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.

 

Compendium, oh Compendium

Hasbro/Wizards of the Coast/Dungeons&Dragons I enjoy your products very much. And you do cool stuff to make it better, like making this D&D Compendium. At least I think it would be cool. A huge, comprehensive, searchable database of all things D&D. What a useful tool! Oh wait, it’s only useful for people who pay a monthly subscription. Boo!

I get that you’re a company and you want money, and I also understand that subscription gets you more than the D&D Compendium, but come on. You are doing yourselves a disservice. This compendium is exactly the sort of thing that when offered for free encourages interest in your products and ultimately makes you money.

If I knew whenever I had a spare moment or a stray thought about D&D I could plug in a quick search to the compendium and scratch an itch, I would be all over this compendium. And while I’m search for the exact wording of Feat X, I’d see there is another feat I didn’t know existed, and I’d find that it was in The Planes Below which would get me thinking about how it would be cool if my party did x y z. And I’d search for y or z and find more things in The Planes Below of interest to me. And then, what is your thinking? I just find everything from The Planes Below in the compendium and copy it down on note cards? NO! I go buy your book. And you get my money.

*sigh* I think that my scenerio is way more likely than someone going to your website and thinking, “Hey, neato, a compendium. Sure I’ll pay $7 a month for this.” Plus there’s general good will amongst your customer base.

Ok. Rant over. I do think they’re missing out. And I really want to use the thing, but I can’t justify paying for it when I don’t even have any 4e games going. /pout

PAX and stuff

I recently completed the first day back from a 4 day weekend. Friday, Saturday, and Sunday were pretty much exclusively taken up going to, attending, and returning from, PAX. The nerd conference/expo of choice for the Pacific Northwest it seems. I went w/ Pat, and we stayed at my uncle’s, so thanks uncle. Keston was also there, so I spent some time hanging out with him and his companions from Intel. The experience was much as years prior, only bigger, so fun and entertaining and expensive parking.

PAX is one of those things that is difficult to explain to people. People always ask what you do there, and when you answer the question literally, you say something like, “walk around and look at video games that are going to come out, and go to panels about video games and stuff, and sometimes play video games that haven’t come out yet.” But that’s not really what PAX is about or what’s cool about it. Part of what is cool is taking what is generally a isolated minority, nerds, and making them an overwhelming majority. Putting 50,000 nerds into one building has a strange effect. Everything kinda goes backwards. Like, you get peer pressured into playing Magic or D&D, and if someone finds out you don’t know what keyboard cat is they laugh at you. It’s a good change of pace from real life. So I’m going to say that this upside down social world is the real reason to go to PAX, and there are panels and video games as bonus. So PAX was a success. I mean, Pat had never seen another gphone in the wild, and I musta seen 20 @ PAX w/o even looking.

Pat was pretty sick on Sunday, so that sorta sucked, mostly for him. I’m told he feels mostly better at this point, and I still feel fine so I think I’ve resisted infection, so those are good things. News is out about a confirmed case of swine flu at PAX and a whole website has sprung up to report confirmed cases and what flights you were on and stuff, so if you went to PAX and you get sick, go to the doctor.

Monday, day of labor, I pretty much just watched Mythbusters. It’s a pretty amazing show. For me it’s a show I watch w/o really knowing why I like it. Although I have identified one aspect, and that is the actual building. I have very little experience, and, I think, probably, very little skill in the area of mechanically building stuff. The mythbusters are really good at it, and the show presents rapid fire problems and solutions in an interesting way, so I like that aspect a lot. Plus, I think I like guessing the outcomes of stuff and almost always being right, but not always always.

I also downloaded and watched the pilot of Leverage, which I didn’t really know anything about except all my celebrity nerd friends on twitter are talking about it, and Wil Wheaton is somehow involved. Anyway, it looks kinda cool. I have to watch more before I can really comment.

Yeah, so life is good I think. My newest pay check indicates that the amount I’m losing to taxes and other automatic subtractions is 3% greater than previously estimated, but that’s not very much. ūüėõ Closer to what I expected anyway. Lauren is starting school in Spain in about 6 hours. Everythings pretty standard and genial. ttfn

Can’t blog, must consume internet media

The Central gang is coming back to visit in like 39 hours.¬† Yay!¬† We’ve set up Skype and webcams and stuff so I’m pretty sure I talk to them more now than before.¬† They’re being very nice to me.

