Original Card Games by David Parlett
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Players 2 (or 3)   Cards 52 (±Joker)   Type Win pairs of matching cards
I was going to call it Sock Drawer, as the layout resembles a drawer from which you keep pulling matching pairs. But who wants to play a game called Sock Drawer? Boring! So I corrupted it to Sockjaw to make it sound more punchy.
Cards and deal
From a 52- or 53-card pack deal 25 cards face up in a 5x5 rectangle. Each player in turn removes from the layout two cards in accordance with the pairing rules below.
The aim is to take as nearly equal a number as possible of each of the three types of pair. Place each pair in one of three piles in front of you, one for each type.
Sockjaw layout
From this layout you can take ♥K and ♠J, or ♣7 and ♠7;
♠3 and ♠6 or ♠7; ♥10 and ♠A; and several other pairs
Pairing rules
You can take -

1. Two cards of the same rank lying in the same row or column, eg two Aces, two Fives, or whatever. For this purpose all face cards (J-Q-K) and the optional Joker are considered identical - you can count any two as being of the same rank.

2. Two cards of the same suit lying in the same diagonal line (the Joker belongs to no suit), or

3. Two adjacent cards (horizontally, vertically or diagonally) totalling 11. For this purpose numerals count at face value from Ace = 1 to Ten = 10. Face cards (J-Q-K-Joker) count 5½ each, so any two next to each other sum to 11. Regardless of whether they are horizontally or diagonally adjacent they go in your Elevens pile, not your rank or suit pile.

After taking two cards fill the spaces they leave with cards from the remainder of the pack dealt face down to help you keep track of rows, columns and diagonals.

When no more cards can be legally taken, turn the down cards face up and continue as before. When no more replacements remain to fill spaces, keep going till no remaining cards can be legally paired.
Ending and winning
Finally, then count the number of pairs you have taken of each type and multiply them all together. Whoever gets the highest total wins, and scores the difference between both players' totals. If tied, whoever took the most face cards adds 10. If still equal, this bonus goes to whoever took the last pair. Note: If you have taken none of a type of pair (rank, suit or eleven) your total score will be zero.
The highest possible total is 80 (4x4x5), or 90 with the tie-break bonus.