == Ability checks == | ||
Ability checks are dice rolls made to determine whether a creature succeeds or fails at a task. They are rolled against the task's Difficulty Class | Ability checks are dice rolls made to determine whether a creature succeeds or fails at a task. They are rolled against the task's Difficulty Class, which is generally predetermined by the game. Each ability check is made using one of the six abilities in the game, and creatures add an ability's corresponding ability score modifier to the results of ability checks they make. | ||
=== Skills === | === Skills === | ||
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==== Expertise ==== | ==== Expertise ==== | ||
[[File:Expertise.png|right]] | [[File:Expertise.png|right]] | ||
Characters can also have expertise in a skill, which allows them to add {{em|double}} their proficiency bonus when making a corresponding ability check. While it is possible to have proficiency {{em|and}} expertise in a skill at the same time, they do not stack. Some sources of expertise do, however, require the character to already be proficient in a skill. | Characters can also have expertise in a skill, which allows them to add {{em|double}} their proficiency bonus when making a corresponding ability check. While it is possible to have proficiency {{em|and}} expertise in a skill at the same time, they do not stack. | ||
Neither proficiency nor expertise stack: there's no benefit to having multiple sources of proficiency for a skill, nor is there any benefit to having both proficiency and expertise at the same time. Some sources of expertise do, however, require the character to already be proficient in a skill. | |||
Sources of expertise that require prior proficiency in the respective skill include: | Sources of expertise that require prior proficiency in the respective skill include: | ||
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* [[Gnome#Rock Gnomes|Rock Gnomes]] have expertise in [[History]]. | * [[Gnome#Rock Gnomes|Rock Gnomes]] have expertise in [[History]]. | ||
* The [[Illithid Expertise]] feature grants expertise in [[Persuasion]], [[Deception]], and [[Intimidation]]. | * The [[Illithid Expertise]] feature grants expertise in [[Persuasion]], [[Deception]], and [[Intimidation]]. | ||
There is no special benefit to having both proficiency and expertise at the same time – the proficiency bonus is still only doubled. Some sources of expertise do, however, require the character to already be proficient in a skill. | |||
=== Common scenarios === | === Common scenarios === | ||
; Automatic rolls | ; Automatic rolls | ||
: Some ability checks are automatic. For example, when a creature approaches an | : Some ability checks are automatic. For example, when a creature approaches an unactivated trap, the game rolls a [[Perception]] ability check to determine whether the creature notices the trap. Perception is a Wisdom skill, so the character adds their Wisdom modifier and, if proficient in Perception, their proficiency bonus to the ability check. Once the trap is discovered, the character can interact with it to attempt to [[Disarm]] it, which requires a successful [[Sleight of Hand]] check, a Dexterity skill. | ||
; During dialogue | ; During dialogue | ||
: 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. | ||
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== Saving throws == | == Saving throws == | ||
Saving throws | Saving throws representa creature’s attempt to “'''save'''” themselves from harm. Spells and actions taken by other creature frequently allow their targets to attempt a save, as do hazards like [[traps]] and [[surface]]s. | ||
Each save has an associated ability – referred to using terms like '''Strength saving throw''' or '''Dexterity save''' – and a save DC that creatures attempting to save roll against, adding their corresonding ability score modifier to the results. | |||
When attemptint a save, a creature adds an ability score modifier corresponding to that save's associated ability. If they are also proficient in saves made using that ability, they add their proficiency bonus as well. | |||
Saving throws do not automatically fail or succeed on natural 1s and 20s, except when made during dialogue. | Saving throws do not automatically fail or succeed on natural 1s and 20s, except when made during dialogue. | ||
A [[List of features and items that affect saving throws|number of features]] affect saving throws, | While the outcome of an attempted saving throw is always binary – it is either a success or a failure – the exact outcome of a successful save depends on the effect in question. Often, the damage or conditions inflicted by the associated effect will be reduced in severity, or sometimes ignored entirely. | ||
A [[List of features and items that affect saving throws|number of features]] affect saving throws, | |||