Pat’s gonna DM a few of us TC locals.¬† We decided we’re rolling stats straight down.¬† I got good rolls.¬† The restrictive nature of the chosen character creation process has me leaning towards Bard.¬† I need to wait and see what Gar and Kim do, though, before I make any firm decisions.

Also, I had the idea that one could probably sell some sort of self help doctrine around the idea of harnessing one’s need to go to the bathroom as a source of motivation for success in the rest of one’s life.¬† Kinda like one of those self empowerment strategies and stuff wackos are always spending money on.¬† I know it sounds crazy, I just want to say I thought of it before it comes out for real so people will believe me when I say I thought of it first.

Tomorrow I am going to play some board games with Mom and Ms. Craig, my kindergarten – 2nd grade teacher.¬† And then Kim is gonna come over and work on her character, supposedly.¬† That’s the plan.

update post

I’ve been not blogging because I’ve been so swamped trying to eek out seconds of the “last” days w/ Lauren and Sidney, and Dan, I guess.¬† I use the “” incorrectly to mean that I don’t think the days are actually the last.¬† I mean, modern times and all, and I’m just 2 hours away.¬† Seems like them moving to opposite ends of the globe will be more of a strain on our relationships, but whatever.

So, we left Lauren’s and came to my place and hung out.¬† Mostly just hung out.¬† We watched Watchmen and Dan lost his wallet, but that was pretty much the only structured activity.¬† We started a new campaign that includes Dan.¬† I’ve got it all set up so MapTools should allow us to continue over long distances, provided the internet doesn’t get crappy on us.

On Thursday they drove me to my interview at PNNL.¬† Everything went really well and I was feeling pretty confident I’d get the internship and also feeling pretty good about it being a sweet gig, but then the boss lady e-mailed me and told me she needed transcripts and letters of recommendation.¬† So, if they still need those things kinda shakes the confidence a bit.¬† But, we’ll see.¬† They also were supposed to tell me on Monday or Tuesday if I’m part of the team, but that won’t happen now since I can’t get them the transcripts or letters that fast.¬† Transcripts are gonna prove to be problematic I bet, since I don’t have access to unofficial ones from Linfield anymore and I can’t seem to find a complete copy anywhere.¬† /sigh¬† I hate paperwork.

I also got an e-mail from CWU telling me that they wouldn’t give me my Math minor.¬† For some reason the people in charge of giving out such things think I never declared it and I need 7 elective math credits.¬† This despite the math department telling them I fulfilled all the requirements.¬† I dunno.¬† They want me to pay $20 or something to re-enroll for spring and who knows what else.¬† Personally I don’t really care about it, but I’ll ask the folks.¬† Again with the hating of paperwork.

Today everyone left except Yusuke.¬† We did the whole parting thing dry eyed which I’ve pleased about.¬† I mean, not on my part, that’s unsurprising, but on the others.¬† I know how they miss me so.¬† ;P

Pat came over and got Yusuke and I to help him move Heidi’s crap.¬† She’s moving to Bellingham and Burmingham or something.¬† Who cares.¬† She’s not gonna be here anymore.¬† It took us, and 2 other people who actually helped, about 4 hours to get the stuff out of her apartment.¬† Pretty incredible.¬† We totally jam packed thie big ol’ U-Haul.¬† Tomorrow Pat and the other’s unfortunate enough to be directly affiliated with Heidi will make the dangerous trek accross the pass in the early morn and unpack everything.¬† Weeee!¬† Poor them.¬† I was going to be counted among them, but Yusuke’s staying here has saved me.

Oh, I got all my grades in an I officially have graduated again.¬† I guess that’s noteworthy.¬† Got A’s except for Boris’s class (B+) so whatever.

Before he left Dan gave me a t-shrit he claims say Korea on it as a parting gift.¬† Looks pretty cool.¬† It’s still in the bag, but I can only assume it’ll look better with me involved.¬† Lauren gave me the gift of talking to her at least 30 minutes a day.

