D&D Next Advantage/Disadvantage Math

I have the public beta package for D&D Next that has been released so far. Just the first batch. I haven’t play tested it, and I don’t intend to write a review, now. This is just a quick post for people looking for a bit of math regarding one of the new mechanics they’ve revealed, Advantage/Disadvantage.

A brief description: the guide states that if the DM declares you, the player, to have Advantage in a situation any d20 roll you would normally make you instead roll 2 d20’s and use the highest roll. If you have Disadvantage you use the lowest. The DM can determine Advantage or Disadvantage for any number of circumstances, but a common one would be during a surprise round, or if the target of an attack was unconscious or something.

So, I was curious so I did some calculations and I’ll share my results. The average d20 roll is 10.5. The average result from an Advantaged roll, basically the max of 2d20, is 13.825. The reciprocal average Disadvantage roll is 7.175. That’s a change of 3.325 on average. If you have advantage against an opponent with disadvantage you have on average a 6.65 bonus.

Still, the nature of the system is pretty volatile. The standard deviation of a normal single d20 roll is 5.916. The standard deviation of an Advantage/Disadvantage roll is 4.717, so you don’t lose much of the luck factor. I don’t have all the numbers, and don’t want to calculate them now, but I would be remiss if I didn’t point out that this system introduces and uneven distribution. Basically, it’s not an even benefit for each number. With 1d20 you have a 5% chance of getting any result, so if you have to roll more than 1 you have a 19/20 chance, higher than 2 a 18/20 chance, and so on. If you have Advantage it’s not so simple. You have a 399/400 chance to get higher than 1 and a 396/400 chance to get higher than a 2, and a 391/400 chance to get higher than a 3. See how the differences in odds aren’t increasing evenly? This means that depending on the DC the boon/bane of Advantage/Disadvantage varies. But that’s as deep as I want to get into that subject.

Anyway, there it is. Hope you find it interesting/useful.

Edit: Well, this was bugging me and I can’t sleep so I ran some more numbers. I have created a public doc here. Please check it out if you want all the numbers related to the asymmetrical distribution mentioned at the end of the original post. I have graphed the benefit of Advantage compared to a normal roll for each possible required roll to make it as clear as possible. All the raw numbers are there as well, so you can see that Disadvantage’s curve would be identical, just upside down.

One additional thing that comes to mind is critical hits. So far the rules for criticals are that if you roll a 20 you do maximum possible damage. Pretty simple. But the Advantage system tied into the critical system though. If you have Advantage you have almost 2x the chance to crit, and if you have Disadvantage you have almost no chance, 1 in 400. Still, the effect of Advantage/Disadvantage is minimized at the extremes of rolling, so Advantage is much more likely to make you hit when you would have missed than to make you crit when you would have hit. Of course, if you have a 15-20 crit range, like is possible is some systems, then this is dramatically no longer true. I suspect they don’t intend to allow this, however.

I think this pretty much covers all the math related to the mechanic.


I’m like Oprah

I discovered today that Andes has a cookie. Mom bought them and brought them to the house… so, that’s how I made the discovery. Anyway, they’re very good. My new favorite thing. Just thought you might want to know.

P.S. In finding the links for this post I discovered lots of cookies made using Andes Mints. I think I’ve had such things before once or twice. To my recollection they were good. They certainly look good.

The more you know

As of the 2009 census there are 6,664,195 people living in Washington State. If we assume that people that voted in the least popular ballot initiative voted in all the ballot initiatives then we get a maximum voter turnout percentage of 19.66%. That’s roughly 1.3 million votes.

So, hypothetically, lets say a person voted for every initiative but in every case the election went against him. How many other people voted as he did?

Well, I did the math and the answer is 130, and according to Pat the standard deviation is 11.4. So not very many. For comparison, a person who was in the majority on every initiative would have about 16820 people who agree with him.

Here is where I show my work and here is the source of my numbers.

Chrome goodness

Maybe I’m behind but I just learned something awesome about the Chrome awesome bar. This was something that I had looked into once or twice before, briefly, and failed to find an answer to. I always thought there should be a way to search Google images directly from the bar, instead of going to images.google.com first, and then searching.

This time when I searched around I found this which explained that you can right click on the awesome bar and select Edit search engines. There you can input alternative search engines, including images.google.com or any website and associate a keyword with that engine. So now if I want to search Google images I can just type image [search term]. Google even auto populates this list with frequently visited sites, so the engines you are likely to want to use might already be there. I just didn’t know to look. It’s very handy, so I thought I’d make sure you all knew.


Just now I noticed a friend of mine from middle school has posted on facebook that she’s engaged and pregnant. I’m sure the two are pretty unrelated. This friend of mine, and I, have 9 mutual friends on facebook. So, including her, that’s 10 people, all about 25, all from my middle school/early high school years. 1 is gay. 2 don’t have any children, that I know of. The other 7 have either adopted, had kids, or are pregnant. 70% is higher than is generally represented amongst my friends, probably, but I found it noteworthy. It seems like that ratio can’t change much in the near future.

Ay Carumba

It was brought to my attention today by news of recent events that the voice of Bart Simpson, Nancy Cartwright, is a Scientologist.  As a result I will boycott the Simpsons, and watch it no more.  I have watched every episode of the nearly complete 20 seasons, and the movie, so far, so this will be the most difficult boycott I’ve made against celebrity stupidity yet.  Still, I have my principles.