Original Card Games by David Parlett
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Players 2-5   Cards 54   Type Arithmetical
"We all in my house enjoy many of your original card games, only breaking into abstract meta-theoretical discussions on the rules once every few weeks! We have been playing Key of the Door this past week, finding that it is a rewarding game such that under the rules, play of cards towards value 21 can be cloaked with the same unravelling mystery which a good trick-taker is. We peg on the crib board while playing, and find balancing early Jack keys to later King / Joker keys a very fresh take on what holding long suit in hand can mean." (Riley Friedrich)
If many of my card games are arithmetical it's not just because I like everything to do with numbers, but perhaps mainly because I'm aware that arithmetical games are an insufficiently explored genre compared with, say, trick-taking, rummy and shedding games. This one is rather tricky and demands close attention. In case anyone doesn't know, Key of the Door is a bingo term for 21, which in Britain used to be the age of consent before it was lowered to 18.
A "key" is a group of cards of the same suit totalling 21 and headed by a face card (Jack, Queen, King, or Joker). For this purpose numerals count at face value, from Ace = 1 to Ten = 10. The face card has no independent value but duplicates that of exactly one of the accompanying numerals. For example, Q-6-4 can be read as either 16 (6-6-4) or 14 (6-4-4), and if an Ace is played next then all three together can be read as 17 (6-6-4-1), 15 (6-4-4-1), or 12 (6-4-1-1). These could in turn be made up to 21 by playing a Nine, (9-6-4-1-1), or a Five (6-5-5-4-1), but not by any other single card.

Completed hands
In a three-handed game, this player scored
4 (Jack = 5) + 10 (Queen = 4) + 10 (Queen  = A) + 9 (King = 9) + 15 (Joker = 2), total 48.

Extract all 14 face cards, including Jokers, and put them to one side. If more than two play, deal the remaining 40 around one at a time. It doesn't matter if some players have one more than others, but the haves must play before the have-nots. If two play, deal two hands of 10 cards to each. Place one of these hands face down in front of you to draw a card from every time you play from hand to table.
Face cards
After dealing, take a Jack of each suit, place them separately face up on the table, and lay the other faces to one side. Each Jack is to be built up in suit until it counts 21 by the rules stated above, when it is won by whoever plays the last card.
To complete and win 21-point keys, bearing in mind that (a) longer keys (containing more cards) score higher than shorter ones, and (b) those made later in the game, headed successively by Queens, Kings and Jokers, score more than earlier ones.
Dealer's left-hand neighbour leads and the turn to play passes to the left. At each turn you play from hand any card to the part-formed key of its suit. You may, but need not, announce the possible total so far. Thus if the first card played is a Seven, you may announce "14", and if the next is a Two, it may be announced as "16 or 11"; but beyond that you may find it too cumbersome to bother.
Upon making 21, you remove that key and place it face down in front of you like a won trick. Then, immediately before the next person plays, you start a new one of that suit with its next-higher face card. So the second in each suit is headed by a Queen, the third by a King, and the fourth (if any) by a Joker. Only the first two completed keys will be replaced with new ones headed by a Joker.
Jokers as key cards
Jokers belong to no suit but are used to head keys of mixed suits in order to mop up otherwise unplayed numerals near the end of the game. However, you may not play to a Joker key if you are legally able to play to an unfinished suit key.
Stealing keys
If you notice a key on the table that is faulty in one of the ways described below you may point it out and steal it as if you had won it yourself. But you may only steal on your turn and immediately before playing a card.
Unclaimed keys. An unclaimed key is one that already counts 21 but was not claimed by whoever made it. If it contains any unnecessary additional cards you take these as well.
Bust keys. A key is bust if its cards count more than 21 with none of them doubled (e.g. 9-7-6). However, if somebody busts a key before the next person has played you may force them to take their busting card back and play something else.
Bent keys. A key is bent if it can't possibly be made up to 21. This may be because the only card or cards required have already been played. If so, you must first verify your claim by having everyone examine their hands to see if they still hold the missing card or cards. Alternatively, it may be bent because it is not even theoretically possible to make it 21 no matter what cards are available. Such bent keys are harder to spot and you must prove your claim to everyone's satisfaction before stealing one. Examples include some keys worth 20 (e.g. 2-4-6-8), some worth 19 (e.g. 1-4-5-9), and perhaps even lower, though I can't construct one. Don't forget that exactly one card must be duplicated, so 2-4-6-8 can't be made 21 by the addition of an Ace.
Ending and scoring
The game ends when nobody in turn can play to an unfinished key. It doesn't follow that all 14 keys will be made; in fact sometimes the Kings never come into play. For each key you took, you score the number of cards it contains multiplied by the value of its header, namely Jack 1, Queen 2, King 3, Joker 3.
A game consists of as many deals as there are players, with each dealing in turn, though two may prefer to play four deals.
Getting stuck
You must always play one card at each turn so that everyone finishes in the same round. I don't think it can ever be possible to hold no card that can be legally played. However, in case it is, you must play a card face down to the key of its suit. It will have a face value of zero and so leave the count unaffected, though it will contribute one card to the score of whoever wins that key.
Four may play in partnerships, if preferred. In this case it is helpful to make your first play from your best suit, unless you can win a key immediately. A longer suit is better than a shorter one; odd numerals are better than even ones; and low ones are better than high ones.
The shortest possible keys are of three cards: J-A-10, J-3-9, J-5-8, J-6-9. (The duplicated numeral is printed bold.)

The longest contain six cards and there are ten of them: J-A-2-3-4-10, J-A-2-3-5-9, J-A-2-3-6-8, J-A-2-4-6-7, J-A-2-4-5-8, J-A-3-4-5-7, J-A-2-3-4-9, J-A-2-3-4-8, J-A-2-3-5-7, J-A-2-3-4-7.

It's possible to make four 21-point keys using all 10 cards of a suit: J-A-10, Q-3-9, J-4-8, Jo-2-6-7, but with only three face cards in each suit the others must be headed by Jokers. You could, therefore, increase the number of Jokers to three or four. With four, you could make a total of 16 one-suited keys with no cards left over.

You can also make three keys using all ten cards (J-A-9-10, Q-3-7-8, K-2-4-5-6), but not just two, as you'll soon see if you try it. Indeed, if you think about it for a moment you won't even need to try it.