/shrug¬† I’ve got nothing else right now.¬† I’m abnormally sleepy today.¬† I must not have slept well knowing I’d be sans so many CWUians.

why o why o why o

My site was down for a day or two a day or two ago.  I trust you all survived.

Work is slowly encroaching in on me from all sides.  I can feel it coming.  It will crush me and drive any will to get a job from me before I graduate.  Send your condolences and cash to my parents.

The gang only plays D&D for like 2 or 3 hours at a time.¬† I dunno if they get into grooves that way.¬† It doesn’t seem to groove right, exactly.¬† I need that groove to improve my DMing.¬† /sigh¬† Still, at least they play, which is more than can be said for the game I’m in.

Perhaps on a related note, Pat’s grandpa died.¬† Pat’s making the trek back up from Vegas, consequently.¬† That is all I know on the subject, but I imagine Pat’s sad to some degree.¬† So… sux0r.

Finished the first book of Dune.¬† Not the actual book, the book within a book.¬† You know how they divide books into books sometimes.¬† I’m at the part where Paul attains a higher consciousness or whatever.¬† Prekky sweet.

It was snowing outside.¬† ForcastFox says it will some more.¬† Right now we’ve got a slight covering, is all.

Today I swim, and shave, and shower, and various other words that start with S.¬† Step, shimmy, shake, swallow, scramble, shamble, stagger, scamper, salivate, sashay, skip, start, succumb, stop, stroak, shed, scratch, slurp, snap, sniff, sneer, smile, slouch, slur, slump, shoot, splash, stride, strafe, sing, and possibly sneeze.¬† But, first, sleep… snooze, snore, slumber.

status report

Free weekend had I.¬† No homework really, yet.¬† Played D&D, thought about D&D, worked on D&D, read about D&D, watched movies about D&D… my 5 favorite things.¬† Well, not quite really, since by played I mean DM’d, but DMing is quite fun in my current situation, as well.¬† The gang leveled and thought they were going to defeat their arch nemesis, but were tricked by my clever placement of a different human in the dungeon.¬† :0

A bunch of us went swimming today.¬† Consequentially, I took a shower.¬† Strange happening was noticed recently.¬† It is pictured below.¬† There’s not a lot to see, but some of you still might not get it.¬† See if you can see what troubles me.

It is in a mirror... which could make it tricky

I’ll leave you all to puzzle over that.¬† Or at least, I think I will.¬† Probably totally obvious to everyone and it’s only I that would never notice if it weren’t for it being me.¬† /shrug

Also, listen to Stephen Fry’s podcast thing.¬† It’s good.¬† I’ve only listened to the most recent one, on language and grammar, but I suggest you check it out.¬† Especially you linguists out there (Donny).

I’m sure work will commence in earnest soon.¬† Boy how I’m looking forward to that.

rambly

I made lentil stew this weekend.¬† One of those days, Saturday I think.¬† I even had a little veggie side portion for Sidney.¬† Lauren did the grocery run for me cause there was a preponderance of people wanting to go, but she didn’t believe me when I wrote tomato juice on the list so she got tomato sauce.¬† We just diluted it 1/3 and it worked fine.¬† Might actually be cheaper that way.¬† Got leftover ingredients.¬† All I need is onions and beef and I could make some more.¬† I thought it was good.¬† It never gets the acclaim my milkshakes do, though.

Got to a 7:20 mile today.¬† So that’s faster than last time, and is extra impressive since my legs were sore when I started because I’ve been doing fairly extensive DDRing over the weekend.¬† Lauren has been showing increased interest in DDR lately, so I have a partner.

I also got the highest score on the physics test.  33.5 out of 34.  Low was 9.5, but, I think, that must be quite the outlier.

