“The difference between courageous and foolish is knowledge of risk.”—Adventurer Handbook

Early in our Deep Halls explorations, we were careful and systematic. Lantern overhead, we probed with pole into the advancing pool of light.

It was in making adjustments for experience stocked but unearned that we first diverged from the central hall. The way less certain, we made use then of the notion of a clever party. In brief, the amount of experience stocked in a dungeon level enables a party of average cleverness to be successful, while allowing some room, on one side, for a more clever party to achieve greater success and, on the other side, ample room for failure.

Upcoming explorations take us farther into The Deep Halls’ convoluted caverns. In upcoming articles, we adjust for party size, consider awarding more XP for treasure, and propose solutions for the noncontiguous problem.

Having determined the deadliness of The Deep Halls Level 1 and adjusted to a ratio of 2:1, stocked XP to that necessary for a party of three to gain 2nd level, we now consider it fixed. That is, regardless of further adjustments, we do not recalculate the deadliness ratio. This because each adjustment increases uncertainty, and with increasing uncertainty, the meaning of a “deadliness ratio,” already tentative, is drained. Therefore, where we must consider earned XP, we assume the raw value without multiplying by the ratio.

Furthermore, though Levels 2 and 3 have differing numbers of rooms, each inhabited by stronger monsters and more valuable treasures, we leave the math for deeper levels undone. Instead, we apply the treasure sequence that enables success on Level 1. Leaving open the question of survivability, we descend into The Deep Halls with the thrill of risking our lives.

The deadliness ratio serves as a warning. Knowledgeable of the risk, we dare to enter, if acceptable, or, if not, chose adventure elsewhere without questioning our courage.

Having decided the endeavor is not foolhardy, we delve deeper, keeping in mind the clever party. It is by ability that players must overcome the challenges of this “twisted and nightmarish” dungeon. Where further adjustments seem to invalidate the deadliness ratio, we examine how the clever party compensates.

Reading Map

Let’s hire a light bearer and give him the ten-foot pole. From here on: weapons in hand.

• Adjusting for Party Size
• More XP for Treasures
• The Noncontiguous Problem

This is a continuation of a previous article: “One Deadly Dungeon.” It is the sixth in a series in preparation for a Holmes Basic D&D campaign Dreaming Amon-Gorloth.

Problem: Whereas, a party of three 1st-level adventurers needs 6,513 XP to advance a level, the maximum they might extract from The Deep Halls Level 1 is 4,277 XP.

Solution: Add more treasure.

Reading Map

While probing ahead with the ten-foot pole, do not be alarmed by any clinking noise.

• How Much Gold
• Adjustments
• Rolls per Treasure or Treasure Sequence
• Deadliness Ratio
• Treasure-to-Monster Ratio
• “Monty Haul”

How Much Gold

Exploring Level 1, our clever party of three should earn 6,513 XP. Of that, 1,525 come from monsters. The balance of the necessary XP must come from treasure.

6,513 − 1,525 = 4,988 XP from treasure

Previously, we found that the average value for a roll on the M&T Level One treasure table is 143 g.p. As a “single” treasure on the Flying Dungeon Stocking Table, one roll is not enough to achieve a 1:1 ratio, experience stocked to that necessary.

To find out how much treasure is needed per single treasure, we reverse the equation, substituting t′ for one roll on the treasure table. Again, I add parentheses around each treasure denomination, unnecessary in mathematical notation, for the sake of readability.

(5 areas × 2t′) + (8 areas × t′) + (2.5 areas × ½t′) = 4,988 g.p.
19.25t′ = 4,988 g.p.
t′ = 4,988 ÷ 19.25
t′ = 259 g.p. (dropping the less precious metals)

So, to get a single treasure worth 259 g.p., we need to roll 1.81 times on the treasure table.

259 g.p. ÷ 143 g.p. = 1.81 rolls

If we round up to two rolls on the table for a single treasure, we roll four times for a double, and only once for a half treasure.

Where t equals 143 g.p.,
(5 areas × 4t) + (8 areas × 2t) + (2.5 areas × t) = 38.5t
38.5t = 5,505 g.p.

Now our party of three earns a total of 7,030 XP or 2,343 each.