=== Save proficiency === | === Save proficiency === | ||
All classes give save proficiency with two abilities | All classes give save proficiency with two abilities; when multiclassing, only the {{em|first}} class taken gives its save proficiencies. An additional save proficiency can be gained by taking the [[Resilient]] feat. | ||
=== Save DCs === | === Save DCs === | ||
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Different mechanics calculate save DC differently: | Different mechanics calculate save DC differently: | ||
; Danger save DC : In scenarios such as traps, the game chooses an appropriate Difficulty Class, depending on how serious the danger is. This includes consumable items such as elemental arrows or throwables. | ; Danger save DC : In scenarios such as traps, the game chooses an appropriate Difficulty Class, depending on how serious the danger is. This includes consumable items such as elemental arrows or throwables. | ||
; Spell save DC : | ; Spell save DC : For the Difficulty class of a spells 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}}. | ||
; Weapon save dc : Each weapon action can grant its own inherent bonus DC that isn't listed anywhere, but most frequently it's +2. The Difficulty Class of saves allowed by weapon actions is calculated as follows: | |||
; Weapon save | :: {{InfoBlob|1=Weapon Action DC = 8 + proficiency bonus + [[Strength|Strength]] or [[Dexterity|Dexterity]] + inherent weapon action bonus DC}} | ||
:: {{InfoBlob|1=Weapon Action DC = 8 + proficiency bonus + [[Strength]] or [[Dexterity]] | : Certain weapon actions, notably [[Concussive Smash]], instead use allow the acting creatures to either use their spallcaster DC or weapon Action DC with a +2 bonus, whichever is higher. | ||
: Certain weapon actions, notably [[Concussive Smash]], instead allow the acting | |||
==== Other effects ==== | ==== Other effects ==== | ||
In the case of threats that don't originate from a | In the case of threats that don't originate from a spell caster, such as a trap or a poisonous apple, the game sets the DC based on how serious the threat is intended to be. For example, a rather ineffective trap could have a DC of just 5, whereas an effective trap could have a DC of 15. A slightly spoiled tart could impose a Constitution save of DC 5, whereas a potent venom from a snake could impose a DC 15 Constitution save on the victim. | ||
=== Death saving throws === | === Death saving throws === | ||
Death saving throws are a special type of saving throw made by playable characters after they have been {{cond|Downed}}. | Death saving throws are a special type of saving throw made by playable characters and companions after they have been {{cond|Downed}}. Three successful saves will let a creature stabilise, no longer needing to make saves, and three failures will lead to the creature becoming {{cond|Dead}}. | ||
Three successful saves will let a creature | |||
Death saving throws are not associated with an ability score and so don't | Death saving throws are not associated with an ability score and so don't add any modifiers or the proficiency bonus. They only benefit from bonuses that apply to all saving throws (such as {{SAI|Bless}}) or specifically to death saves. Death saves are a success on a result of 10 or higher, and otherwise a failure. A character dies when three failures are accumulated, or becomes Stable (they no longer make death saves) when three successes are accumulated, whichever happens first. | ||
== Attack rolls == | == Attack rolls == | ||
Creatures make attack rolls when they attack a target, usually with a [[Weapon|weapon]] or a [[Spells|spell]]. | Creatures make attack rolls when they attack a target, usually with a [[Weapon|weapon]] or a [[Spells|spell]]. | ||
Attack rolls are rolled against the target's AC. If the attempt is successful, the attack ''hit'', and the attacker rolls for damage. If the result was less than the target AC, the attack was a ''miss''. | |||
=== Attack roll modifiers === | === Attack roll modifiers === | ||
Attack rolls are always made using an associated ability: | Attack rolls are always made using an associated ability: | ||
* | * Attacks made with melee weapons, including thrown weapons, generally add the attacking creature's Strength modifier, unless they have the [[Finesse]] property, in which case they add either the attacker's Strength or Dexterity modifier, whichever is higher. | ||
* Attacks made with ranged weapons add the creature's Dexterity modifier. | * Attacks made with ranged weapons add the creature's Dexterity modifier. | ||
* Spell attacks add the caster's [[Spells#Spellcasting|spellcasting ability modifier]], generally determined by their [[Class|class]]. | * Spell attacks add the caster's [[Spells#Spellcasting|spellcasting ability modifier]], generally determined by their [[Class|class]]. | ||