That’s about the end of the good news school wise, though.¬† Well, I haven’t done poorly on anything yet, it’s just the work that’s upcoming that is lame.¬† Resume thing due tomorrow, which I already did, but it wasn’t very fun.¬† Plus, it’s one of those stupid assignments with no real point and it is therefore difficult to know what is expected.¬† Then I might have a test on Wednesday.¬† Can’t tell because the professor doesn’t know, or didn’t during class, and his online schedule has no dates.¬† Useful.¬† It’s sometime this week though for sure.¬† I also have another one of those stupid research papers.¬† They’ve gotten stupider because he explained how he wants us to use super official references.¬† References are fine if it’s a real research paper, but there’s no primary literature on the history of RAM, so referencing bad sources is just going to get harder.¬† Whatever.¬† I also have a basic weekly homework assignment in that class, but I did that already.¬† That was fine.¬† Then in my other class with that prof I have a test on Friday, and normal homework, also finished already.¬† Kinda really lame, but easy.¬† And the resume professor is giving me a test on Friday, too.¬† That’s all, except I’ll get homework in physics tomorrow.

I’m irritated that I’m in 3 upper level computer science classes, we’re in week 5, or something, and I’ve written no code.¬† Not a single line.¬† You know what I like about computer science?¬† Code.¬† You know how I learn computer science?¬† By coding.¬† /rolls eyes

/sigh

On another note, there may or may not be a person I know who has Fable 2 early.¬† I’ve spent a few hours watching.¬† Looks basically like Fable… only better?¬† It’s fairly fun to watch and make jokes and stuff.

Oh, and like it says on Lauren’s blog, we watched Wayne’s World for free today.¬† Kinda like back in the Linfield days.¬† I got the 3 noobs, Yusuke, Elisabeth, and Lauren, to come see it, and then there was Sidney and I as old fans.¬† It was a big hit.¬† I re-love that movie.¬† Maybe they liked it enough they’ll rent the sequel?¬† Maybe?

Also on Lauren’s blog, everyone’s leaving this weekend like they did weekend before last.¬† This time they’re going to Sidney‘s.¬† It’s her mom’s birthday.¬† It’s great that I’ve got all my work this week so this weekend when I have all this free time I won’t have anything to do.¬† More D&D delay.¬† These Central people only managed to stay focused for 2 hours this weekend.¬† They had a bit of a brutal fight, and poor Yusuke was unconscious basically the whole time.¬† Gotta go through with them and get them better acquainted with their powers to speed up combat.¬† Other than that Elisabeth needs to stop pouting about her bad rolls, and we need to get them far enough to have some better role playing hooks.¬† /shrug

Also I voted.¬† Thanks to Lauren‘s stamp.

K.¬† Well, I’m spent.

It’s good to have a few friends that don’t drink

My ear buds are dead, so I’ve been walking around campus with my giant headphones.¬† It’s pretty cool.¬† They double as earmuffs.¬† They fit underneath my giant hood of the sweatshirt I’m always wearing, too.¬† The cord is so long it goes from my pocket, to my shins, to my head.

Took a physics test yesterday.¬† First one, so I dunno how I did.¬† I’m not concerned, though.¬† I did well on the practice test and I am just taking the class for fun, so I think I’m getting what I came for.

A bunch of us went to play badmitton in the gym yesterday.¬† At one point Hiro and I played against Dan and Luke in a match where we actually kept score.¬† I wasn’t paying close attention but I was told at one point that the score was 10-2 them and we were playing match point.¬† When we won that volley I told Dan and Luke they better watch out, we were gonna come from behind.¬† Guess how that ended.¬† That’s right, 9 unanswered points for Hiro and I.¬† Go team short and apathetic!

Today in class Paul stole someone’s sunglasses, and was still wearing his beanie and was just sitting in the middle of the lecture with that look going.¬† So Liam has a beany and sunglasses and copies him.¬† And then like 3 more of us sitting in the vacinity put our hoods way up and I had my hair in my face.¬† The professor was writing a bunch of stuff on the board while this was going on and he turned around and was all like, “Jesus!¬† What is this uni-bomber class?”¬† And we were all sitting in the second row so the whole first row had no idea what was going on.¬† It was pretty funny.

I jogged a 7 minute 50 second mile today.¬† That’s according to Elisabeth, I wasn’t timing.¬† I was surprised at the speed since I can’t remember the last time I officially ran a mile, unless that’s what Donny and I did that one time last year.¬† Gonna try and keep doing it fairly frequently and see if I can improve.

Tomorrow I might go grocery shopping for lentil stew fixings which I might make sometime soonish.¬† After this shopping we’re gonna play D&D again, finally.¬† Hopefully tomorrow will be a good day.