1,525 + 5,505 = 7,030 XP ÷ 3 characters = 2,343 XP per character

Everyone, save the magic-user and any elves, advance one experience level before proceeding downstairs with some confidence.

Adjustments

“We should consider that some monsters prove too tough and some treasures go undiscovered. Further, attrition extracts earned experience from the pool.”—from “One Deadly Dungeon”

We aren’t done yet. Remember the clever party. It is a clever party indeed which defeats all the monsters in the dungeon and finds all the treasures. Furthermore, if we stock only just enough experience, then the DM may be tempted to fudge combat rolls and to hint and cajole less clever players into searching where they would have gone on to the opposite door.

Instead of treasures, it’s the clues to the treasures, but it’s the same “give away show” the editor warned us about. Players learn to look for the DM’s cues and

“seldom become truly able, often losing interest in the game because there is no challenge, no thrill of ‘risking your life.’” (Holmes, 22)

Too-tough and Undiscovered

By how much should we pad the ratio to account for too-tough monsters and undiscovered treasure? I’ve no idea how to calculate it. But “a clever party” provides a different approach.

Using the rule of thirds, if “a clever party indeed” finds all the treasure, then “a clever party” finds two-thirds of it, while “a less clever party” finds only one-third.

In other words, where the clever party is successful, the less clever party fails, and the clever party indeed clears the dungeon and carries the dagger +1 hidden in the spider’s abdomen back to Portown.

So, by multiplying stocked XP by 1.5, we enable success for the clever party, while allowing room for the clever party indeed to be more successful. Needing two-thirds of stocked XP ensures the game doesn’t become the give away show.

Attrition

Another consideration, as important, is attrition. Slain player characters take earned experience with them beyond the veil. Again, the factors involved are beyond calculation. Let’s apply the rule of thirds one more time.

Twice The Rule of Thirds

On the rule’s first application, the clever party needed to find two-thirds of the treasure. A second application reduces that number by one-third again. Now the clever party needs 44% of stocked XP to advance a level.

²⁄₃ × ²⁄₃ = ⁴⁄₉ or 44%

By the equation below, a clever party of three finds 44% of 14,803 XP, which is 6,513 or 2,171 XP each.

Where s is the number of stocked XP,
44% × s = 6,513 XP
    44%           44%
s = 14,803 (rounded up)

Rolls per Treasure or Treasure Sequence

So, we have to recalculate the number of treasure rolls based on 14,803 as the target for stocked XP. We remove the XP from monsters, which doesn’t change,¹ and recalculate t′.

14,803 − 1,525 = 13,278 XP needed from treasure
(5 areas × 2t′) + (8 areas × t′) + (2.5 areas × ½t′) = 13,278 g.p.
19.25t′ = 13,278 g.p.
t′ = 13,278 ÷ 19.25
t′ = 689 g.p.

To get 689 gold, we roll 4.81 times on the treasure table for a single treasure.

689 ÷ 143 = 4.81 rolls

Rounding up to five rolls for a single treasure, a half treasure would be 2.5 rolls. When we round 2.5 to three, a Fibonacci sequence appears ahead in the shadowy limit of the lantern’s glow. Let’s look at that in a moment.

Preliminary Sequence: 10-5-2

With a single treasure of five rolls, we have before us a double treasure worth ten rolls.² If we round down half of five to two rolls for a half treasure, we have a treasure sequence³ of 10-5-2, which shoots 307 g.p. over the mark.

Where t equals 143 g.p.,
(5 × 10t) + (8 × 5t) + (2.5 × 2t) = 95t = 13,585 g.p.
13,585 − 13,278 = 307 g.p.

Base Sequence: 10-5-1

Since the party finds it in a room without a monster, I favor reducing a half treasure (though hidden and trapped) to a single roll.

Where t equals 143 g.p.,
(5 × 10t) + (8 × 5t) + (2.5 × t) = 92.5t = 13,227 g.p.
13,227 − 13,278 = -51 g.p.

It falls just short of the mark, but it puts the party within “a 10 foot circle of protection”—to use a Holmesism. Let’s call this our base sequence.

Fibonacci Sequence: 8-5-3

By adjusting the number of rolls for each of three magnitudes of treasure—double, single, half—many variations are possible. As an example, let’s have a closer look at the Fibonacci sequence.

