Dice rolls: Difference between revisions
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(→Karmic Dice: Karmic dice only fudges dice to stop bad roll streaks, does nothing for good roll streaks.) |
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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 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 == | ||
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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 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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== Other rolls == | == Other rolls == | ||
; Healing : [[Healing]] restores a target's [[hit points]] | ; 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 {{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. | ||
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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 | 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 | ==== 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 | 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. | ||