Sunday, April 15, 2007

Magic Number Seven

When we think about games in general, and D&D in particular, a lot of us have the complaint nowadays that "the game is too complicated". But can we agree on how "complicated" something really is? One thing I wish game designers would consider is concrete research from cognitive science about how people process information (and how much they can deal with at once).

Consider the following Wikipedia article, "The Magical Number Seven, Plus or Minus Two":,_Plus_or_Minus_Two

In this article, you'll see two related (apparently coincidental) research observations. (1) Working memory capacity for most adults is in the range of 7+/-2 objects (i.e., 5 to 9 objects). That is, people can consider about 7 separate entities at once and make a choice among them at a high level of functionality. (For specific material, the limit may be 7, or 6, or 5). Beyond this limit, mental functioning rapidly drops off. (2) Short-term memory capacity is also 7+/-2 when measured for English speakers memorizing, say, a string of random digits. For example, the book Modern Structured Analysis recommends a 5 to 9 limit on the number of subroutines called from the main block of any computer program (for the convenience of maintenance programmers).

Now, I'm sure that lots of us (possibly reading this) may personally skew on the high side of these numbers. I bet that math- and computer-oriented folks have higher working memory capacities, possibly significantly so. (The guy who inspired the Rain Main character could instantly "chunk", or count, a whole box of toothpicks spilled on the floor, for example; so it varies a great deal by individual.) A lot of caution must be taken in over-expanding the results of research like this, but nontheless, it serves as an excellent starting point for discussions of "how much is too much?".

So, how many options are reasonable for a person to consider at once in a D&D-like game? I would argue for: Seven, plus or minus two. Best would be a number of about 5 or less, which is easily workable by everybody. Slightly less optimal would be a count of 6 or 7, which is parsable by most people. At most 8 or 9 options would be okay, which seems to tax most functioning adults, and feels less like fun and more like work to a lot of us.

Consider this in the context of OD&D and how many choices have to be made when a person creates a new character:
- Abilities: 6 (Str, Int, Wis, Dex, Con, Cha). Excellent.
- Races: 4 (Men, Dwarves, Elves, Hobbits). Perfect.
- Classes: 4 (Fighter, Wizard, Cleric, Thief). Perfect.
- Alignment: 3 (Lawful, Neutral, Chaotic). Perfect.
- Armor: 5 (leather, chain, plate, shield, helmet). Perfect.
- Weapons (Melee): 13. Too many to consider at once.
- Weapons (Ranged): 5. Perfect.
- Mounts: 5. Perfect.
- Wizard Spells (1st-level): 8. Acceptable.
- Cleric Spells (1st-level): 6. Excellent.

For all of the key considerations, OD&D just happened to appear "magically" with the perfect number of choices to be interesting and enticing, but not overwhelming to the brand-new player. I particularly find the initial options of 4 races, 4 classes, and 3 alignments to be extremely mentally satisfying. There are just three main categories here, each with a perfectly manageable number of options, but generating 48 different possible starting characters! (Assuming all race-class-alignment combinations are permitted.) That's a lot of variety blooming from a very small and manageable number of choices.

Compare this to the current state of D&D. We've always maintained the 6 core abilities (with a lot of resistance when AD&D tried to insert a 7th for "Comeliness"). In the 3E PHB we have:
- Races: 7. Acceptable, but borderline for some people.
- Classes: 11. Too many to consider at once.
- Alignment: 9. Almost too many to remember.
- Skills: 45. Far too many to consider at once.
- Feats: 74. Far too many to consider at once.
- Armor: 21. Too many to remember at once.
- Weapons (Melee): 56. Far too many to consider at once.
- Weapons (Ranged): 14. Too many to consider at once.
- Mounts: 8. Almost too many to remember.
- Wizard Spells (to 1st-level): 58. Far too many to consider at once.
- Cleric Spells (to 1st-level): 38. Far too many to consider at once.

Obviously, expert players have a working knowledge of almost all these options, but it's probably been built up over years or decades of play experience -- and they probably mentally "chunk" this material into certain categories (warrior vs. spellcaster classes, ethical vs. moral alignments, skills by ability, feats for fighters vs. items vs. metamagic, spells by attack/defense/utility or school) that may not be totally explicit in the rules.

OD&D has a score of 9:1 (say, 90%) categories ok:not-ok under this "magic number seven" cognitive rule analysis. Meanwhile, 3E D&D has a score of 4:8 (say, 33%) under the same analysis. OD&D seems to hit the "sweet spot" for working memory considerations in character creation, whereas 3E is clearly far, far more complicated. (Consider also something unrelated to character creation, like the number of giant or dragon types: OD&D with 6 dragon types, 3E D&D with 10.)

I truly wish that the D&D designers had the capacity to focus very specifically on the new-player experience, and think about what the ideal setup would be if we truly honestly wanted to expand the hobby, and make it accessible to everyone (not just old players and math whizzes). If this were the case, the options that lured us all into OD&D in the first place would be an excellent foundation to build on.

Here's some brainstorming in that regard. Let's say 1st level creation is set up to be accessible by any player who's never even heard of D&D or RPG's whatsoever. Provide the 6 abilities, 4 races, and 4 class options from OD&D (as above). Provide limited types of armor, weapons, and spells (again as per OD&D). Give fighters feat-like options, around 5 or so at 1st level (maybe melee/ archer/ mounted/ swashbuckler types); make sure that thief skills are limited to 6 or so to be memorable.

