guess: there is a pair of identical letters separated by at least two more letters such that the separating letters and one of the identical letters are all unique
I think I understand now. So, there's two rules: one that declares valid koans and one that declares special ones. We take turns saying "master" followed by a valid koan to determine whether it has the special property, or "mondo" and a valid koan to have everyone guess whether it has the special property. Whoever guesses correctly gets a guessing stone, which allows a player to guess the special property at any time. The master must provide a counter example in order to continue the game.
A valid koran is one that satisfies the regex /\d+(\.\w+|\[\.\d+\])/ (one or more digits, followed by either a dot and alphanumeric (including underscore) characters or a decimal without a number before the dot surrounded by brackets). Examples: 623.BaNaNaa63, 7[.6070]
Human name that is not ridiculously uncommon: a name that is actually given to humans, whether in reality or fiction, that isn't something that sounds riddiculous.