Cumulative Chance

If you want to see a hilarious list of bad things that happen to a D&D character, look through the 1e DMG for the word “cumulative”. Gary invented the peculiar mechanic, which as far as I know wasn’t widely imitated in other editions and games, of the “cumulative chance”. If something had a 1% cumulative chance of happening, there was a 1% chance the first time, 2% the second, 3% the third, etc. The cumulative chance was invariably used for calculating the odds of something terrible happening to a PC.

It seems logical to have a bad event become more likely the more times you do something stupid, but “cumulative chance” is strange because normal chance is already cumulative. If there’s a regular old 1% chance of a bad outcome of an action, and you do it 50 times, your odds of triggering the outcome are reasonably close to 50%. (Actually 40%.) If you have a 10% chance of the event, it takes between 5 and 6 times to bring you to 50%.

Cumulative chances accelerate the process in a startling way. A cumulative 1% chance has a 50% chance of having triggered after only 11 uses; a cumulative 10% chance after 3 uses. Cumulative chances give you a pretty good chance to survive a handful of repetitions of a dangerous activity: then, WHAM! Brutal punishment is almost inevitable. Of course, all this is tracked secretly by the referee: the PC’s only clue is the fact that the DM makes a note and maybe gets a pokerface every time he uses the Horn of Blasting. Typical arbitrary cruelty that makes old-school gaming so hilarious.

For your enjoyment, here are some of the appearances of the cumulative chance mechanic from the 1e DMG:

-There always exists a chance of discovery, no matter how simple the mission. The base chance to be discovered is a cumulative 1% per day of time spent spying, subject to a maximum of 10%, minus the level of the spy. Even if the latter brings chance of discovery to a negative percentage, there is always a 1% chance.
[This one is peculiar: seems like a lot of calculation for something that is happening offscreen, and a good argument to hire a level-9 spy. And never shell out extra for a level-10 spy.]

-If continually provoked and irritated in order to get a response, there is a 1% cumulative chance per round that the insane individual will react with homicidal mania.

-Clerics and druids making an item which is applicable to their profession must spend a fortnight in retreat, meditating in complete isolation. Thereafter, he or she must spend a sennight fasting. Finally, he or she must pray over and purify the item to become magical (this process takes but a day). Of course, the item must be of the finest quality just as detailed in the enchant an item spell description. Thereafter the cleric or druid must place the item upon his or her altar and invoke the direct favor of his or her deity to instill a special power into the item. There is a 1% per day cumulative chance that the item will then be empowered as desired, providing the cleric or druid has been absolutely exemplary in his or her faith and alignment requirements.
[The only good outcome of a cumulative chance that I found. It’s also notable because this passage includes not only the word “fortnight” but “sennight”. I guess it’s because it’s describing a ritual, so the rules should sound appropriately sonorous; the word “week” is used frequently elsewhere.]

-The longevity potion reduces the character’s game age by from 1-12 years when it is imbibed, but each time one is drunk there is a 1% cumulative chance that it will have the effect of reversing all age removal from previously consumed longevity potions.

-Starting with the second round of continuous use, there is a 2% cumulative chance per round that the wand will temporarily malfunction.

-It will act as a bag of holding (normal capacity), but each turn it has a 5% cumulative chance of “swallowing” the contents and then “spitting the stuff out” in some nonspace.
[This description of the Bag of Devouring is one of the rare instances where the “cumulative chance” actually REDUCES the work of the referee. Realistically, D&D people stuff things in bags and don’t think about them again for days. If someone leaves something in a Bag of Devouring for 20 turns (3+ hours), it is 100% gone; no need to roll the dice. On the other hand, with a straight 5% chance per turn, a conscientious DM would have to roll the percentile dice for each elapsed turn until a 01 to 05 came up.]

-If a horn of blasting is winded magically more than once per day there is a 10% cumulative chance that it will explode itself and inflict 5-50 hit points of damage upon the person sounding it. There are no charges upon a horn, but the device is subject to stresses as noted above, and each time it is used to magical effect there is a 2% cumulative chance of the instrument shivering itself.

-Any person reading its 99 damned pages is 99% certain to meet a terrible fate (1% cumulative chance per page).
[This actually seems in error: someone reading a book with 1% cumulative chance per page of damnation would be 99% certain to meet a terrible fate after only 28 pages.  The 1e PHB is around 100 pages long; if it were the book in question, as many 80s moms believed, that would only bring us up to the Assassin class description. If it were the Monster Manual, we’d still be in the Dinosaurs. In his glee at finding another way to permanently destroy characters, Gygax must have put in “cumulative” out of force of habit.]

-Body rot is 10% cumulative likely whenever a primary power is used, and part of the body is lost permanently.

-Item is a prison for a powerful being; and there is a 1%-4% cumulative chance per usage that it will break free, kill the possessor’s soul, and, using his or her body, proceed to slay all associates and henchmen of this character.
[The math is weird because there is a huge probability difference between 1% cumulative chance and 4% cumulative chance. Well, not huge. It’s the difference between TPK and total campaign end after ~= 5 uses or ~= 11 uses.]

-Each time it is used in melee in anger against a foe, there is a 5% (1 in 20) cumulative chance that it will function against its wielder, and once so functioning it cannot be loosed without a remove curse spell.
[Must DMs would be content to wait until the player rolled a 1 before unleashing a curse, but not Gary – he was impatient.]


2 Responses to “Cumulative Chance”

  1. qa says:

    are you missing some headers here?

  2. baf says:

    This all reminds me a lot of the Sanity mechanic in Call of Cthulhu. It’s not quite the same there, but the basic idea is that when you have an encounter with something horrible, you roll against your sanity skill to see if your sanity skill goes down. (If it’s sufficiently horrible, you lose sanity regardless; the roll just determines how much.) The effect, I think, is much the same as a cumulative chance: the more risks you take, the worse it is to take further risks.

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