There are many variations of King's Corners. The object of this particular implementation is to fill the edge of the table with face cards, according to the cell labels: the jacks taking the sides, the queens at the top and bottom, and the kings in the corners.
The game starts with an empty table and a standard 52-card deck. The player draws a card from the shuffled deck and must lay the card on one of the cells of a 4x4 matrix. If the card is a face card, it must be placed on an appropriately-labeled cell along the edge. Regular cards can be placed anywhere, even on a labeled cell. If a face card cannot be placed (because each of the 4 possible cells already has a card), the game is lost. Otherwise, the player will continue placing cards until all 16 cells of the matrix are filled.
Once the matrix is full, the player has a chance to remove and discard regular cards from the table by matching them in groups with values that add up to 10. Each number card is valued the same as its number, and aces are valued as 1. Therefore, possible matches include an ace with a nine, two fives, or even a group larger than a pair, such as 2 twos and a six or 3 twos and a four, etc. Tens can be matched trivially.
After the player has matched and discarded at least one group of cards so that the matrix has empty cells, the player can revert to drawing unused cards and placing them on the table in exactly the same fashion as before. However, if the matrix is full and none of the regular cards can be matched, the game is lost. It is also not possible for the player to start matching cards until the matrix is full.
At the moment that all of the face cards have been placed on their appropriate cells, the player has won the game!
Since you don't want to get "caught" in a position where you are unable to place a card, it can be wise to fit as many regular cards in the unlabeled cells as possible before putting any cards on the labeled cells. Yet, there may be other strategic reasons to ignore this rule-of-thumb. For example, you may want to try to put easily-matched cards on some of the labeled cells.
Notice how every regular card in the deck can be paired with another card to form a match. If you always match pairs, you are discarding both high and low value cards evenly. However, if you match groups of 3 or more, you are eliminating low cards faster than you are eliminating high cards. That will make it more difficult to match high cards later on and will spell trouble if you have eights or nines on a labeled cell.
Source code © 2011 Charles McGarvey, released under the 2-Clause BSD License.
Playing card images modified from the classic cards pack at jfitz.com.
Download the code and resource files in a nice little package for your enjoyment.