Where t equals 143 g.p.,
(5 × 8t) + (8 × 5t) + (2.5 × 3t) = 87.5t = 12,512 g.p.
12,512 − 13,278 = -766 g.p.

We fall 766 short of the target for XP from treasures. Considering the target XP, including monsters, of 14,803, we’re looking at a 5% difference—I’m guessing, well within a margin of error.

Deadliness Ratio

Using the base sequence above, we come to a stocked-XP to necessary-XP ratio of 23:10.

13,227 + 1,525 = 14,752 stocked XP to 6,513 necessary
14,752:6,513 or 227:100 or, rounding further, 23:10

Lest players be too comfortable with all the padding in the dungeon, we may preserve some “thrill of ‘risking your life’” by rounding down the ratio to an even two times the necessary XP.

6,513 × 2 = 13,026 stocked XP
13,026 − 1,525 = 11,501 XP from treasure

Recalculating t′:

(5 areas × 2t′) + (8 areas × t′) + (2.5 areas × ½t′) = 11,501 g.p.
19.25t′ = 11,501 g.p.
t′ = 11,501 ÷ 19.25
t′ = 597 g.p.
597 ÷ 143 = 4.17 rolls for a single treasure

Thrilling Sequence: 9-4-1

Plugging in a treasure sequence of 9-4-1, we’re only 133 gold short, which is a stocked-to-necessary XP ratio of 198:100 or as close to 2:1 as makes no difference.

Where t equals 143 g.p.,
(5 × 9t) + (8 × 4t) + (2.5 × t) = 79.5t = 11,368 g.p.
11,368 − 11,501 = -133 g.p.

11,368 + 1,525 = 12,893 XP
12,893:6,513 = 198:100 or rounding to 2:1

We could have saved some calculation by adjusting to 50% from 66% on the second application of the rule of thirds. Now we know, though, that the difference between 44% and 50% is near 2,000 XP.

12,893 − 14,803 = -1,910 XP

Our clever party, earning 44% of stocked experience, may struggle.

12,893 × 44% = 5672 ÷ 3 = 1,890 XP each

Only fighting men with a high Strength score (10% prime requisite bonus) advance an experience level along with clerics and thieves.

Treasure-to-Monster Ratio

With a 2:1 stocked-to-necessary XP ratio, our 9-4-1 sequence yields a treasure-to-monster ratio of 75 to 10.

11,368:1,525 = 745:100 or rounding to 75:10

This is almost two times Quasqueton’s ratio and three times the ratio (25:10) calculated using the simple treasure sequence, 2-1-½, from the Flying Dungeon Stocking Table.

“Monty Haul”

Jim Ward is a legend in the role-playing game industry. His design credits include Metamorphosis Alpha (1976), Gods, Demi-Gods & Heroes (1976), and Greyhawk Adventures (1988). Ward learned to play D&D at Gary Gygax’s table, exploring the co-creator’s Greyhawk city and dungeon.

Ward describes, in “The Origin of Monty Haul,” his first experience as a Dungeon Master, running the group gathered at the Gygax home through his own creation. On the dungeon’s first level, the low-level adventurers find an ioun stone and “special sashes that give the wearer martial arts powers,” with which they easily defeat the level’s biggest challenge—three bugbears. Afterward, Ward writes:

“Gary critiqued [the dungeon] by calling me a PRICE IS RIGHT Monty Haul style DM. I gave out too much treasure for the effort.”

With a treasure-to-monster ratio between 7- and 8-to-1, we may, without unreason, expect similar critique.

Proceeding in this “Monty Haul style,” we should wear the term, as Ward does, “as a badge of honor.”

The lantern wanes again, and we’re out of oil. While we make our way back to the entrance, we’ll talk about awarding more experience for gold and look at adjusting for party size and the noncontiguous problem.

Notes

¹ In these Deep Halls, we don’t up the strength of monsters to compensate for increased treasures, as Holmes advises. For extracting XP via more slain characters defeats our purpose. If we did increase monster strength, I expect The Deep Halls, though rich in rewards, would become known as a “killer” dungeon.

