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Gnomish Workshop: Hidden Advantages

This article was first broadcast in Episode Sixty-seven on 3rd April 2019.

Lennon: By the rollacks of Ralishaz, not again!
Ryu: What happened?
Lennon: Well, how would you describe… that?
Ryu: Well, Ostron’s unconscious neatly laid out on the floor of the Workshop again… there are absolute piles and piles of dice around… so either he miscast a sleep spell and knocked himself out, or…
ROSTRO: Ostron’s command of thaumaturgical rituals seems significant enough to make that event unlikely… Ostron needed help with Advantage. It appears the concept is more complex than it would seem at first glance. 



On the face of it advantage and disadvantage seem simple; if you have advantage or disadvantage on a roll, generally an attack or ability check, more rarely a saving throw, you roll two d20s instead of one. In the case of advantage, the higher of the two dice is chosen. With disadvantage you pick the lower one. Advantage is good, disadvantage is bad.

While most people content themselves with the simplistic conclusion that “advantage is good, disadvantage is bad,” Ostron believed it was worth delving more into the details.

Considered from a mathematical standpoint, advantage drastically shifts the probabilities of a d20 roll. In the case where a d20 is rolled singly, there is an equal 5% chance of getting any value. When rolling with advantage, however, the probability graph is slanted so the roller has almost a 10% chance to roll a 20, while their chances of rolling a 1 drop to 0.25%. Also, chances of rolling values above 10 become 75%.

If we think about things mathematically, we can say advantage actually means “chances of rolling a value above 10 are greater than 50%.” In that case there are a number of mechanics in D&D that provide what could be called “Hidden advantage” on d20 rolls.

We’ll start with a minor example. The Guidance cantrip allows a player to add a d4 to an ability check. That immediately makes a total of 1 impossible and introduces the possibility of rolling 21 to 24. In terms of probability, it means that rolling a value above 10 increased from a 50% chance to a  68% chance. It doesn’t increase the chances of rolling an actual 20, but the overall total of the roll is higher.

You can take characters that have multiple attacks and think of it as granting advantage to a single attack. Assuming the character has to roll at least a 10 to hit, which is fairly common when you think about most creatures ACs and the attack bonuses a lot of characters will have, they enjoy the above 5% chance to roll over 10 if they have two attacks. This is as long as they don’t have their heart set on hitting with both attacks.

It is worth noting at this point that characters with three or more attacks have probability even more on their side. Any two of their attacks considered together enjoy the mathematical bonus of advantage, but with three attacks they have a 91% chance that at least one of them will roll above 10.

However, if you’re a spellcaster or a rogue who relies on your one precious attack hitting, you have to find examples that are more like traditional advantage. I think it’s worth reminding people that the Inspiration granted by DMs, not bardic inspiration dice, can be used to gain advantage on any attack, ability check, or save — including death saves.

Although even at lowest levels, the bardic inspiration die makes the probability of rolling above a 10, 68%, approaching the statistical level of true advantage.

However, if you want actual advantage available whenever you need it, grab the Lucky feat. It allows you three opportunities to reroll any attack roll, saving throw, or ability check. Since you reroll the die and can choose the better of the two rolls, it functions exactly like advantage and can even be used to get around those situations where disadvantage is cancelling out advantage you might have otherwise enjoyed.

There are some more examples of quazi-advantage if you start looking at some class archetypes. Divination wizards, for example, have portent rolls, which are two d20 rolls they bank at the beginning of a day and can pull out to use whenever it’s convenient. If one or both of those is above 10 it works like advantage. And they get more divination dice as they go up in levels.

Technically it is different, however. Since the portents must be applied before any die is cast, the probability of the roll being over 10 is either 100% or 50% as normal. They are not mathematically equivalent systems.

Apart from Divination wizards and the bardic inspiration dice we already mentioned, there are a few other class abilities and spells that achieve similar effects, like a berserker barbarian’s frenzy, the Haste spell, and some others. Basically any time you’re adding a die to a d20 roll, or getting to choose the better of multiple d20s, you have something like advantage.



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