We are often told that the great thing about OSR is that all of the materials are mutually compatible. The idea is that it doesn’t matter if it says D&D, AD&D, OSRIC, Swords & Wizardy, or Old School Essentials on the cover of the module — regardless you can run it with any of the above with minimal conversion. This makes sense as these editions all have similar rules for a) combat and b) dungeon exploration and most modules are mostly about a) combat and b) dungeon exploration. However what about other play styles? The hexcrawl dates back at least to X1 Isle of Dread published in 1981, but it is increasingly popular now with OSR hexcrawls like Hot Springs Island, Hideous Daylight, and Dolmenwood being esteemed for their creativity and design. Likewise hexcrawl theory is an active topic on the OSR blogs (e.g., the October 2022 Glatisant has four links to hexcrawl theory posts). So the question is, can OSR hexcrawls boast the same mutual compatibility as OSR dungeons? If I buy a hexcrawl that says OSE on the cover, can I trust that it will run OK using Swords & Wizardry? If I write a hexcrawl, is the decision of which edition to identify it with as incidental as it would be for a dungeon?

A hexcrawl is about exploration and resource management relevant to wilderness travel. In many editions, you face random encounters as a function of time, and these random encounters can be brutal. This makes travel time a key issue since the slower you travel, the more danger you face and more resources you consume per unit of distance. Moreover, encumbrance also plays a role since if you’re carrying a lot of gear or treasure, this slows you down. And finally, a good hexcrawl should encourage travel through favorable terrain by giving differential penalties in terms of speed and getting lost by terrain types. There are other mechanics that could be relevant to hexcrawls (e.g., resource management magic like goodberry), but the big one is how fast can you travel, through what terrain, and will you get lost. And it turns out these vary a lot between editions, as shown in the following tables. Note that I ordered these by “family” of rules, with all the B/X varieties together, all the AD&D varieties together, etc. “Miles/day” is for an unencumbered human on easy terrain. I include road travel time as a special case given that systems inspired by B/X tend to have a 1.5x rule for roads. I describe terrain and lost rules as “vague” if it’s a blink and you miss it “DM may adjust” in the middle of a paragraph type rule.

Edition	Miles/day cross country	Miles/day road	Terrain modifiers?	Lost rules?
Castles & Crusades	2mph	2mph	vague	no
DCC	24	24	vague	no
5e	24	24	yes	yes
Five Torches Deep	10 + STR mod	10 + STR mod	yes	no
AD&D	30	30	yes	yes
OSRIC	24	24	vague	vague
Hyperborea	24	24	yes	yes
ACKS	24	36	yes	yes
Basic Fantasy RPG	24	32	yes	yes
Labyrinth Lord	24	36	yes	yes
Lamentations of the Flame Princess	16	24	yes	yes
Old School Essentials	24	36	yes	yes
Worlds Without Number	30	60	yes	no
Crypts & Things	12	12	no	no
Swords & Wizardry	12	12	vehicles	yes
White Box FMAG	12	12	vague	yes

It turns out that a simple question like “how far can you walk in a day under ideal conditions” varies from about 10 miles to 60 miles! The 60 miles figure for Worlds Without Number is an outlier, but B/X-inspired games in general include a generous road modifier, and so games based on B/X tend to have maximum distances per day more suited to a bicyclist than a pedestrian. If the characters are traveling cross-country, it’s not as bad, but even for cross-country travel B/X, AD&D, and d20 style games still tend to let you travel twice as fast as do OD&D style games. One implication of this is that Swords & Wizardry may be similar enough to Worlds Without Number that you can run a dungeon written for one using the other, but for hexcrawl purposes, you’ll need to rescale the map.

Now there’s the question of what rules should you use. The simulationist answer is to use the Lamentations of the Flame Princess rules. In real life, the average human walking speed is 3mph and a healthy adult can walk about 20 miles a day under ideal conditions. This matches pretty well with Lamentations’ rule that you can go a bit more than that on a road and a bit less cross country. Plus Lamentations has sensible, well-presented, and generally easy to use rules for terrain, encumbrance, and getting lost.

The gamist answer might well be different. Dolmenwood is written with OSE‘s canonical B/X assumptions in mind and so however unrealistic it might be to expect that you could walk from Sacramento to within site of San Francisco Bay in a weekend, those are the assumptions that campaign setting was written with and if you make characters go slower than that you’re throwing off game balance elements like “are these locations within one day’s travel of each other.” In addition there’s always a compromise between what would the ancient or medieval world really be like and what do players from modern cultures expect. Just as we give D&D a capitalist economy rather than simulating some type of gift exchange or palace economy, there’s a certain appeal if not logic to playing to the intuitions of people who regularly commute in cars or on trains and so think of ten miles as a quarter hour, not all day or half a day. In addition, having a road multiplier is a great incentive to funnel characters along set routes.

