Editing Advantage

{{NoExcerpt|''For a comprehensive summary of the mechanics behind all rolls and modifiers, see: [[Dice Rolls]]''}}

{{Advantage}} and {{Disadvantage}} are gameplay mechanics that can greatly affect the success of dice rolls.  They only apply to {{D20}} rolls: [[Attack Roll]]s, [[Saving Throw]]s, and [[Ability Check]]s. They never apply to [[Damage Roll]]s, though other features and effects can make a character re-roll damage dice in other ways.

When you roll with {{Advantage}}, you roll two dice and use the '''higher''' result. You either have advantage or you don't: it doesn't stack to grant more than a second die, regardless of how many sources of advantage you have.

'''Having advantage raises the average of your roll by 3.325 to 13.825.''' (For the math, see below.)

Examples of situations that grant {{Advantage}} on attack rolls:  

==Disadvantage ==

When you roll with {{Disadvantage}}, you roll two dice and use the '''lower''' result. As with advantage, you either have disadvantage or you don't: it doesn't stack to force you to roll more than a second die, regardless of how many sources of disadvantage you have.  

Example: You roll two {{D20}} for an Attack Roll. The results are 16 and 4. Your effective result is 4.

'''On a D20, having disadvantage lowers the average of your roll by 3.325 to 7.175.''' (For the math, see below.)

==Advantage and Disadvantage==

=== Chances of succeeding a specific roll===

|+Chance of rolling a target number or above on 1d20

!Target on 1d20!!Normal Roll!! Roll With Advantage!!Roll With Disadvantage

|1|| 100% || 100%||100%

|2||95%|| 99.75%||90.25%

|3||90% ||99%||81%

|4 ||85%|| 97.75% ||72.25%

| 5||80%|| 96%||64%

|6||75% || 93.75%|| 56.25%

|7

| 70%||91%||49%

|8||65% ||87.75%||42.25%

|9||60% ||84%||36%

|10||55%||79.75%||30.25%

|11||50%||75%||25%

|12 ||45%|| 69.75%||20.25%

|13||40%||64%||16%

|14||35%|| 57.75% || 12.25%

|15||30% ||51%||9%

|16||25% ||43.75%||6.25%

|17||20% ||36%||4%

|18||15% ||27.75%||2.25%

|19||10% ||19%||1%

|20||5%|| 9.75%||0.25%

=== Effects 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. On average, the bonus/penalty is +/-3.325. 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|i}}, {{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}}.

Applying that to the formula of an average of a die D{{math|n}} we get

{{math_block|1= \mathbb{E}[\text{D}n \text{ with advantage}] = \frac{2}{n^2}\left(\frac{n(n+1)(2n+1)}{6}\right) - \frac{1}{n^2}\left(\frac{n(n+1)}{2}\right) = \frac{2n}{3} + 1 + \frac{1}{3n} - \frac{1}{2} - \frac{1}{2n} = \frac{2n}{3} + \frac{1}{2} - \frac{1}{6n} }}

{{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 we get that having advantage is equivalent to an average bonus of +3.325.

=== Effects on critical successes and failures ===

 

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.

 

 

 

== Similar effects ==

While advantage and disadvantage only apply to {{D20}} rolls, some character features can grant a similar bonus to other rolls. The clearest example is [[Savage Attacker]], a [[feat]] which has a character roll all melee damage dice twice, taking the highest result. This is effectively advantage on melee [[damage rolls]], though none of the advantage rules apply: the effect can stack with others that double damage dice, and there is no similar negative effect that gives you the equivalent of disadvantage on damage.

 

Using the result of the calculations above to see what the average bonus to our damage becomes, depending on what dice the weapon uses.

 

|1d4||0.625||+25.0%

|1d6||0.972||+27.8%

|1d8||1.313||+29.2%

|1d10||1.650||+30.0%

|1d12||1.986||+30.6%

|2d6||1.944||+27.8%

For example, the [[Halberd of Vigilance]] (1d10 slashing damage and 1d4 force damage) which was [[Dip#Condition:_Dipped_in_Fire|dipped in fire]] (1d4 fire damage) will, on average, do 1.65 + 0.625 + 0.625 = 2.9 (+27.6%) more damage with Savage Attacker.