Thursday, November 19, 2009

Precognition -- Card Game

This is a card game for a plural number of players.

First, the cards from a standard deck (no jokers) are dealt face-down to the players, so that each player has the same number of cards.

The players then each examine the hand they have been dealt, keeping their cards secret from the other players. (Of course, if there are two players, you know the cards your opponent has are exactly those cards you don't have.) :)

All that matters in this game as far as the cards are concerned are their numerical values. (Ace = 1, Jack = 11, Queen = 12, King = 13.)

The players each secretly on their own piece of paper write down a series of letters ("U" for up, "D" for down, "S" for stay), corresponding to a predicted outcome. (See below.) The players can write down any number of these letters they each choose -- 1 letter, up to a string of letters of length equal to the number of cards.

Next, the players take turns placing cards face-up, one card per move, making a single row of cards on the table between the players. The cards are placed in the row from the left to the right. (I suggest that each card be placed on top of the card below it, being placed a little to the right so that the value of each card is showing.)

After all cards are placed in the row, the players reveal their lists of letters.

Consider the "changes" between consecutive numbers in the row of cards. Either a number goes up (U) from the previous number in the row, goes down (D), or stays the same (S). Form a list of these changes written in order from left to right.
The winner is the player with the longest string of letters that corresponds to any subset of consecutive changes within the row of cards.

For example, if we have the (short) row of cards:

2,6,5,4,7,9,7,1,2,2,5,8

And a player has "UUDDUSU",
then this corresponds to:
2,6,5,(4,7,9,7,1,2,2,5),8

because 4 to 7 is U (up), 7 to 9 is U, 9 to 7 is D (down), 7 to 1 is D, 1 to 2 is U, 2 to 2 is S (stay), and 2 to 5 is U.

If this is the longest matching string (7 letters) of U's, D's and S's by any player, then this player wins.

(Note: A player can almost always get a match, for example, by having a string of one letter U or D. But then there is a good chance someone else will have a longer matching string.)

If there are a number of players that all tied for first place, then these players play again amongst themselves as many games as necessary, eliminating players each round, so as to determine a final champion.

Thanks,
Leroy Quet

Tuesday, November 3, 2009

Procession

This is a game for any plural number of players.
Needed: piece of paper and a pen/pencil.

Start by writing a row of n 0's on the piece of paper. (n is a positive integer decided beforehand by the players. I suggest an n between 5 and 10 for a 2 person game. Slightly more for more players.)

After writing the row of n 0's, write the value of n to the right of this row.

Next, the players take turns. On a player's move, he/she copies the row (which will be of 0's and 1's) immediately above, but with either one 1 changed to a 0, or one 0 changed to a 1. (The player can change any one digit she/he chooses, under restrictions -- see below.)

Next, that same player writes down (to the right of the row) the lengths of the runs of both 0's and 1's in the row he just wrote down.
Each "run" is made up completely of 0's or completely of 1's, and is bounded by runs of the other digit or by the edge of the row. (No two consecutive runs are of the same digit.)
It doesn't matter if a run is of 0's or 1's. All that matters in this game is where each boundary is between each run of 0's and the adjacent run of 1's.

* A player, though, cannot change a digit on his move such that the multiset of run-lengths (of the row of 0's and 1's just created) has already occurred in the game.
(A "multiset" is a list of numbers where the order of the numbers in the list is unimportant, but the number of occurrences of each number is indeed important. For example, {1,2,1,3) and (2,1,1,3) would be considered to be the same multiset, but (1,2,1,3) and (1,2,3,3) would not be the same.)

The last player able to move is the winner.

Sample game. Simple example:
(n=5)

00000 5
00010 3,1,1
10010 1,2,1,1
10011 1,2,2
(Can't do 10111 here, for example, because the run-length multiset 3,1,1 already occurred.)
00011 3,2
00001 4,1

The player who wrote 00001 wins, because 10001 (run-lengths 1,3,1), 01001 (1,1,2,1), 00101 (2,1,1,1), 00011 (3,2), and 00000 (5) each have a multiset of run-lengths that already occurred.

FYI: The total number of moves in a game is no more than the number of (unrestricted) partitions of n. (So, there is a maximum of 7 moves in an n=5 game.)

Thanks,
Leroy Quet