Original Card Games by David Parlett
Players 2   Cards 52   Type Arithmetical
One of my earliest games, this only failed to appear in the first edition of Original Card Games because I felt it to be rather shallow, and in any case I don't much care for games where you have to keep writing scores down as you go along. (But you could use a Cribbage board, counting each hole as 5 instead of 1.) I've since discovered it to be more interesting than I thought, especially in deciding when best to play your face cards (King, Queen, Jack) and when to withhold them.
Cards
Deal 13 cards each from a 52-card pack and stack the rest face down.
Object
Primarily, to play cards to a sequence in such a way as to keep bringing the running pip-value to a multiple of five. Secondarily, to manage your face cards in such a way as to maximise your score.
Play
Starting with the non-dealer, you each in turn play a card face up to the table, announce the total numerical value of all cards so far played, and draw a replacement from stock. The cards so played form an overlapping row of cards called the Caterpillar. A completed caterpillar will look something like this:

A fully formed caterpillar

If the first card played is a Five or a Ten, its player scores 5 or 10 respectively. At each turn thereafter you must play either -
• a numeral card of the same suit as the previous one, or
• a face card of any suit.
If you play a numeral you announce the new sum total that it makes, and if that total is a multiple of five you add it to your score.
If you play a face card, it adds nothing, and you repeat the same total. If that total is a multiple of five, you only add that total to your score if the card you played matches the suit of the previous card. If, not, it changes the suit that now has to be followed, but doesn't increase your score.
You are allowed to play a face card on a face card, and, as described above, it adds to your score if it matches suit, or changes the suit to be followed if it doesn't.
Ending and final scoring
Play continues until the last card has been drawn from stock, leaving 26 cards in the Caterpillar and 13 in each player's hand.
You then each total the amount you scored for multiples and add 100 for each face card left in hand.
Getting stuck
You must play in such a way as to allow your opponent to be able to continue. If your opponent can't play because they can't follow suit and have no face cards with which to change it, they are said to be "court short". In this case, after spreading their hand face up to prove it, play ceases. You both score what you made in running totals, but your opponent scores 100 for each face card remaining in your own hand and you score nothing for them. That'll teach you to hog all the face cards!
Illustration
In the game illustrated above the first player scored 280 for running totals and 400 for four face cards in hand. The second scored 750 for totals and 200 for two face cards in hand, thus winning by 950 to 680. The first score made by the leader was 10 for the 10, that of the second player was 35 for the A. The second player's last four cards scored respectively 90 (for Q), 100, 110, and 120 for a rousing finale.