1 2 (3) Infinity
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"What I tell you three times is true."

—- The Hunting of the Snark by Lewis Carroll

Basic Information

The human mind is wired to find patterns. One of the ways this manifests can be summed up as "1 2 (3) Infinity", aka "Incidence, Coincidence, Precedence".

  1. If something happens once, it's a fluke.
  2. If it happens a second time, it starts getting our attention. It may make us suspicious.
  3. If it happens a third time, we automatically assume it will continue to happen again and again. Three takes up the same mental space as infinity.

That's a broad generalization, but it's been shown to be true in three different scientific experiments, so I'm forced to conclude it will always remain true in all circumstances. :)

The military version is "Once is happenstance. Twice is coincidence. Three times is enemy action."

See also:

"Once, you're smart. Twice, you're cute. Three times, you get a sock in the teeth."

—Old Yiddish Proverb


2. Wikipedia on Guess 2/3 of the average - a puzzle in game theory that formed part of the experiment in the technical paper above
3. Delta's D&D Hotspot - gaming blog
4. Transitive Property of Gaming - this arcanist's gaming blog

Game and Story Use

  • You will be tempted 3 times. Challenges or tests often have 3 parts. If you resist the temptation all three times, the god or Princess assumes you'll remain trustworthy forever.
  • Anything the fae tell you three times will be true … the trick is being sure that they said the same thing all three times.
  • Calling the name of an entity three times is often an entry level form of invocation.
  • If you want something to feel magical or special, only have it happen once or twice.
    • A power you can use every round isn't special, it's mundane. As it turns out, a power you can use three times per session starts to feel the same way.
    • Two encounters with orcs can be interesting and distinct - but a third such encounter will seem boring. A lot of older adventure modules run afoul of this. Make sure you change something significant so no three encounters seem similar.
  • If you want something to feel unavoidable, or even just commonplace, have it happen 3 times in a session.
    • You don't have to bother past the third, most everyone will assume it's just keeps on going.
  • Resources characters can expend should perhaps be structured along those lines. Either I get it once, twice, or as often as I like. Not only does it make the special things feel more special, it also saves book-keeping.
    • This argues for not tracking ammunition on guns or bows, but at the same time putting very strict limits on magic (even magical healing).
  • This notion is especially useful in relation to clues and mysteries.
    • If the players overlook a clue, drop it again a little later, and then again sometime after that. On the third repetition, they'll identify it and assume it's important.
    • If something happens once or twice, it might be a red-herring.
    • Actual red-herrings should never happen 3 or more times, or the players will fixate on them and assume they're a clue.
  • And of course, this is an important part of humor and comedy. Running gags in movies tend to follow the pattern "Once, Twice, wait a while, then Thrice with a variation." You not only get the extra joke of the variation, but the way your mind suddenly lurches to infinity from two makes it more potent. "I should have seen that coming," is what you think, but you didn't because there wasn't a third instance before this, and the first two were an hour ago. If it happens a fourth time it won't be nearly as funny. See Rule of Three for more information.
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