² We might think ten rolls is a lot just to get a treasure. Consider, though, that a special or selected monster (as are the double treasures monsters) in any dungeon likely has a lair-type treasure. Take orcs, for example. To determine Treasure Type D, we make at least six rolls—if the orcs have already been cleaned out—and up to a maximum—if the orcs have been lucky—of 15 dice rolls. Then we must multiply by the fraction of the lair’s inhabitants.

³ What I call a “sequence” here is properly a ratio. I use the former to avoid confusion; we have already ratios for deadliness and treasure-to-monster. Further, where a ratio uses colons between terms and a sequence uses commas, I use dashes, again for clarity.

Before we go on to remedy the dearth of experience points stocked in The Deep Halls, I want to check our work against a Holmes-era published module.

In “One Deadly Dungeon,” we use the probabilities for monsters and treasures on the Flying Dungeon Stocking Table to calculate how much experience might be earned in The Deep Halls Level 1. In 51 encounter areas, we count 4,277 XP from treasures and monsters, including the wandering type.

On his D&D Hotspot, Dan “Delta” Collins treats Dungeon Module B1 In Search of the Unknown with similar scrutiny. In the two-level complex called the Caverns of Quasqueton, Dan counts 4,264 stocked XP in 56 encounter areas. He omits wandering monsters.

So as not to compare daggers to broadswords, we remove wandering monsters (425 XP) from The Deep Halls—3,852 XP.

Comparing Experience Points per Encounter Area

Rounding brings the XP per area to the same. This should not be surprising. I derived the Flying Table from guidelines given in Holmes Basic with the two earlier supplements B1 replaced. The correspondence only suggests that, one, module designer Mike Carr used the same guidelines, and two, at least regarding monsters and treasures, the Flying Dungeon Stocking Table hits the mark.

While we’re poking around in Carr’s Quasqueton, let’s look at how the total XP is distributed between treasures and monsters.

Comparing Treasure-to-Monster Ratio

The same amount of XP is delivered in a different balance. More monsters dwell in The Deep Halls. Quasqueton contains more wealth. There is room yet in our dungeon for at least half again the treasures.

“…if the party were second level, or the first level monsters were encountered on the second level of the dungeon, the number of wandering monsters encountered should be doubled. In a like manner, the number of monsters should be tripled for third level adventurers or in the third level of the dungeon if the monsters appearing are first level.” (Holmes, 10)

Other than a hint in the wandering monster table, with more and more powerful monsters found on levels two and three, this allusion to the increasing danger in deeper levels is as close as Holmes¹ gets to a standard conceit of old-school dungeons: the strength of the average monster encounter on a given dungeon level matches that of a player party of the same experience level.

That accepted, a dungeon’s deadliness might be expressed as a ratio of the number of experience points in stocked monsters and treasures a given level contains versus the amount necessary for an adventuring party to gain an experience level.

A party of 1st-level characters, for example, exploring the first level of the dungeon, should earn enough experience to gain a level before descending to the second level. For, while the adventurers still have a fighting chance, the dangers below are more likely to overwhelm them.

Scratched with an iron spike on the inside of a neophyte adventurer’s shield is the maxim, “Level up before level down.”

Closed Dungeon

I assume here a “closed” dungeon. That is, one which must be explored without delving elsewhere. Whether due to time constraint or DM fiat, the only experience to be gained is in this dungeon.

An even 1:1 ratio—experience stocked to that necessary—may not be enough to approach a minimum level of survivability. We should consider that some monsters prove too tough and some treasures go undiscovered. Further, attrition extracts earned experience from the pool.

I am not one to scrutinize the numbers. But the dungeon’s limited size prompts me to further examination. I conclude below that any foray into The Deep Halls of Amon-Gorloth is doomed to failure. This is how I figure.

Reading Map

This is another longish bit. The math is no more complicated than simple probabilities and basic algebra,² but following each step requires tenacity on the part of the author as well as the reader. I try to move quickly through the calculations and, at the same time, remain coherent.

If you are able to follow the text—and do, then we are exploring The Deep Halls together. Suggested equipment: lantern and ten-foot pole…

• Encounter Areas per Level
• Experience Necessary to Gain 2nd Level
• Mean Experience per Encounter
• The Cause for Concern

Encounter Areas per Level

As an initial measure to ensure some modicum of survivability, I previously merged The Deep Halls’ seven levels into three, thereby increasing the number of encounter areas per level. Counting the areas by color, we get the following numbers, sub-totaled by level.

