Magic Distribution in OD&D Dungeons

An observation: Boy, magic is really rare if using the dungeon treasure table in OD&D Vol-3 ("The Underworld & Wilderness Adventures", i.e., the DM's book). Prior to this table you get the dictate, "It is a good idea to thoughtfully place several of the most important treasures... Naturally, the more important treasures will consist of various magical items and large amounts of wealth in the form of gems and jewelry." Then for the rest of the dungeon, rules that 2 in 6 of rooms have monsters; with treasure present 3-in-6 with monsters and 1-in-6 without. Then this table is given for such treasure:

Now, I've sort of made my peace with this table for gems & jewelry; while rare (esp. at the lower-numbered levels), when present they come in batches and generally large values, so they sort of give some reasonably high value. (A bit like hockey or soccer: scoring is rare but each goal makes a big difference!) However, magic is very rare throughout dungeon levels 1-3, apparently only shows up one item at a time, and has the added limitation that when you turn to the magic tables, 25% of the time it turns into a treasure map, and not actually any magic.

Let's compute. Say on a standard piece of graph paper you get around 40 rooms per levels (that's what I tend to get), and randomly stock the whole dungeon with this method. Then on the first 3 levels combined you'd expect (adding terms for both with-and-without monster cases): 3 levels × 40 rooms × (2/6 with monsters × 3/6 treasure + 4/6 without monsters × 1/6 treasure) × 5% = 120 × (1/6 + 1/9) × 5% = 120 × 0.277 × 0.05 = 1.66 positive results for magic items. Adjusting for the chance of maps, we get 1.66 × 0.75 = 1.25 actual magic items. So on average we may likely get just one single potion on all of levels 1-3 of the dungeon, and no other magic whatsoever. That could make it a bit hard to fight 4th-level monsters like lycanthropes, gargoyles, or wraiths, that start showing up on the [checks notes]... um, 1st level of the dungeon.

Anyway, here's a complete table of expected number of magic items (discounted for chance of maps) per dungeon level under these assumptions:

As we've seen, on levels 1-3 we only expect about 1/3 of a magic item per level, so rounding to the nearest integer, this appears as zero (0) in the table above. At other levels you may get 1, 2, or 3 magic items on average from the Vol-3 random method. If you make a dungeon of 12 levels (~500 rooms?), then we'd expect a grand total of around 14 magic items in the whole complex.

So I think that most of us would agree that simply can't stand; we have to do something else to supply fighters with magic arms and armor, wizards with wands and spell-scrolls, non-renewable potions of healing et. al., and other stuff. The most obvious way is by DM fiat, thinking of the "thoughtfully place" dictum. But then we are left with no other guidelines for what kind of distribution is recommended in that advance process.

Perhaps one faint idea is to shift magic-positive results from one single item to 1d6 at a time (roughly tripling the numbers estimated above, on average). Any other ideas?


Edit: Some folks in the comments take the interpretation that maps should not be generated from that dungeon-treasure table, actual magic only (maps for wilderness treasure only). There's definitely an intriguing case to be made there, but I'm not sure it's ironclad.

On the other hand, if we do permit maps in dungeon hoards, then perhaps we should account for the magic items to which they can lead you. Random maps have a 30% chance of leading to a "Magic Map" table, and 10% to a "Magic & Treasure Table". Those are both d8-based, and coincidentally, they each have an expected production of 19/8 = 2.375 magic items (individual results go as high as 5 items!). So together any random map expects to lead to 0.40 × 2.375 = 0.95 magic item. We might as well round that to "1", which tells us that we can effectively just ignore the map discount itself (each map leads to an average of one magic anyway). Either way, we're then back to an expectation of 1.66 items in the first three levels of the dungeon (not a big difference).

Or taking Daniel Wakefield's idea, maybe that gives us a clue for what a thoughtfully-placed "big magic cache" might be: 1-5 magic items or something like that. Other ideas are to scale it to the expected number of items PCs might have per level (almost embarrassed I didn't think of that earlier).

Consider: These days I roughly assume that pre-generated PCs might have a 1-in-6 chance for magic per level in each of 3 categories. (So: a 6th-level fighter with +1 sword, shield, and armor seems reasonable.) That implies about 3/6 = 1/2 item per level. If one PC level correlates with one dungeon level, and we have 4 PCs, then it suggests we want 4 × 1/2 = 2 items per level (permanent items?). Compare that if we say that random magic finds include 1d6 items (similar to the 1-5 range in the maps), take the expected magic finds for a single level (1.66 / 3 = 0.553), and multiply them together to get 3.5 × 0.553 = 1.94 ~ 2 items per level. So those figures seem synchronous.

On the other hand, if you have big 8-person parties then you might consider the need to double that again? Geoffrey McKinney's stats for B2 indicate the per-area magic rate at about 80% × 50% × 46% = 0.184. So one of my 40-room levels would expect 40 × 0.184 = 7.36 items, or almost quadruple the figure in the prior paragraph. Hmmmm. At least that gives us a starting upper/lower bound for what we might choose.