If you’re writing a hexcrawl for publication, my suggestion is to either a) include the hexcrawling rules in the hexcrawl itself or b) give the hex scale in terms relative to the system’s speed. For instance, “the scale of 6 miles per hex is based on the expectation that, given favorable terrain and light encumbrance, characters can travel up to 24 miles or 4 hexes a day. If you are using a game like Swords & Wizardry with a slower movement rate, you might want to use a scale of 3 miles per hex.” There’s also the radical option of not writing a hexcrawl at all but instead writing a pathcrawl, which effectively replaces the system rules with ones specific to the locations.

Some additional notes.

Several games allow a forced march for more distance. Swords & Wizardry and Crypts & Things both let you “force march” to double your distance by a strength check. White Box FMAG (which shares a genealogy with these games) allows a force march but doesn’t give any downsides to doing so.

Some games, e.g., Swords and Wizardry, gives terrain modifiers for vehicle speed but not pedestrians.

Filling out the table and searching through all the, often poorly organized, rules made me appreciate modern design and organization exemplified by OSE all the more.

Beyond the Wall and Through Sunken Lands (which are mechanically the same game) don’t have hexcrawl rules at all in the core books, though Through Sunken Lands says to read the supplement Further Afield for hexcrawls. I don’t own this supplement, but from reviews I gather it gives a movement rate of 20 miles / day.

One of the basic differences between modern and old school D&D is whether ability checks are roll high (modern D&D) or roll under (old school D&D). I’m going to bracket various aesthetic issues of which mechanic is more elegant, simple, etc. and only look at the math of how swingy they are and in particular how much does the ability score matter to the roll. Whether swingy is desirable or not is itself a matter of taste or circumstance, but it seems to me that some tasks should be like arm wrestling, where strength matters way more than luck, and others should be more like looking for a lost set of keys, where luck should matter at least as much as wisdom (in the sense of how observant you are).

My hunch is that the ability scores should matter more in the roll under mechanic than the roll high mechanic, but let’s see if I’m right. (Spoiler: I was right). It’s the kind of thing you could do with probability theory but it’s much easier to do via simulation and so that’s how I did it. You could probably do it in anydice, but I ran it in R.

First, let’s review the relevant mechanics.

The 5e version of roll high has the following rules and guidelines.

• Roll equal to or higher than a target number. An easy task is 10, a medium task is 15, and a hard task is 20. There are more gradations, some of which are more difficult than the merely “hard” but we’ll leave it there.
• There is nothing special about a natural 1 or natural 20.
• Apply the relevant ability score modifier. These are very swingy, with mods ranging from -4 to +4 over the ability score range of 3-18.
  • The ability scores themselves are generated by 4d6 keep 3, so on average mods are positive.
  • Players can assign score arrays to abilities. (I will be ignoring this rule).
• Apply proficiency modifiers. (I will be ignoring this rule).
• Savings throws, rogue abilities, etc. are all special cases of ability checks.

The OSE (B/X) version of roll under has the following rules and guidelines.

• Roll equal to or under your ability score.
  • Ability scores are rolled as 3d6.
  • Scores are rolled down the line. (I will be ignoring this rule).
• A natural 1 is an automatic success, a natural 20 is an automatic failure.
• Use difficulty to modify the die. An easy task is -4 and a hard task is +4. Implicitly, a medium task is a straight roll.
• Savings throws, thief abilities, etc. have their own mechanics unrelated to ability scores.

The first step is creating a set of ability scores. I’ll do the OSE rules as written approach of 3d6 first.

n.sims <- 10000
results.3d6 <- vector(length = n.sims)
for (i in 1:n.sims) {
  results.3d6[i] <- sum(sample(seq(1:6),3,replace=TRUE))
}
hist(results.3d6)

As you’d expect, it’s a pretty much perfect bell curve.

Since I want to compare a pretty low to an average to a pretty high ability score to see how much ability score matters, let’s use 10th percentile, median, and 90th percentile.

deciles.3d6 <- quantile(results.3d6,probs = c(.1,.5,.9))
p10.3d6 <- deciles.3d6[1]
p50.3d6 <- deciles.3d6[2]
p90.3d6 <- deciles.3d6[3]
deciles.3d6
## 10% 50% 90% 
##   7  10  14

Now let’s do the same for 4d6, keep 3, which is both rules as written for 5e (and AD&D) as well as a popular house rule for OSE.

results.4d6 <- vector(length = n.sims)
for (i in 1:n.sims) {
  results.4d6[i] <-  sum(sort(sample(seq(1:6),4,replace=TRUE),
  decreasing = TRUE)[1:3])
}
hist(results.4d6)

The 4d6 keep 3 method gives us a left-skewed distribution.

