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Advantage and Disadvantage in D&D Next

Advantage and Disadvantage in D&D Next: The Math
Originally Posted on May 24, 2012 at OnlineDungeonMaster.com


rotd-diceEveryone will be sharing opinions about D&D Next today and for the foreseeable future. I wanted to do something a little different and focus on just one thing: the math behind the Advantage and Disadvantage mechanic.

For those who haven’t read the playtest material yet, if you have Advantage for a die roll, you get to roll twice and take the better result (kind of like the Avenger in 4th Edition). If you have Disadvantage, you have to roll twice and take the worse result.

In reading through the rules, I noticed that being blinded gives you disadvantage for your attacks, while being prone gives you the same -2 to your attack that you would get in 4th Edition. So what’s the impact of disadvantage? Is it similar to a -2?

 

Averages
My first thought was, what’s the average of 2d20 keeping the highest (advantage), and what’s the average of 2d20 keeping the lowest (disadvantage)? I know that the average of a single d20 roll is 10.5, so knowing the average of advantage or disadvantage should tell me whether it’s equivalent to +/-2, +/-3 or what, right?

I decided to simulate this by having Excel roll a whole bunch of dice (over a million pairs of d20 rolls) and then taking some averages. For those fellow Excel geeks out there, my d20 roll formula is: =ROUNDUP(20*RAND(), 0). I generated two columns of these, then a column that was the maximum of the two results (=MAX(A2, B2)) for advantage and one that was the minimum (=MIN(A2, B2)) for disadvantage.

I got a result of about 13.83 for a roll with advantage and 7.18 with disadvantage. I later learned that the precise values are 13.825 and 7.175.  Comparing this to the 10.5 average you get for a single d20, advantage adds 3.325 to the average roll and disadvantage subtracts 3.325.

Done! Right?

 

It’s not all about the averages
However, as my fellow EN Worlders soon pointed out, this isn’t the most useful way to look at things. In D&D, what you care about is your chance of success or failure on a die roll. And when you change the distribution of results from a uniform d20 roll (equal 5% probability of every number from 1 to 20) to the maximum or minimum of 2d20, the impact is not the same as a straight plus or minus to a d20 roll.

The most useful way I’ve found to look at this is with the following table. The first column shows you the target number you need to roll on the die in order to succeed. (Note that if you need an 18 to hit but you have +6 to hit, then the target number on the die is a 12.) The second column shows the percentage of time you’ll get that result or better on a single d20 roll. The third column shows how often you’ll get your number with advantage, and the fourth shows the same for disadvantage.

 

What does it all mean?
Let’s take an example from the table. Assume you need to roll an 11 to succeed. With a straight d20, you have a 50% chance of success. With advantage, this goes up to 75%. That’s the equivalent of a +5 bonus to the roll, since you would also have a 75% chance of success if you only needed a 6 or better on a single d20. Pretty impressive!

On the flip side for the target of 11, disadvantage means you only have a 25% chance of success, equivalent to a -5 penalty to the roll (when you need a 16 or better on a d20, you also have a 25% chance of success).

So does that mean advantage/disadvantage is equivalent to +/- 5? Not all the time. In fact, it’s only that big when you need exactly an 11 on the die.

Let’s say you need a 15 on the die to succeed. With a single d20, you’ll only get this 30% of the time. With advantage, you’ll get it 51% of the time – about the same as you would get an 11 or better on a single d20. So advantage in this case is worth about a +4. Disadvantage, similarly, is about a -4: You only succeed 9% of the time with disadvantage, which is about the same as a single d20 with a target of 19.

At the extremes, advantage makes the least difference. If you need a natural 20 to hit, that’s only going to happen 5% of the time normally. Advantage ups your chance to 9.75% – equivalent to getting a +1. Disadvantage takes your chance down to 0.25%, or 1 in 400. That’s the chance of rolling back to back criticals – not a common occurrence. But in terms of a modifier, it’s not much different from giving you a -1 to your roll when you need a 20 – it’s just about impossible.

 

7-dice-setIn reality
Most of the time, D&D tends to set things up so that you need somewhere between a 7 and a 14 to succeed on a task unless it’s trivially easy or ridiculously hard. If you look at the percent success in the d20 column for those rows, then find the equivalent percent success in the Advantage column, you’ll see that this is usually similar to getting a +4 to +5 bonus to the roll. Disadvantage is exactly the same in the opposite direction.

So there you have it. For target die rolls that are reasonably close to the middle of the range, advantage or disadvantage is about the same as having a plus or minus 4 or 5 to your die roll. It’s pretty powerful – much more powerful than the +2 for combat advantage that you get in 4th Edition.

Note that I haven’t factored in the additional chance of a critical hit with advantage, since I don’t really care about damage per round or anything like that. Suffice it to say that your chance of critting with advantage is 9.75% instead of 5%, and you can do the rest from there.

 

 – Michael the OnlineDM

Michael Iachini, known in RPG circles as the Online DM, has written extensively about playing RPGs online at onlinedungeonmaster.com. These days you can mainly find Michael designing and publishing board games at claycrucible.com. Follow Michael on Twitter @ClayCrucible. 

