D&D 5e: Probabilities for Advantage and Disadvantage

1. What Does Dmg Mean In Dnd Stand
2. What Does Dmg Mean In Dnd Pdf

If a creature or an object has resistance to a damage type, damage of that type is halved against it. If a creature or an object has vulnerability to a damage type, damage of that type is doubled against it. Resistance and then vulnerability are applied after all other modifiers to damage. It’s the attack roll result that an opponent needs to achieve to hit you. Your AC is equal to the following: 10 + armor bonus + shield bonus + Dexterity modifier + size modifier Note that armor limits your Dexterity bonus, so if you’re wearing armor, you might not be able to apply your whole Dexterity bonus to your AC.

The new rules for D&D 5e (formerly known as D&D Next) are finally here:

D&D 5e introduces a new game mechanic, advantage and disadvantage.

Basic d20 Rules
Usually, players roll a 20-sided die (d20) to resolve everyting from attempts at diplomacy to hitting someone with a sword. Each thing a player tries to do has a difficulty and rolling greater than or equal to the difficulty (with various modifiers for ability and training and magic items) means the character was successful.

Advantage and Disadvantage
As of 5th Edition (5e) rolls can be made with advantage or disadvantage. The rules are:

• Advantage: roll two d20 and take the max
• Normal: roll one d20 and take the result
• Disadvantage: roll two d20 and take the min

So what are the chances that you’ll roll equal to or above given number with advantage, normally, or with disadvantage? Here’s a table.

roll	disadvantage	normal	advantage
20	0.002	0.050	0.098
19	0.010	0.100	0.191
18	0.022	0.150	0.278
17	0.039	0.200	0.359
16	0.062	0.250	0.437
15	0.089	0.300	0.510
14	0.123	0.350	0.576
13	0.160	0.400	0.639
12	0.202	0.450	0.698
11	0.249	0.500	0.751
10	0.303	0.550	0.798
9	0.361	0.600	0.840
8	0.424	0.650	0.877
7	0.492	0.700	0.910
6	0.564	0.750	0.938
5	0.640	0.800	0.960
4	0.723	0.850	0.978
3	0.811	0.900	0.990
2	0.903	0.950	0.998
1	1.000	1.000	1.000

The effect is huge. There’s less than a 9% chance of rolling 15 or higher with disadvantage, whereas there’s a 30% chance normally and a 51% chance with advantage.

[Update II: Turns out that The Online Dungeon Master, a blog I read regularly for 4e module reviews and play reports, generated the same table over a year ago (using Excel simulations, no less; a commenter provides a good breakdown of the analytic solution). That’s been the story of my life coming into a new field. I agree that this tabular form is what you want for reference, but the easiest way to understand the effect is looking at the non-linearity in the graph below.]

Here’s a plot (apologies for the poor ggplot2() and png() defaults — I don’t understand ggplot2 config well enough to make titles, clean up labels, axes, tick mark labels, boundaries, margins, colors, and so on to make it more readable without spending all night on the project).

The vertical distances at a given horizontal position show you how much of a bonus you get for advantage or disadvantage.

[Update: There’s analternative plot on the Roles, Rules, and Rolls blogthat displays the difference between advantage and a simple +3 bonus, as used in previous D&D editions.]

Analytic Solution
The probabilities involved are simple rank statistics for two uniform discrete variables.

You can compute these probabilities analytically, as I show in Part III of the page where I explain the math and stats behind my simple baseball simulation game, Little Professor Baseball.

The basic game is a cross between All-Star Baseball and Strat-o-Matic. I wanted a rolling system where both players roll, one for the batter and one for the pitcher, and you use card for the player with the highest roll to resolve the outcome. The winning roll is going to have a distribution like the advantage probabilities above (except that Little Professor Baseball uses rolls from 1–1000 rather than 1–20. As a bonus, earlier sections of the math page explains why Strat-o-Matic cards looks so extreme on their own (unlike the All-Star Baseball spinners).

I developed the game after reading Jim Albert’s most excellent book, Curve Ball, and I included the cards for the 1970 Cinncinnatti Reds and Baltimore Orioles (which for trivia, were mine and Andrew’s favorite teams as kids).

Simulation-Based Calculation
I computed the table with a simple Monte Carlo simulation, the R code for which is as follows.

What Does Dmg Mean In Dnd Stand

I'm sure Ben could've written that in two or three lines of R code.

I have often wondered the statistical differences between2d6 and3d4. They both have a maximum of12, but both the minimums and the averages are higher with 3d4. This isespecially applicable for character generation. As a DM/GM/super-powerfulnarrator, I decide how the characters get to roll up their attributes. Dothey use 3d6 like 2nd edition, orperhaps 4d6, dropping the lowest?My old method even let you rerollones and that left you with an even higher average with more of atendency of higher numbers.

I wrote this analyzer so you can see the differences between whatevertype of rolling method you pick. I don't suggest you use a high number ofdice, otherwise it will take significantly longer to generate statistics.My machine bombs out at about 10 dice.

Sample rolls for character generation:3d6,4d4 + 2,6d3,4d6, drop lowest,4d6, reroll 1s, drop lowest (really it rolls 4d5 and adds 1, but that's effectively the same),3d6, drop the highest (penalty of some sort).

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Feel free to try out your own die rolling strings, like '5d4 + 3' or'6d8'. The 'd' must be lowercase. To drop the lowest x dice, use anuppercase D, like '4d6D1' means to roll 4d6 and drop the lowest 1 die. To drop the highest x dice, use an uppercase P, like '4d6P1' means to roll 4d6 and drop the highest 1 die roll.

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Besides the links above, I have also seen these ideas:

What Does Dmg Mean In Dnd Pdf

• 4d6, drop lowest, reroll if max < 14 or reroll if the sum of themodifiers is < 1
• 5d6D2 (5d6, drop the two lowest rolls)
• Roll up 12 characters using the 3d6 method, then pick the best character
• Roll 3d6 six times, then pick the best result. Roll each attribute inorder – do not assign numbers to stats as you see fit.
• Roll a pool of 12 scores using 3d6, pick the best 6 scores.

I have also been contacted about making some stats that would be useful for Legend of the Five Rings (L5R). In there, you have a stat and a skill. when you roll against that, you keep a number of 10-sided dice equal to your stat. You can also 'roll up' by rolling again when you roll a ten and adding the new roll to the ten. You can continue rolling up as long as you keep rolling tens.

I wrote up a small c program to only do the rolling of 1-10 10 sided dice and keeping just the highest digit, then averaging the rolls. Let me know if you would like alternate die roll stats and I will see what I can do to help out.

1. Rolling 1d10, keeping the highest: average roll of 5.5
2. Rolling 2d10, keeping the highest: average roll of 7.15
3. Rolling 3d10, keeping the highest: average roll of 7.975
4. Rolling 4d10, keeping the highest: average roll of 8.4667
5. Rolling 5d10, keeping the highest: average roll of 8.79175
6. Rolling 6d10, keeping the highest: average roll of 9.021595
7. Rolling 7d10, keeping the highest: average roll of 9.1919575
8. Rolling 8d10, keeping the highest: average roll of 9.32268667
9. Rolling 9d10, keeping the highest: average roll of 9.425695015
10. Rolling 10d10, keeping the highest: average roll of 9.5085658075