As levels go up, allow more options to be unlocked. More spells at higher levels (again like OD&D), as players get to know their spellcasters better. Feats (such as for fighters) allow access to more feats in a tree-like fashion. Prestige classes may still be digestible in limited numbers. Expert players should be encouraged to start play with heroes of 3rd level or higher, having more of these options on the table to begin with. (Note how the upcoming Star Wars Saga rules start characters at 3 hit dice.)

But at the same time, the branching options can't be so many that statting out high-level NPC's becomes unmanageable for the DM. Allow only a total of 7 or so feats absolute maximum, so that DMs can slot them out mentally when needed. A total of 7 or so spell levels is a good choice (see OD&D: a perfect 6 spell levels vs. 3E D&D: a swollen 10 levels). NPCs shouldn't need more than 7+/-2 magic items at most, nor should any monster have more than 5 to 9 special abilities at most.

Regardless of the actual choices or construction of the game (or even the specific cognitive research studies used to support them), rules-of-thumb like these would be extremely useful for determining when "more is too much", and when new added options serve as repellant to part of the hypothetical new-player base.


  1. Obviously you've hit upon the reason to go back to OD&D, instead of the later editions! :)

    If you're interested, I am working on a synthesis of the original rules into a coherent document (with a few tweaks from my end as well, I suppose) at

  2. Wow...that is excellent information from a game design perspective. Thank you!

  3. Hmmm, a very thought-provoking piece. Kudos. I'd like to see an analysis of other RPGs, such as AD&D, D&D 4th Edition, Vampire/other WoD games, Call of Cthulhu, Shadowrun, GURPS, FATAL, etc. It would be very interesting to see how various systems stack up against one another, when seen through the prism of manageable complexity.

  4. Monte Cook just liked to this, might get a spike in hits!

    While I was reading this I was thinking of in-play options too. What can a character do in a given round, how many powers and feats are you managing (and then add on status effects, etc). Too many options during character creation is difficult, but managing too much "in real time" during play is also a problem!

  5. ^ Very cool! Yes, I agree that options at both character generation and in-action need to be not too burdensome. I'm also a big proponent of different classes implying different levels of complication, so the player can pick to their personal satisfaction (like OD&D fighters vs. wizards).

  6. I very much agree with this, particularly with regards to feats, which I feel is my single least favourite part of 3e, and gets worse with both pathfinder and 4e, as the rate at which you get feats increases. I can spend ages mulling over feats during character gen, but I have no desire to do so.

    The only exception to your analysis is for alignment. 3e alignment is not 9 different alignments, it's two sets of 3 (the law-chaos axis, and the good-evil axis). Arguably 4e with its 5 alignments is actually worse, since there the original pattern is gone, but 5 is still well within the ideal limits.

  7. I'm posting this comment from the future. IIRC 5e blew it, and so did 6E. Last year someone found your post and it worked brilliantly, but unfortunately we have little time to play D&D in the Vault.

  8. I always pay close attention to messages from the Time-Fax. Thank you!!

  9. I know this post is old as heck, but I wanted to thank you for writing it. This is a fantastic analysis and has given me a lot to think about as a Pathfinder GM.

  10. LS, thanks for the kind words! Glad you saw it.

  11. This is very late, but I great post. I've had this issue with most modern games, but didn't know how to put it into words. I only recently found 0ednd (having started in 4e and quickly changed to Pathfinder and then floated around looking for a system to do what I wanted) and it seems to be an elegantly simple system. Not perfect by any means and confusing if I didn't already know some basics of DnD, but what's there is easy and the best part is how easily customizable it is without breaking the system. After a cursory reading I'm already able to see some rules I want to add/change and I don't feel worried that I'll break the system like I did with 3e or Pathfinder.

  12. Regardless of age, this is a great article. I intend to write a whole article in response, but I'd like to leave a few comments.

    1) IT's interesting that the primary goal of 4th Edition was to make it easier to introduce new players. However, it very clearly broke this rule. Powers made classes really unwieldy. Even a first level character had at least 10 powers, way more than a new player can consider on their turn.

    2) For options that need a large number of choices (like feats), it's possible to mitigate the problem by providing a short list of recommended options. Classless systems tend to do this, and D&D Next gives suggested feats for common builds like two-weapon fighter, healer, archer, and such.

    3) One thing that the article doesn't address is whether those options have sufficient impact to warrant the complexity they offer. Sure, 3 alignments, 4 races, and 4 classes might give you 48 combinations, but how significant are those combinations? Is there any difference between being a lawful human fighter and a neutral elf fighter? Probably not that much. Most of the differences between races are numerical. Personality does help but you can easily make a human that acts like an elf and vice versa.

    1. Thanks for the comment! It does seem like this particular observation has legs, and I keep thinking about it myself over time. Personally my favorite solution is a tree-type type affair where the options at 1st level are very limited, they branch out at higher levels (like OD&D spell levels; opposite of 3E skills & feats), and expert players can choose to just start at those higher levels.

      You probably have a pretty good point on (3) that the impact of the alignment/racial options is not that great. I can't argue with that.