My prompt suggested rolling a d6 for each shot and jamming on a 1; OR, if that is too often, on the second 1 in a cylinder of 5.
GROK likes the two 1's requirement and ran the probabilities for me:
A solid, historically grounded rule for your Paterson 5-shot revolvers would be to roll a d6 for each shot fired, but treat a malfunction (full jam, no further shots possible until the ranger spends an action to clear/fix it) as occurring only on the second "1" rolled in that cylinder.
This gives you a clean, easy-to-track mechanic that feels "prone to malfunction" without making the gun a paperweight in the fights where the Texas Rangers actually used it to win. Here's why it fits reality and your tabletop needs:
Historical flavor: Contemporary and modern sources describe the Paterson as fragile, with close tolerances, delicate small parts, and a notorious tendency for spent percussion caps to fall into the open-frame action and jam the cylinder or lockwork. The U.S. government called them "excessively fragile and prone to malfunction." Black-powder fouling and the lack of modern timing/bolt strength made binding or lock-up a real risk after a few shots. Yet Rangers (Hays' men at Walker's Creek, Bandera Pass, etc.) carried pairs of them + spare cylinders and won fights precisely because of the five rapid shots versus single-shot pistols.
Malfunctions happened often enough to be a documented drawback (and one reason the Walker Colt was developed), but not so constantly that the guns were useless in combat.
Probability that matches "common but not crippling":
You fire up to 5 shots per loaded cylinder. Number of "1"s follows a binomial distribution (n=5, p=1/6).
Chance of 0 or 1 "1" (cylinder fires cleanly or has only a harmless single cap-drop that doesn't jam yet) ≈ 80.4 %.
Chance of 2 or more "1"s (malfunction triggers) ≈ 19.6 %.
So roughly one cylinder in five will jam somewhere during the five shots. In a typical short skirmish where a ranger might burn one or two cylinders, you'll see the occasional dramatic "click… jam!" moment that forces an action to fix—exactly the "problems were common enough to be mentioned" vibe—without the gun failing more often than it succeeds. Your original "1 on d6 = immediate jam" is ~16.7 % per shot, which compounds to ~60 % chance of at least one jam per full cylinder—too punishing for guns that gave the Rangers a decisive edge.
How to run it at the table (simple tracking):
Ranger declares shots.
For each shot: roll to hit / damage as normal and roll a d6 "reliability" die.
Keep a running count of "1"s on the reliability dice for the current cylinder only.
The second time a 1 appears, the shot either (a) fails to fire or (b) fires but the gun immediately jams—your choice for flavor. No more shots until the ranger spends a full action (or whatever your rules define as "fixing the problem"—clearing a cap, reseating the cylinder, etc.).
After the cylinder is empty or jammed, it's reloaded normally (historically a slow partial-disassembly job, which you can already represent with action cost or out-of-combat time).
Optional tweaks for your campaign's tone (pick one if the base rule feels off after playtesting):
Slightly more reliable (for heroic Ranger play): Use d8 instead of d6 → malfunction only on the second "1." Drops jam chance per cylinder to ~9 %.
Slightly harsher / more historical fouling feel: The first "1" does nothing; the second triggers the jam and you add +1 to all future reliability rolls in that cylinder (simulates powder residue building up).
Even simpler one-roll version: Before the cylinder is fired, roll one d6. On a 1 the whole cylinder will have a malfunction on a randomly determined shot (roll 1d5 when it happens). On 2–6 it runs clean. Gives ~17 % jam chance per cylinder with zero tracking.
Misfire vs. hard jam distinction (if you want more nuance): On the first "1" treat it as a misfire (hammer falls, no bang, but gun still works—recock and try again). Only the second "1" = hard jam requiring the action to fix.
Any of these keeps the Paterson feeling like the groundbreaking but temperamental weapon it was—powerful enough to turn the tide against Comanche lances, but with that early-1840s Colt "clockwork that sometimes breaks" personality. Playtest a couple of fights and you'll see it adds tension without frustrating players. If your rules have other black-powder quirks (fouling over multiple cylinders, chain-fire risk, etc.) this slots in cleanly. Let me know how the playtests go or if you want probability tables for different dice!