If the attacker is proficient with the weapon they are wielding, or if the attack is a spell | If the attacker is proficient with the weapon they are wielding, or if the attack is a spell attack, they also add their proficiency bonus. | ||
=== Critical hits === | === Critical hits === | ||
[[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 | When a creature rolls a natural 20 on an an attack roll, the attack is not only an automatic hit – it is also a ''critical hit'', and the attacker rolls twice the normal number of dice to determine damage dealt, including additional dice such as those from smites or combat manoeuvres. 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 | 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 19 or higher on attack rolls. Multiple sources of this effect stack, allowing the critical hit threshold to go even lower than 19. | ||
Some conditions, such as {{cond|Sleeping}} and {{cond|Paralysed}}, automatically turn all incoming attacks into critical hits. | |||
=== Armour Class === | === Armour Class === | ||
Armour Class (AC) is a measurement of how difficult a creature is to be hit by an attack. In order to successfully hit a creature, the results of an [[Attack roll|attack roll]] must | Armour Class (AC) is a measurement of how difficult a creature is to be hit by an attack. In order to successfully hit a creature, the results of an [[Attack roll|attack roll]] must have a number equal to or greater than the target's Armour Class. AC can be increased by equipping [[Armour|armour]] and [[Shields|shields]], by selecting certain [[Feats|feats]] when leveling up, or utilizing certain [[Spells|spells]]. | ||
==== Formula ==== | ==== Formula ==== | ||
The formula that determines AC | The default formula that determines AC is: | ||
: {{InfoBlob| | : {{InfoBlob|10 + [[Dexterity|Dexterity modifier]] + armour bonus + shield bonus + other bonuses and penalties}} | ||
The AC bonus from Dexterity | The AC bonus from Dexterity modifier may be capped when wearing [[Armour#Medium armour|medium]] and is ignored entirely when wearing [[Armour#Heavy armour|heavy]] armour. | ||
Medium armour caps the Dexterity Modifier to +2,{{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]].}} whrereas heavy armour ignores the modifier entirely. | |||
Shields will grant the listed AC bonus to whomever equips it, regardless of which weapon slot they are currently using. | |||
==== Other formulas ==== | ==== Other formulas ==== | ||
Unarmoured creatures may use a different formula if they have certain features. Creatures always use whichever formula – which they have access to – would result in a higher AC.{{note|Alternative formulas are only used if {{em|no}} armour is worn in the chest, hands, helm or bloots slots.|name=slots}} | |||
Unarmoured creatures may use a different formula if they have certain features. Creatures always use whichever formula they have access to | |||
{{SAI|Mage Armour}} and {{SAI|Draconic Resilience}}: | {{SAI|Mage Armour}} and {{SAI|Draconic Resilience}}: | ||
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{{SAI|Unarmoured Defence (Barbarian)}}: | {{SAI|Unarmoured Defence (Barbarian)}}: | ||
: {{InfoBlob|10 + Constitution | : {{InfoBlob|10 + Constitution modifier† + Dexterity modifier + shield bonus + other bonuses and penalties}} | ||
{{SAI|Unarmoured Defence (Monk)}}: | {{SAI|Unarmoured Defence (Monk)}}: | ||
: {{InfoBlob|10 + Wisdom | : {{InfoBlob|10 + Wisdom modifier† + Dexterity modifier + other bonuses and penalties}} | ||
== Damage rolls == | == Damage rolls == | ||
The base damage dealt by a [[weapons|weapon]], [[spells|spell]], class action | The base damage dealt by a [[weapons|weapon]], [[spells|spell]], class action or condition is usually determined by a ''damage roll''. Damage rolls always have an associated [[damage type]] that is also given following dice notation: {{DamageText|1d4|Piercing}} damage. | ||
=== Damage modifiers === | === Damage modifiers === | ||
Modifiers added to damage rolls are only added {{em|once}} per source, even | Modifiers added to damage rolls are only added {{em|once}} per source, even multiple dice are rolled. | ||
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 | * When making weapon attacks, the attacking creature's usually add theability score modifier that they added to the attack's 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 by {{SAI|Agonising Blast|h=20px}} – which allows a warlock to add their Charisma modifier to the damage rolls of their {{SAI|Eldritch Blast|h=20px}}. | ||
Proficiency bonuses are {{em|not}} added to damage rolls | Proficiency bonuses are {{em|not}} added to damage rolls. | ||
== Other rolls == | == Other rolls == | ||
