Lines and proximity
A line is a triple of cards, whose faces are all the same or all different, and whose numbers are all the same or all different, and whose suits are all the same or all different. Any set of ten cards will contain at least one line.
Given any pair of cards, there is a single other card that forms a line with them, their pivot. In each dimension, the pivot is the same as the other two cards if they are the same, or the third option if the other two cards differ. For instance the pivot of Q1P and J3P is K2P.
Two cards are askew of they differ in all dimensions; they are diagonal if they differ in two dimensions; and they are adjacent if they differ in one dimension. For any given card, it is askew to 8 other cards, diagonal to 12, and adjacent to 6.
A line is skew if its cards are all askew to each other. For instance the line J2R, Q3S, K1P is skew.
A line is tilted if its cards are all diagonal to each other. For instance the line K1S, Q2S, J3S is tilted.
A line is flat if its cards are all adjacent to each other. For instance the line K2R, K2S, K2P is flat.
A flat line is alphabetical is its cards are in alphabetical order. For instance the line Q1P=M, Q2P=N, Q3P=O is alphabetical.
There are 36 skew lines, 54 tilted lines, and 27 flat lines, 9 of them alphabetical. You can rank lines by proximity this way:
Tilted < Skew < Flat < Alphabetical
Two lines of the same type can be ranked alphabetically by their alphabetically-last cards.
Line and Proximity Games
Deal 9 cards face up, then give one card each to 2 players. The first to find a line gets to keep it. Replace cards. Continue until only 9 cards remain, then count lines won.
Deal 6 cards each to 2 players. Players draw and discard cards until they have lines. Rank lines by proximity. Repeat twice. Count lines won.
Play Line Finding; you win if you sort the entire deck into lines.
Deal 7 cards each to two players. Lay out a card from the deck. Starting with the dealer, each player must then cover the last card played with a card that is diagonal to it. Cover with once-alike.
Draw from the deck if necessary and if the deck runs out, then shuffle and use the discard pile. The first player to run out of cards wins.
Ends Askew is like Tilt, but you must cover with a card that is askew or has letters A or θ. Cover with unalike or alphabet-end.
Alphabet Askew is like Tilt, but you must cover with a card that is askew or alphabetically adjacent. Cover with unalike or nearest letter.
Vowels Adjacent is like Tilt, but you must cover with a card that is adjacent or bears a vowel. Cover with twice-alike or a vowel.