 

 

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Gen Con Rookie and Ask the Paizo GMs

medieval-crusades-1While I’ve been to conventions before (Otakon being prime among them) I’ve never had the pleasure of going to one devoted to entirely to gaming. Everything I’ve read tells me that my expectations will be defied and that it’s too much to absorb in only four days.  The people I ask tell me either to make no plans or stick to panels and discussions.

 

To put it succinctly, I am utterly ignorant about what’s going to happen next.

 

Travel arrangements have been prepared, the hotel reservation was made weeks ago, my tickets and badge have come in; the stage is set for what I expect to be a momentous occasion. During the convention I’ll be taking copious notes about my experience as a first timer at GenCon and am going to do my absolute best to grab some good photos along the way (albeit on my phone).
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So it turns out they were right; it’s far too much to take in all at once. The vast majority of my time was spent talking to publishers and attending seminars, some of which I cannot talk about. However, I do have one that I can talk about and my notes from the event are below.

Ask the Paizo GMs

1. Remix content players unintentionally skip.

Did you have a really intricate dungeon scenario with multiple encounters on the right, but nothing on the left, which is where your players went? Then just flip things around. You can work things out later (Ryan Macklin mentioned at some point or another that one of his favorite things to see is the long bathroom break, and expounded on the use of it as a private place to plan the remainder of an adventure on the fly.)

 

2. You don’t need high levels for high drama.

With the correct atmosphere and approach an encounter with an otyugh can be just as death defying and harrowing as the raid on a red dragon’s lair.

 

3. Respect the GM

The rules are a social contract; if you want to be respected, you have to respect the players in turn. If you’re hearing this – “The rules aren’t as written? How do I know what they are?” – then you’ve bent things too far out of shape and need to reassess (and possibly apologize). This doesn’t mean you aren’t the GM anymore (indeed, you are the ultimate arbiter of rules) it’s instead a reminder that respect is a two-way street; don’t cause a traffic jam with your ego.

 

4. Reward tiny free XP presents for good roleplay

Remember that every time you do this, only one player benefits; instead reward everyone for one player being awesome or allow sharing of experience among PCs.

 

5. Game as a team effort

This is a particularly good one; of course you need a traps guy to get through the dungeon hall but engaging in teamwork to succeed on a given task isn’t the same thing as actually making a team effort throughout the gaming experience. Think about it.

 

6. Re-incorporation is good GM improv (seeing NPCs again)

Not only does this make the world more believable (for both you and your players), it gives them an incentive to treat NPCs like real people; while I haven’t killed, robbed or otherwise been malignant to anyone in real life, I understand there are serious (and sometimes innocuous) repercussions for doing so.

 

7. “Failure can be the cost of success.”

Sometimes this means the players fail and sometimes it means you fail; either way there’s plenty of learning to be done. Don’t allow the party to enjoy victory every time (indeed, our highest moments are often mirrored by our deepest depths) and don’t beat yourself up if some well-laid plans get thrown to the winds. Take away what you can from the experience and be better for it next time through.

 

8. Err on the side of the players.

This brings us to something Wes Schneider referenced about a dozen times:

The 2 Rule – A general, situation-based bonus/penalty to ensure game fluidity.

Did you really need the fighter to make it over the ledge? Grant him a +2 bonus for some equipment that fortuitously snagged on a rock and can be briefly used as a point of leverage. Was it important that the lich not get disintegrated? Give out a -2 penalty to the Spell Resistance roll because of its proximity to a potent magic item. While this shouldn’t be abused, don’t let your excellent story get bogged down by some unexpected dice rolls and implement The 2 Rule instead.

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WarmachineI also snapped a few nice photos – the gentleman that co-stars in some of these is my primary playtester (and chief minion), a fellow named Dixie Carr. His talent for enduring the trials of my adventures is matched only by his excellent talent for providing scale in a photograph.GenCon Marvel

 

Of course, I didn’t ignore the gigantic spider queen by the D&D Next Booth. For whatever reason, Dixie is not overly concerned with his imminent demise; some players just never learn.

Lolth D&DNext Gencon 2013PS: The Damned Souls of Fenleist PDF is live! Go buy it here!

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D&D NEXT has a new home on Wizards.com!

Wizards of the Coast has just launched a brand new hub of information for D&D Next, the “next” iteration of the game, at http://www.wizards.com/DnD/DnDNext.aspx. The new page features all the latest and greatest on D&D Next including articles from Wizards, discussions about the future of the game, and seminar transcripts from the recent D&D Experience event. It will also soon house features like Live Chats, a calendar of upcoming events and, once playtesting begins, materials will be available for download through this page. (Please note that this new site does not signify the start of playtesting – we will, of course, let you know once that begins!)

Also, as you may have noticed, the D&D site has been redesigned with a spiffy new look which went live this week at http://www.wizards.com/dnd.

Check out the new pages and, as always, let me know if you have any questions. In the meantime, check out the site and sign-up for the playtest if you haven’t already done so!