Adventures per Character Level

“As a guideline, it should take a group of players from 6 to 12 adventures before any of their characters are able to gain sufficient experience to attain second level.” (Holmes, 22)

In my experience with both Holmes Basic and B/X, a low-level party, having not unusual luck, can explore about five rooms, before running low on spells and hit points. If by “adventures” the editor intends forays into and out of the dungeon, ten of these would clear the 51 encounter areas on Level 1.

Note that, for the present purpose, we consider only The Deep Halls’ first level. The calculated ratio is specific to that level. It is not applicable to the dungeon’s other levels or to any other dungeon. Though the calculations to derive the ratio could apply.

Experience Necessary to Gain 2nd Level

“The number of wandering monsters appearing should be roughly equal to the strength of the party encountering them. First level adventurers encountering monsters typically found on the first level of a dungeon should be faced with roughly equal numbers, i.e. a party of three would encounter 2-6 orcs, 3-12 giant rats, etc.” (Holmes, 10)

The goal is determine how many experience points to stock on Level 1 so a 1st-level player party might advance one level of experience before going down to the next.

Party Size

Cross-referencing Holmes’s example for balancing encounters with the Monster & Treasure Assortment Set One, we see, on the First Level table, entries for both monsters: “Orcs (2-5)” and “Giant Rats (3-12).”

Averaging the dice rolls for the ranges and dropping halves, a party of three might encounter three 1-HD orcs or seven ½-HD giant rats—a “roughly equal” match for a party of three 1-HD characters.

On M&T’s second level, the party of three, now 6-HD, encounters 3-12 orcs (average 7) or 5-20 giant rats (12). On the third level: 4-24 orcs (14) and 5-30 giant rats (17) versus the party’s 9 HD. Tenuous, but the match holds.

Further examination of the monster tables (not shown) reveals similar correspondence. We conclude that, though the M&T instructions do not say, three is the target number of party members for listed encounters.

Therefore, we use a party of three adventurers to determine a baseline. We can adjust for larger and smaller parties later.

Hereafter, I show the math immediately following the text that refers to it.

Averaging the XP necessary for each class, as a whole the party must earn 2,171 XP per member. (Note that only 4,000 XP are necessary for an elf to advance to 2nd level in the fighting man class.)

2,000 + 2,500 + 1,500 + 1,200 + 2,000 + 2,000 + 4,000 ÷ 7 = 2,171 XP

For our party of three, Level 1 should be stocked with 6,513 XP to arrive at a ratio of 1:1, stocked-to-necessary XP.

2,171 × 3 = 6,513 XP

Magic-users and elves lag—as usual.

Noncontiguous Levels

We needn’t venture far into The Halls before we have an indication of their depths. Level 1 is not contiguous (nor is any level). A 1st-level party is obliged to descend into dark green sections (level 2A) early in the exploration. We keep it in mind for later consideration. By this though, we are warned: The Deep Halls is one deadly dungeon.

Mean Experience per Encounter

Here we calculate the average XP to be gained per encounter from monsters and from treasures. Considering only Level 1, we round to 50 encounter areas for simplicity.

On the Flying Dungeon Stocking Table, monsters entries should be read as one roll on the M&T monsters table. In addition, let’s assume the “double” treasures (first two entries) are accompanied by double monsters—two rolls on the table. Likewise, single and double treasures on the Flying Table are one and two rolls for treasures.

XP from Monsters

Here, where we calculate the average value for XP from monsters, it is for a roll on the M&T tables, not for a single monster. We see on the Flying Table that monsters inhabit 33% of rooms (17), plus 10% of rooms are double monsters (add 5). So, Level 1 might contain 22 monsters.

The mean XP value of a roll on M&T’s First Level monsters table is 50. Don’t ask me how I know this.

Therefore, our party should receive 1,100 XP from monsters for their efforts.

(17 + 5 encounters areas) × 50 XP per monster roll = 1,100 XP

Wandering Monsters

It’s difficult to estimate how quickly a party explores a dungeon. By the Bluebook, we roll for wandering monsters every third turn. Considering an armored adventurer’s 120-foot move rate (Holmes, 9) and the room density on The Deep Halls map, a clever party (see below) might explore one room every three turns. A rough estimate, but it serves.

