Something indie tabletop RPG authors have got to accept is that random dice tables of Weird Shit cannot be brief. A haunted doll that looks like the party leader's mother as a child is creepy in isolation, but when it comes up four times in one session because the table it's on only has like twelve entries it's a running gag.
As a very general rule, a table of Oddly Specific Shit that's expected to be used more than once per session needs at least 20 entries total per roll beyond the first. There's a reason the d100 table is popular beyond pleasing symmetry; it's just the right size to be rolled on half a dozen times per session without constantly kicking out incongruous duplicates.
Here's a table of the number of table entries required to reach a given probability of no repeats after a certain number of rolls. E.g. if you're going to be rolling on a table five times, a table with 17 entries will give slightly better than even odds (52.3%) of not yielding a repeated entry, while a table with 16 entries will not (47.0%). Rolling a half-dozen times on a table with 100 entries will give slightly better than an 85% chance of no repeats. Rolling twice more, and the probability drops to 75%.
The "20 entries per extra roll" rule of thumb undersells the size of table needed past half a dozen rolls or so: for a dozen rolls, you'd need a table with over 400 entries for the same 85% probability of avoiding a repeat. (The number of entries needed seems to grow superquadratically, but empirically the exponent is something like 2.0025: e.g. for an 85% chance, the number of entries approaches 3.024 * rolls²·⁰⁰²⁵ as rolls increases > 150.)
The flip side, though, is that as the number of rolls increases, the acceptability of a single repeat does as well. Using the rule-of-thumb, a 220 entry table still gives a 70+% chance of no repeats after a dozen rolls, and maybe that's fine.
Yeah, the "twenty entries per roll beyond the first" guideline doesn't really scale if the expected number of rolls on the same Oddly Specific Shit table in a single session exceeds ten. You're quite right that it's often less of a concern at that scale, though; a small number of duplicate results among a large number of rolls is potentially interesting, but a large number of duplicates among a small number of rolls is rarely anything other than comical – see @healthylevelsofmagicthegathering's anecdote in the tags about playing a Lord of the Rings inspired game with a twelve-entry random encounter table and bumping into Gandalf three separate times in the course of the same journey!
#Shadowdark's carousing tables have this problem#we met a friendly bard again? (via @howieduet)
Carousing tables are definitely a frequent offender in terms of including entries that are too oddly specific for the number of potential outcomes. I recall one OSR game where, if you use the carousing rules exactly as written, every time you go out drinking you have a one in ten chance of waking up the next morning with a severed human hand wearing a golden signet ring in your inventory and no memory of how you got it – which is a fantastic adventure hook the first time it comes up, but raises several pressing questions by the third or fourth.
#if multiple player characters went out drinking together they each rolled separately #so there was a small but non-zero chance of a single night of carousing yielding multiple hands
I can think of two separate ways to address this.
One is to cross off items as they come up. If you've already rolled Gross Signet Ring Hand once, either jump down to the next item in line (which may still be too deterministic) or roll again (which can take too many rerolls if the number of eliminated items is too high).
The other is to have a deck of items. Shuffling randomizes the sequence, and moving discards to the bottom of the deck or to a separate pile eliminates repetition. The downside is the preparation involved.
(I've just thought of a third option. Pre-print a shuffled list of random numbers, and use them in order. It works like shuffled cards but you don't need to do so much Arts and Crafts.)
Yeah, a deck of random encounters would work especially well. No repeats until you shuffle the deck again, but also you can easily control what cards are in the deck, so you can weight in favor of certain sorts of encounters or account for the terrain the party is in or level they're at. (Personally, I think random encounters that are inappropriate for the level are fine though - sometimes discretion is the better part of valor, and sometimes it gives an opportunity to engage with an intelligent 'monster' that no longer presents a threat and possibly reassess how 'monstrous' they really are.)
"You are in the middle of a wide, flat plain. The grass is brown and dry. You encounter [pulls card from deck] a sea serpent." Now instead of a naval battle it's a rescue mission to find or summon enough water to keep this creature alive.