deciles.4d6 <- quantile(results.4d6,probs = c(.1,.5,.9))
p10.4d6 <- deciles.4d6[1]
p50.4d6 <- deciles.4d6[2]
p90.4d6 <- deciles.4d6[3]
deciles.4d6
## 10% 50% 90% 
##   8  12  16

Now let’s create our mods. The range is 3-18 but I’m creating mods for the range 1-18 for ease of value indexing. We only really need the 5e mods as the OSE mods are irrelevant for this mechanic but including them anyway.

scores <- seq(1:18)
mods.ose <- c(NA,NA,
  -3,
  -2,-2,
  -1,-1,-1,
  0,0,0,0,
  1,1,1,
  2,2,
  3)
mods.5e <- c(-5,
  -4,-4,
  -3,-3,
  -2,-2,
  -1,-1,
  0,0,
  1,1,
  2,2,
  3,3,
  4)
mods <- cbind(scores,mods.ose,mods.5e)

Now let’s create a ton of d20 rolls. We’ll do two sets of rolls and store it as straight rolls, rolls with advantage (keep high), and rolls with disadvantage (keep low).

rolls.a <- sample(seq(1:20),size = n.sims,replace=T)
rolls.b <- sample(seq(1:20),size = n.sims,replace=T)
rolls.adv <- pmax(rolls.a,rolls.b)
rolls.dis <- pmin(rolls.a,rolls.b)
rolls <- cbind(rolls.a,rolls.adv,rolls.dis)

OK, now let’s see how often our players succeed on their rolls for every combination of easy roll/medium roll/hard roll and low score/medium score/high score using OSE checks with the OSE 3d6 scores.

matrix.template <- matrix(nrow = n.sims,ncol = 3)
colnames(matrix.template) <- c("p10","p50","p90")
matrix.template <- as.data.frame(matrix.template)

ose.raw <- list(matrix.template, matrix.template, matrix.template)
names(ose.raw) <- c("easy","medium","hard")

for (i in 1:n.sims) {
  ose.raw[["easy"]][i,1] <- ifelse(rolls[i,1]-4<=p10.3d6,1,0)
  ose.raw[["easy"]][i,2] <- ifelse(rolls[i,1]-4<=p50.3d6,1,0)
  ose.raw[["easy"]][i,3] <- ifelse(rolls[i,1]-4<=p90.3d6,1,0)
  for (j in 1:3) {
    ose.raw[["easy"]][i,j] <- ifelse(rolls[i,1]==1,1,ose.raw[["easy"]][i,j])
    ose.raw[["easy"]][i,j] <- ifelse(rolls[i,1]==20,0,ose.raw[["easy"]][i,j])
  }
  ose.raw[["medium"]][i,1] <- ifelse(rolls[i,1]<=p10.3d6,1,0)
  ose.raw[["medium"]][i,2] <- ifelse(rolls[i,1]<=p50.3d6,1,0)
  ose.raw[["medium"]][i,3] <- ifelse(rolls[i,1]<=p90.3d6,1,0)
  for (j in 1:3) {
    ose.raw[["medium"]][i,j] <- ifelse(rolls[i,j]==1,1,ose.raw[["medium"]][i,j])
    ose.raw[["medium"]][i,j] <- ifelse(rolls[i,j]==20,0,ose.raw[["medium"]][i,j])
  }
  ose.raw[["hard"]][i,1] <- ifelse(rolls[i,1]+4<=p10.3d6,1,0)
  ose.raw[["hard"]][i,2] <- ifelse(rolls[i,1]+4<=p50.3d6,1,0)
  ose.raw[["hard"]][i,3] <- ifelse(rolls[i,1]+4<=p90.3d6,1,0)
  for (j in 1:3) {
    ose.raw[["hard"]][i,j] <- ifelse(rolls[i,1]==1,1,ose.raw[["hard"]][i,j])
    ose.raw[["hard"]][i,j] <- ifelse(rolls[i,1]==20,0,ose.raw[["hard"]][i,j])
  }
}

colMeans(ose.raw[["easy"]]
##    p10    p50    p90 
## 0.5578 0.7011 0.9009

colMeans(ose.raw[["medium"]])
##    p10    p50    p90 
## 0.3601 0.4834 0.7155

colMeans(ose.raw[["hard"]])
##    p10    p50    p90 
## 0.1596 0.3121 0.5074

An easy task is one that a character with a low score can complete a bit over half the time and a high score character can complete about 90% of the time. A hard task is one that a character with a low score can complete about 1/6 of the time and a high score character about half the time. That’s both plausible and shows a strong influence from the score.

