I learned about an amusing game recently which I haven't seen described
very much, called "Quantum Fingers". This game is much like "Go Fish",
with the crucial twist that the hands dealt are determined only by the
statements made by players as the game proceeds.
The game is played with N players, N >= 3. Each player starts with 4
fingers, held up for all to see. The fingers belong to suits; there
are N suits, and each suit has 4 fingers. Each player A, in turn,
asks a question of the form: "<Player B>, do you have any <suit S>?".
If B answers "yes", then B gives A one finger of the suit S, and A
gets another question. If B answers "no", then A's turn ends and the
next player gets a turn. In addition, during A's turn, A can put down
4 fingers of a suit.
There are two ways the game can end. If one player gets rid of all
her cards, she wins. On the other hand, if a player creates a logical
contradiction (either in response to a question or when laying cards
down), then that player loses. To avoid trivial wins, there is one
initial condition: no player starts with all 4 fingers of the same
suit.
Here's a sample game, between Alice, Bob, and Carol.
Alice: Carol, do you have any primes?
Carol: Yes, I do. Here, have one.
[Carol gives Alice one prime finger. Now Carol has 3 fingers and
Alice has 5.]
Alice: Bob, do you have any primes?
Bob: No, I do not.
Alice: Aw, shucks.
[Alice's turn ends.]
Bob: Alice, do you have any primes?
Alice: Yes, I do. Here, have one.
[Alice gives Bob one prime finger, perhaps the finger she got from
Carol.]
Bob: Alice, do you have any primes?
Alice: No, I'm all out.
[At this point, Alice loses. The four primes originally in the game
were distributed between Alice, Bob, and Carol. Bob did not have
any, so Alice and Carol had all the primes. Carol could not have
had them all (by the initial condition), so Alice must have had at
least one initially, and could not answer "no" at this point.]
There are a couple of questions I have about this game:
1) If you actually try playing this game, it seems to get very
confusing. One might ask: Given the number of players and a sequence
of moves, is it NP complete (in the length of the sequence) whether
the moves are consistent?
2) What can you say about good strategies? Two colluding players
can usually force a win among themselves (the first player to get a
move asks the other for cards to complete two sets). But there does
seem to be some intuitive notion of "good play"; often this consists
of not letting anyone else win immediately and waiting for someone to
make a mistake.
One hint about teaching others: when two people already know the game,
it helps to just start the game and start asking questions, explaining
as you go.
Enjoy,
Dylan Thurston and Chung-chieh Shan
