time, movement, and action economy in dungeon games

let me just give the rundown!

in the original dungeons & dragons (1974), a dungeon turn was not the amount of time it took to perform an action. instead, a turn is the interval of time between wandering monster checks. this means that after each turn, the referee rolls a die for a 1-in-6 chance of a monster appearing. what happens in between these checks is basically up in the air, and the rulebook invites liberal guesstimation. the party is afforded two "moves" (120 feet for an unarmored character) in one turn. there are ten "rounds" of combat per turn. thought-detecting can take just a quarter turn. searching a room takes a full turn. ultimately, the rulebook says, "Time spend searching for anything [...] will be adjudged by the referee as to what portion of a turn will be used by the activity."

edit: if the above paragraph feels like a controversial reading, read the companion piece (link)!

movement rates

the movement rates of dungeon exploration in early d&d games (1974, 1977, 1978, 1981, etc.) have been criticized for being much too slow compared to the actual human movement speed of 3 mph. for example, since an unarmored character in d&d (1974) moves 240 feet per turn (10 minutes), they have a speed of 0.27 mph. characters in the 1981 b/x edition are even slower, because the rulebook only affords the party one move of 120 per turn. since b/x prescribes encounter checks every other turn, a likely explanation is that the authors wanted to redefine a turn as the time to execute an action, while preserving the idea that the party can move twice before an encounter check is made. however, they did not adjust the movement rate or the duration of a turn, resulting in characters moving at half-speed compared to 1974, now 0.14 mph.

there is a more significant difference between the outdoor movement rates of these editions of the game. originally, the party moved 15 miles per day. for an 8-hour walking period, that's 1.86 mph. slightly slow! meanwhile, in b/x, characters could now move 24 miles a day. that's 3 mph exactly, if we assume here again an 8-hour walking period. it seems as though the authors recognized that the original movement rates given were somewhat slow for outdoor exploration (though not inexcusably so), and yet they not have the same opinion wrt dungeon exploration. is there a good reason for this?

people in the hobby aren't stupid! this has been a point of contention for 'outsiders', and the common response is that the movement rate (usually in reference to b/x) makes perfect sense if you consider that the party is moving very slowly, looking out for hazards, and mapping all the way through.

why don't we figure this out by allowing a turn to be one minute instead of ten? if we're using the od&d movement rate, that means that we're walking through the dungeon at 2.7 mph, a little slower than the human average. it also means we're walking 240 feet every minute. my dorm room is about 12 feet long, and i am imagining myself walking across twenty dorm rooms in one minute. given the hazards in a dungeon, that sounds way too fast. even the b/x half-rate (at 1 min/turn rather than 10 min/turn) feels a little too risky for me, having to traverse ten dangerous dorm rooms in one minute.

now, let's go back to the movement rate prescribed by od&d. i'm walking through two dorm rooms in one minute, and i'm being super quiet, watching out for monsters, and drawing a map of what i see. that sounds about right, and even spending a minute in one dorm room (as per b/x) would make sense.

bearing this in mind, it makes perfect sense for b/x to halve (accidentally or intentionally) the movement rates for dungeon exploration while still increasing the original rate for outdoor exploration.

action economy of exploration

something i find admirable about od&d is its insistence that a turn is above all else the interval of time between encounter checks. this means that it rejects the turn as a standard unit of duration for actions, even prescribing that the referee think of actions as taking fractions of a turn. a turn is not an abstraction here!

also interesting is that each character can be useful at any time. at least, before reading od&d, i was under the impression that when a rulebook says that you have a 2-in-6 chance of opening a door, or a 1-in-6 chance of listening through a door, that was it. od&d explicates instead that each participant gets one die. this means that there is a 2-in-6 chance per person of opening a door, or a 1-in-6 chance per person of listening through a door. it reminds me of having read don't give up the ship!, another game published by TSR, where you allocate 'crew factors' of 21 people to accomplish tasks on the ship. each party member in od&d is likewise a crew factor, and the goal is to allocate crew factors to different tasks. who will try to open a door, and who will try to listen through the wall? and so on.

i think then there's an opportunity to rethink how we handle dungeon exploration, if we consider each person to be one useful 'factor', and each factor's productivity/efficacy to be represented by one die. it's at this point where i want to refer to some statistics to describe how we use one-die-per-person to create more interest in dungeon checks, instead of modifying one die based on a number of participants.