; Healing : [[Healing]] restores a target's [[hit points]] | ; Healing : [[Healing]] restores a target's [[hit points]] but otherwise works 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 {{Class|Life Domain}}'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 low rolls. | When the Karmic Dice option is enabled (it is by default), the game will avoid streaks of very low or very high 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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Armour Class becomes more useful the greater it is – the difference in effectiveness between 20 and 19 AC is {{em|greater}} than the difference in effectiveness between 15 and 14. | Armour Class becomes more useful the greater it is – the difference in effectiveness between 20 and 19 AC is {{em|greater}} than the difference in effectiveness between 15 and 14. | ||
To illustrate this, if a defender has 15 AC and 10 HP, and the attacker has +5 to attack rolls, and deals 2 damage per attack, the defender would on average survive for 10 turns | To illustrate this, if a defender has 15 AC and 10 HP, and the attacker has +5 (50% chance to hit) to attack rolls, and deals 2 damage per attack, the defender would on average survive for 10 turns. | ||
If the defender's AC was increased to 16 (chance to hit | If the defender's AC was increased to 16 (45% chance to be hit), they would instead survive for an average of 11.1 rounds (an 11% increase in effectiveness). | ||
Meanwhile, if the defender | Meanwhile, if the defender has 19 AC (30% chance to be hit), they would survive for an average of 16.66 rounds. If their AC was increased to 20 (25% chance to be hit), they would be able to survive for an average of 20 rounds (a 20% increase in effectiveness). | ||
The difference between 25 and 24 is even greater, | The difference between 25 and 24 is even greater, with a {{em|200%}} increase in effectiveness (50 vs 100 rounds). | ||
=== Damage rolls mathematics === | === Damage rolls mathematics === | ||
Note that due to the mathematics of dice rolls, the difference between, say, 1d8 and 2d4 is more than just the higher minimum value of 2 on the 2d4 roll. With the d8, you have an equal chance of getting, say, a 5 and an 8. On the other hand, the 2d4 roll is statistically more likely to lead to a total value of 5, | Note that due to the mathematics of dice rolls, the difference between, say, 1d8 and 2d4 is more than just the higher minimum value of 2 on the 2d4 roll. With the d8, you have an equal chance of getting, say, a 5 and an 8. On the other hand, the 2d4 roll is statistically more likely to lead to a total value of 5, than a total value of 8. This is most easily explained with a table of all possible outcomes: | ||
{| class="wikitable" style="text-align: center;" | {| class="wikitable" style="text-align: center;" | ||
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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. | 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 is only 4.5, because 2d4 can never roll a 1. 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%|| | |9||60% ||84%|| 42.25% | ||
|- | |- | ||
|10||55%||79.75%||30.25% | |10||55%||79.75%||30.25% | ||
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|} | |} | ||
==== Effects of | ==== Effects of advantange 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. | ||
For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math|a}}, {{math|\mathbb{E} }} denotes the average or expected value of a roll, and {{math|1=\textstyle\sum_{i=a}^b x_i}} denotes the sum of a series of numbers {{math|x}} over an index {{math|i}} with {{math|i}} going from {{math|a}} through {{math|b}}. | For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math|a}}, {{math|\mathbb{E} }} denotes the average or expected value of a roll, and {{math|1=\textstyle\sum_{i=a}^b x_i}} denotes the sum of a series of numbers {{math|x}} over an index {{math|i}} with {{math|i}} going from {{math|a}} through {{math|b}}. | ||
The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | ||
In the case of an {{math|n}}-sided die, D{{math|n}}, this becomes: | In the case of an {{math|n}}-sided die, D{{math|n}}, this becomes: | ||
{{math_block|1=\mathbb{E}[\text{D}n] = \sum_{i=1}^n (i \cdot P(i))}} | {{math_block|1=\mathbb{E}[\text{D}n] = \sum_{i=1}^n (i \cdot P(i))}} | ||
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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 | When we apply this expression to a d20 we get 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 criticals ==== | ||
When making an ability check, attack roll | 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 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. | ||
Effectively, rolling with advantage means that critical failures are | Effectively, rolling with advantage means that critical failures are 20 times {{em|less}} likely and critical successes are almost {{em|twice}} as likely, and the inverse is true for disadvantage. | ||
{| class="wikitable" | {| class="wikitable" |