Quantum Fingers (idea)

This is a game for 3 or more players, after the style of such well-loved card games as Go Fish and Happy Families but with one crucial distinction: there are no cards. Instead each player holds up fingers throughout the game to show how many cards it would have in its hand, were any cards in use.

The face value of each card remains indeterminate so long as gameplay is not affected by what it is: as soon as the state of the underlying "classical" game (i.e. the ordinary card game on which the "quantum" game is based) depends on whether a player has a particular card, that player chooses at that point whether or not it holds that card.

All such choices must be made so as to be consistent with previous decisions, that is, there must be some possible initial deal of the classical game which would have resulted in the player in question holding, or not holding, the card at that point in the game. Thus for example, if I begin the game by asking you whether you have any juniper berry, you may legally say either yes or no: but if you say no, you can't then on your next turn ask me for juniper berry (because you're only allowed to ask for flavours you already hold at least one of, and having decided you have none of this flavour you must stick to it.)

Since the quantum game (unlike the classical one) is a deterministic game of total information, the above local consistency rule implies global consistency. In other words, the game won't get into an impossible state unless someone has demonstrably committed a logic error.

Rules for Quantum Fingers

1. Rules for Classical Fingers

   1. For n players, the deck to be used consists of 4n cards (fingers), four of each of n different flavours. All the fingers are dealt out, so each player begins with four.
   2. Each player, on its turn, chooses a flavour of which it already has at least one finger and asks of a selected other player whether it possesses any finger of that flavour. If it does, it must surrender to the asker one finger of that flavour: it need not disclose whether it has any more of that flavour. The asker gets another turn, and may ask either the same player or another for either the same flavour or another.
   3. The asker may continue until the player asked has no finger of the specified flavour. The turn then passes to the left.
   4. A player who has all four cards of a particular flavour must immediately declare a "book" in that flavour and remove the four cards from its hand.
   5. You win if you have no cards left and it is your turn. Hence, in the case where one player completes a winning book by taking all the cards from one or more other players, the asker (the one completing the books) is deemed to be the winner even though another player may have run out of cards earlier in the turn.

2. Quantising it

   1. At the start of the game each player holds up four fingers.
   2. On each turn, players make decisions and inferences about the content of their hand in order to determine legal play. In order to minimise unnecessary confusion, players hold up fingers throughout the game to show how many, well, fingers are in their, um, hand. Forgetting to update your hand when you give or receive a finger is a prime source of confusion for newbies.
   3. The names of the flavours are not determined until they are referenced; they are chosen by the first player to ask for them. Anything is allowed subject to the social conventions of the group you play with.
   4. Players are not permitted to start with four fingers of the same flavour, because that would be silly.

Example game

Here is how a game might go between three players, in order of play A, B and C. (The game quickly becomes more complicated with more players. It might also be interesting to vary the parameter 4, the number of fingers of each flavour.)

A: C, do you have any éclairs?

C: No. (So A and B have all four éclairs between them.)

B: A, do you have any éclairs?

A: Yes. (forced reply, because otherwise B would have begun with all four éclairs which is disallowed)

B: Now I have a book of éclairs. C, do you have any bauxite? (B has only one finger, and now we know it is bauxite.)

C: Yes. (this is forced too, because otherwise C would have begun with all four of whatever flavour hasn't been mentioned yet)

B: C, do you have any bauxite?

C: No. A, do you have any chimpanzees? (We know the full deal now. B has two bauxites, A has two bauxites and a chimpanzee, and C has three chimpanzees. As soon as the deal is known, the player whose turn it is can win.)

A: Yes. (forced)

C: I have a book of chimpanzees, and I win.