opening a stuck door has a 1-in-3 chance of success per person. why not increase the chance by some amount, say 1/3 per person, instead of letting each person as factor roll independently? of course, it makes it so that three people automatically succeed at the task [2], but that's not the interesting thing. allowing one roll per factor allows the difficulty of a task to scale down per factor without eliminating the chance of failure, has diminishing returns per additional factor of effort (i.e. per person), and also acts a visual indicator of effort spent on the task.

one person has a 33% chance of success to open a stuck door. two persons have a 56% chance. three persons have a 70% chance. the percent improvement between the numbers of factors allocated decreases (from +26% to +14%), meaning that this technique has diminishing returns of increasing effort. only three people maximum are allowed to try at once by the book, but with four people there's a 80% chance of success. if you could allow four people at a door, would you rather have that 10% extra likelihood of success, or would you rather have that fourth person look out for monsters (e.g.) while the others push the door?

this is not an action economy insofar as it is an exchange of tokens, but insofar as it is a distribution and organization of effort (labor) during some amount of time. i like what sid meier said about games, that they're only fun and/or interesting insofar as they offer interesting decisions. by emphasizing the role of a player-character as a factor of the party, as something whose efficacy can be allocated to one task or another at a time, we expand the set of possible decisions that could be made. it also encourages cooperation between players to not just decide on one action for the turn, but to decide on how their characters take different tasks (who does what?). and maybe that's something that everyone else has been doing and i'm just bad at reading these rulebooks LMAO

possible actions

let's just make this into more of a 'game', letting each factor (player-characters et al.) represent one die that can be allocated to a task. the die deals with the likelihood or degree of success. when characters are not moving around or holding torches, here are some tasks to which they as factors can be allocated:

• open stuck door (max factors: 3/door, efficacy/factor: 2-in-6)
• search area (max factors: 3/10x10' of area, efficacy/factor: 2-in-6)
• listen behind wall (max factors: 3/10' of wall, efficacy/factor: 1-in-6)
• watch for monsters & prevent surprise (max factors: inf, efficacy/factor 3-in-6). this one is not original to od&d but i think it helps show possibilities for expanding the set of interactions
• hold torch (max factors: inf, efficacy/factor 5-in-6). the die is rolled here simply to ensure that the torch doesn’t go out, and so wielding a torch becomes an “active” task. the important effect is that anyone holding a torch cannot spend their die elsewhere that turn.

percent likelihoods of success for 1-in-6 tasks as a function of # factors (1-6) [3]:

1. 17%
2. 31% (+14%)
3. 42% (+11%)
4. 52% (+10%)
5. 60% (+8%)
6. 67% (+7%)

percent likelihoods of success for 2-in-6 (1-in-3) tasks as a function of # factors (1-6):

1. 33%
2. 56% (+23%)
3. 70% (+14%)
4. 80% (+10%)
5. 87% (+7%)
6. 91% (+4%)

percent likelihoods of success for 3-in-6 (1-in-2) tasks as a function of # factors (1-6):

1. 50%
2. 75% (+25%)
3. 88% (+13%)
4. 94% (+6%)
5. 97% (+3%)
6. 98% (+1%)

thoughts on early dungeon play

seeing how these probabilities scaled (e.g. you can have three people search for a door at once) makes me question whether early dungeon play was so dependent on avoiding the dice. adherents of old school play often claim that early players realized that the odds were stacked against them, and that it was better to narrate one's exploration in-depth (remove room for error) than to let dice take the wheel. this is not to disparage that style of play because i myself find it more engaging than letting every action be abstracted by a roll of the dice, but i can't say whether it's true that this is how all early players actually played.

i can see also how the role of the caller becomes important not just when there’s a bazillion players at once and there needs to be additional organization to handle the game, but when part of the game is the allocation of party members to different tasks. the job of the caller becomes to submit to the referee a finalized plan of action (“three of us will push the door, the rest of us will watch out to avoid surprise”).

[1] the rulebook asks players to use avalon hill's outdoor survival board game as the playing board for outdoor exploration, and it uses hexagons.

[2] unless you introduce some convoluted rule like lamentations of the fire princess had for individuals who have 6 out of 6 skill points in a task, which would otherwise make x-in-6 rolls useless.

[3] factors 1-3 are bolded since this seems to be the usual maximum of factors that can be allocated to a task. the reason for this is usually the width of the hallway or door.