Therefore, during the party’s exploration, the DM rolls 51 times for wandering monsters, which appear 8.5 times. At 50 per encounter, that gives us 425 XP from the wandering type, which we add to 1,100 for those static, to arrive at a total value of 1,525 XP from monsters.

51 ÷ 6 = 8.5 × 50 = 425
425 + 1,100 = 1,525

A Clever Party

In calculating the ratio, I use, as a baseline, the notion of a “clever party.” An oft-touted characteristic of an old-school game is that player ability is as or more important than character statistics. New players are taught by those more experienced (whether DM or adventuring companion), and so, they learn to navigate the dungeon and overcome its challenges.

As a group, the players test their ability against the dungeon. More clever players may be more successful, thereby advancing somewhat faster in experience levels, while those less clever must learn or ultimately fail.³

Later, I expand on the notion, adding the concept of player ability in three tiers: less clever, clever, and clever indeed.

By a “clever party,” I mean one which counts among its members at least one experienced player of at least average cleverness.

XP from Treasures

From the Flying Table again, we calculate how many encounter areas are likely to have treasure and how much. Where treasures are found with no monster, I extrapolate half the amount of a roll.

I don’t find in Holmes any notion of rolling dice, when searching, to discover hidden treasure. He gives no explicit rule. In the sample dungeon, treasure is hidden. If characters take the time to search the hiding place (a layer of refuse, Room G, 43) or perform a certain action (cut open a defeated spider, Room J, 44) they discover the treasure automatically.

The total gold.jpgece value of treasures, ignoring magic item entries, from M&T’s Level One treasure table is 14,326. Don’t ask me how I know this, either. This makes the average value for a treasure roll on the 100-entry table equal to 143 gold, 2 silver, and 3 copper pieces. Please do let me know if your count differs.

Now, we can calculate how much treasure exists, according to the probabilities of the Flying Table, on The Deep Halls Level 1. I add parentheses around each treasure magnitude—double, single, half—for readability.

Where t equals one roll on the treasure table or 143 g.p.,
(5 areas × 2t) + (8 areas × t) + (2.5 areas × ½t) = 19.25t = 2,752 g.p. and change

The Cause for Concern

Adding XP from monsters and treasures, we get 4,277.

1,525 + 2,752 = 4,277 XP

Therefore, the ratio of stocked XP to that necessary is 4,277:6,513 or 66:100—not near 1:1.

Our party of three, if clever indeed, might find all the treasure on Level 1, but still earn only 4,277 XP.

4,277 XP ÷ 3 characters = 1,425 XP per character

Although a thief advances, fighting men lack one-quarter of the XP for 2nd level. Furthermore, we have yet to account for too-tough monsters, undiscovered treasure, and attrition.

So, we see that any expedition to The Deep Halls of Amon-Gorloth is doomed to failure.

 

DANGEROUS DUNGEON
DO NOT ENTER

 

We don’t heed the warning, of course. We’re adventurers after all.

I proposed earlier a fun solution to the problem: “to throw treasure at it.” Next, we’ll see how much treasure we need to stuff into The Deep Halls to make it survivable.⁴

The lantern is dim. Let’s take a break while I refill it.

Notes

¹ Zach Howard of the Zenopus Archives compares “The Holmes Manuscript” to the published 1977 edition of Basic D&D. From Zach’s analysis, it’s clear that some text of the published version differs from that intended by Eric Holmes. The section on balancing encounters is an example. In this and following articles, unless stated otherwise, when I refer to “Holmes” I mean the edition, not the editor himself.

² The math isn’t complicated, but there is plenty of room for error. If you notice a miscalculation, please let me know.

³ The cost of failure in the D&D game is to roll-up new characters and, bolstered by the experience, descend again into the murky depths to face anew the challenges therein lurking. We only fail when we give up.

⁴ Another solution, of course, is to award more than 1 XP per gold piece. Though the practice is not unheard of these days, the first I learned of it was during the early part of the current era, called the Old-School Renaissance, in the 2000s. Whether multiplying treasure or experience for it, read on, for much the same considerations apply. Grognards belch at both.