The following description was rescued from John Hay's Rule Book, formerly at Geocities. An archive copy of the original page is also available at reocities.com. I have unfortunately lost touch with John Hay. If anyone knows how to contact him, or what became of his rule book, please let me know.
John Hay wrote: I put the rules in the form below from information provided by George Klemic and Andrew Lipscomb, to whom I owe a huge thank you.
Players, cards and deal
Number of Players: 2
Deck: Standard Pinochle deck of 48 cards consisting of 2 each of all cards 9 and above (including aces).
Deal: Each player is dealt 12 cards, the next card is turned up to determine trump for the hand and the remainder of the deck (the stock) is placed crosswise on this upturned card. Deal alternates between players.
Bidding: There is no bidding in this game.
The game is played in two phases, described separately below.
Phase 1: As long as cards remain in the stock, the game is in Phase 1. The non-dealer leads to the first trick, the dealer then plays any card from their hand to the trick (not required to follow suit or trump). The winner of the trick takes the top card of the stock and puts it in their hand, the loser of the trick then takes the next card from the stock and places it in their hand. The winner of the trick is now allowed to meld if they wish. (See section on melding below.)
Editor's Note. In this detail John Hay's description differs from the standard rules given in most American card game books. In the book version, the trick winner melds before drawing a new card from the deck. So if the newly drawn card completes a meld the player will need to win another trick before they are allowed to show and score it.
The winner of the trick then leads a card to the next trick (the card led can be in their hand or on the table as part of a meld). Play continues as above until there are no cards left in the stock. When the stock is down to one face down card and the remaining trump card, the winner of the trick may choose which card to take. After picking up these last two cards the winner of that trick may still meld.
Phase 2: Once there are no cards left in the stock, the rules change. There is no longer any melding. Each player picks up any meld they have and place it in their hand. The winner of the last trick from Phase 1 leads to the next trick. The second player must follow suit if able. If not, they must trump if possible. The second player must win the trick if they are able to. The winner of the trick leads to the next trick. Play continues in this manner until all cards have been played.
In Phase 1, when a player wins a trick they may place any meld they have face up in front of them and receive points for it. The various combinations that may be melded and the points they receive are listed below. When a player melds, it is written down on the scoresheet immediately.
Run - A 10 K Q J in trumps - 150 points
Marriage - K Q in same suit - 20 points
Royal Marriage - K Q in trumps - 40 points
Aces around - A in each suit - 100 points
Kings around - K in each suit - 80 points
Queens around - Q in each suit - 60 points
Jacks around - J in each suit - 40 points
Pinochle - J of Diamonds and Q of Spades, - 40 points
Double Pinochle - 2 pinochles - 300 points (Note: A Double Pinochle is the only meld which gives a bonus for having more than one, all other melds simply count twice. e.g. Double aces around count 200 points.)
9 of Trumps (Dix) - 10 points
Special rule concerning Dix: The first Dix to be melded is done so by exchanging it for the face-up trump card at the bottom of the stock (even if it is the other Dix). The card taken from the bottom may be used immediately in meld if desired.
Special notes concerning melding:
A player may use a card in more than one meld provided it is used to make a different type of meld. (e.g. A player melds a marriage in spades. If both cards are still on the table on a later turn, the player may add the other 3 kings for kings around, the other 3 queens for queens around, or the Jack of Diamonds for a Pinochle. They may not add another single King of Spades for a second marriage.)
If a player has melded a Royal Marriage and they later add the A, 10, and J or trumps for a run, they only score an additional 110 points instead of 150.
If a player has melded a Pinochle and they later add another Pinocle for a Double Pinochle (while the original Pinochle is still down), they only score an additional 260 points instead of 300. (If the first Pinochle had already been broken up, they would only score 40 points for the second one.)
In addition to any meld a player scored during the hand they also receive 11 points for each ace, 10 points for each ten, 4 points for each king, 3 points for each queen, and 2 points for each jack they captured in play. The player who captures the last trick also gets ten points. (Total of 250 points to be taken in play.) The first player to get a total of 1200 points wins the game.
Game may be played to 1500 or 1000 points instead of 1200.
An optional scoring method for cards taken in play is to count each Ace and ten 10 points, and count each king and queen 5 points.
Another scoring method is to simply count each ace, ten, and king 10 points. If this scoring method is used, then all scores in the game will end in a zero. Since this is the case, the zeroes can be dropped off the end of the score, effectively dividing all possible scores by 10.
In phase 2 the second player is only required to take the trick if possible if trumps were led.
Any of the "Special notes concerning melding" could be ignored, except for the rule that a player can use a card that has already been melded in additional meld.
As mentioned above, in the standard version described in card games books, the winner of a trick must meld before drawing a new card from the stock, so the drawn card cannot be used in a meld until the player has won another trick.
According to some books, a player may only score one meld per trick, even if they have no common card - for example it is not possible to meld two marriages in different suits at the same time. Dix counts as a meld so this rule also implies that the face-up trump taken in exchange for the 9 cannot be used in a meld immediately.
According to some books, each meld scored must incorporate at least one card newly laid down from the player's hand - it is not possible to score a meld made simply by rearranging cards that are already on the table.
'Mouse' has contributed rules for an interesting variant played by his family which features larger hands, more melds, and 'glups' which are scored for losing several consecutive tricks by following suit.
The collection HOYLE Card Games for Windows or Mac OS X includes a Two-Player Pinochle program, along with many other popular card games.