Palindromic Card Game

This is a card game for 2 players. (Although this game doesn't technically require cards, using them makes the game easier to play.)

Start with 2n cards, n red and n black cards. (You can play with a standard deck {no jokers}, letting n be 26, and all spades and clubs are black, all hearts and diamonds are red. All that matters in this game is the colors of the cards' suits.)

Deal n cards to each of the players.

Players arrange their n cards in any order in a row, face up.
(One row of cards per player.)

After the cards are arranged, each player then tries to find as many distinct palindromes (symmetric patterns of of redness and blackness) within their opponent's row of cards, where each palindrome starts and ends with a red card. By DISTINCT palindrome I mean that each particular arrangement of reds and blacks counts only once. (Also, different distinct palindromes may share some of the same cards. And a palindrome may consist of exactly one red card.)


For example, if we have an n of 12 and we have the following row:

R B B R R B B B R B B R

Then the palindrome (R B B R) would be counted once, even though it occurs twice in the row.
(The palindrome (BBRBB) would not count at all because it starts and ends with black cards.)

A player gets this many points:

(number of red cards in the player's row) - (number of DISTINCT palindromes found by the player's opponent in the player's row).

(This score will always be 0 or higher.)

Highest score wins.


Thanks,
Leroy Quet

PS: See the post (to my blog "Amorphous Trapezoid") about games-related poetry at:
http://prism-of-spirals.blogspot.com/2008/12/blog-post_21.html