I’m not going to include the code for using OSE ability checks with a 4d6 house rule, but here are the results.

colMeans(ose.4d6[["easy"]])
##    p10    p50    p90 
## 0.6042 0.7612 0.9970

colMeans(ose.4d6[["medium"]])
##    p10    p50    p90 
## 0.4104 0.5740 0.8091

colMeans(ose.4d6[["hard"]])
##    p10    p50    p90 
## 0.1970 0.3918 0.5973

(Update: there was a glitch in my code that generated ose.4d6[["hard"]]. Thanks to John for catching it. I have since corrected).

Now, let’s do the 5e system with straight rolls (ie, no advantage or disadvantage).

dnd5e.raw <- list()
dnd5e.raw <- list(matrix.template, matrix.template, matrix.template)
names(dnd5e.raw) <- c("easy","medium","hard")

for (i in 1:n.sims) {
  dnd5e.raw[["easy"]][i,1] <- ifelse(rolls[i,1]+mods.5e[p10.4d6]>=10,1,0)
  dnd5e.raw[["easy"]][i,2] <- ifelse(rolls[i,1]+mods.5e[p50.4d6]>=10,1,0)
  dnd5e.raw[["easy"]][i,3] <- ifelse(rolls[i,1]+mods.5e[p90.4d6]>=10,1,0)
  dnd5e.raw[["medium"]][i,1] <- ifelse(rolls[i,1]+mods.5e[p10.4d6]>=15,1,0)
  dnd5e.raw[["medium"]][i,2] <- ifelse(rolls[i,1]+mods.5e[p50.4d6]>=15,1,0)
  dnd5e.raw[["medium"]][i,3] <- ifelse(rolls[i,1]+mods.5e[p90.4d6]>=15,1,0)
  dnd5e.raw[["hard"]][i,1] <- ifelse(rolls[i,1]+mods.5e[p10.4d6]>=20,1,0)
  dnd5e.raw[["hard"]][i,2] <- ifelse(rolls[i,1]+mods.5e[p50.4d6]>=20,1,0)
  dnd5e.raw[["hard"]][i,3] <- ifelse(rolls[i,1]+mods.5e[p90.4d6]>=20,1,0)
}

colMeans(dnd5e.raw[["easy"]])
##    p10    p50    p90 
## 0.4926 0.5896 0.6879
colMeans(dnd5e.raw[["medium"]])
##    p10    p50    p90 
## 0.2501 0.3471 0.4422
colMeans(dnd5e.raw[["hard"]])
##    p10    p50    p90 
## 0.0000 0.0991 0.2004

We can notice two things about the 3e/5e mechanic as compared to the OSE mechanic.

1. In 3e/5e, success is more a function of task difficulty and less a function of ability score with the notable exception that “hard” tasks are not just hard but impossible if you have a low ability score.
2. In 3e/5e, the mechanic is much harsher, not withstanding that RAW 3e/5e ability scores tend to be higher.

There are a few caveats to the second point though. First, OSE has special mechanics for many of the things 3e/5e uses ability checks for, these tend to be based on level, and at low level your character is pretty much useless. For instance, old school thieves are famously useless as thieves (but have a good shot at scaling El Capitan). Second, 3e and 5e are games of stacking buffs. 5e isn’t as bad about this as 3e or Pathfinder, but there’s still the expectation that straight rolls are for suckers. There are other buffs, such as the “guidance” cantrip (add 1d4 to your roll), but the big buff is advantage (roll twice, keep high). And of course sometimes you have disadvantage (roll twice, keep low), with the really important one that everyone fails to apply being that using darkvision gives disadvantage on perception checks.

I’m not gonna give my code for simulating ability checks with advantage and disadvantage as it’s really similar to above except the code for advantage is similar except it has rolls[i,2] in every line. Likewise, disadvantage has rolls[i,3]. Here are the results.

colMeans(dnd5e.adv[["easy"]])
##    p10    p50    p90 
## 0.7486 0.8410 0.9104

colMeans(dnd5e.adv[["medium"]])
##    p10    p50    p90 
## 0.4414 0.5760 0.7001

colMeans(dnd5e.adv[["hard"]])
##    p10    p50    p90 
## 0.0000 0.1899 0.3625

With advantage, the overall difficulty level is similar to OSE checks. Of course with disadvantage it gets even harder.

colMeans(dnd5e.dis[["easy"]])
##    p10    p50    p90 
## 0.2487 0.3539 0.4795

colMeans(dnd5e.dis[["medium"]])
##    p10    p50    p90 
## 0.0630 0.1223 0.1963

colMeans(dnd5e.dis[["hard"]])
##    p10    p50    p90 
## 0.0000 0.0109 0.0423

Anyway, it seems that the old school “roll under” ability check is actually pretty generous aside from the fact that it doesn’t apply to many situations, being used only when there’s not a more specific mechanic. However it’s not too bad for 3e/5e players as they can get similar ease by stacking buffs.