The discussion of Twenty Questions reminded me of a game I learned
from Alan Frank (who I believe also invented it), called "Plenty
Questions". In this game, all queries must take the form "Is it
more like X or Y?" In the warm-up version of the game, that's
the only constraint. But in the real version of the game, there's
a further catch: each question must re-use the better of the two
matches from the previous question. That is, if the answer to
"Is it more like X or Y?" is "X", then the next question must
be of the form "Is it more like X or Z?", whereas if the answer to
"Is it more like X or Y?" is "Y", then the next question must
be of the form "Is it more like Y or Z?".
This game is rather frustrating to play, because one usually spends
lots of time stuck at local optima, obtaining no new information
from one's successive questions. But what's interesting about
the game is that it is in fact playable. I would have expected it
to be unplayable, given how big "thing-space" is. (Though now
that I think about it, I believe that one reason that the game
is playable by humans is that the answerer, bored with always
saying the same thing, sometimes changes his/her criteria in
mid-game so as to be able to move to a new local optimum, and
in the course of going to a new optimum, he/she reveals new
information about the target.)
It'd be Interesting to know more about the "thing-space" of the
game Twenty Questions, and the distribution of people's choices.
Is it governed by by Zipf's Law? What is its entropy?
Jim Propp
