PIQUET, or Picket, a celebrated game at cards, much in use throughout the polite world. It is played between two persons, with only thirty-two cards; the deuces, threes, fours, fives, and sixes, being set aside.

In reckoning at this game, every card goes for the number it bears, as a ten for ten, only all court cards go for ten, and the ace for eleven; and the usual game is one hundred up. In playing, the ace wins the king, the king the queen, and so down.

( Twelve cards are dealt round, usually by two and two; which done, the remainder are laid in the middle. If one of the gamesters finds he has not a court card in his hand, he is to declare he has carte-blanche, and tell how many cards he will lay out, and desire the other to discard, that he may show his game, and satisfy his antagonist that the carte-blanche is real; for which he reckons ten.

Each person discards, or lays aside a certain number of his cards, and takes in a like number from the stock. The first of the eight cards may take three, four, or five; the dealer all the remainder, if he pleases. After discarding, the eldest hand examines what suite he has most cards of; and reckoning how many points he has in that suite, if the other have not so many in that or any other suite, he tells one for every ten of that suite. He who thus reckons most is said to win the point.

The point being over, each examines what sequences he has of the same suite, that is, how many tierces, or sequences of threes, quartes or fours, quintes or fives, sixièmes or sixes, and so on. For a tierce they reckon three points, for a quarte four, for a quinte fifteen, for a sixième sixteen, and so forth. And the several sequences are distinguished in dignity by the cards they begin from. Thus ace, king, and queen are called tierce major ; king, queen, and knave, tierce to a king; knave, ten, and nine, tierce to a knave, &c.; and the best tierce, quarte, or quinte, in other words, that which takes its descent from the best card, prevails, so as to make all the others in that hand good, and destroy all those in the other hand. In like manner, a quarte in one hand sets aside a tierce in the other.

The sequences being over, the players proceed to examine how many aces, kings, queens, knaves, and tens, each holds, reckoning for every three of any sort, three; but here, too, as in sequences, he that with the same number of threes has one that is higher than any the other has, for instance, three aces, has all his others made good thereby, and his adversary’s all set aside. But four of any sort, which is called a quatorze, always sets aside three.

All the game in hand being thus reckoned, the eldest proceeds to play, reckoning one for every card he plays above a nine, and the other follows him in the suite; and the highest card of the suite wins the trick. However, unless a trick be won with a card above a nine (except the last trick), nothing is reckoned for it, though the trick serves afterwards towards winning the cards; and he who plays last does not reckon for his cards unless he wins the trick.

The cards being played out, he who has most tricks reckons ten for winning the cards. If they have tricks alike, neither reckons anything. The deal being finished, and each player having marked up his game, they proceed to deal again as before, cutting afresh each time for the deal. If both parties be within a few points of being up, the carte-blanche is the first thing that reckons, then the point, then the sequences, then the quatorzes or threes, then the tenth cards.

He who can reckon thirty in hand by carte-blanche, points, quintes, &c. without playing, before the other has reckoned anything, reckons ninety for them; and this is called a repique. If he reckons above thirty, he reckons so many above ninety. If he can make up thirty, part in hand and part play, ere the other has told any thing, he reckons for them sixty. And this is called a pique ; whence the name of the game. He who wins all the tricks, instead of ten, which is his right for winning the cards, reckons forty; and this is called a capot.

Mr Demoivre, who has made this game the object of mathematical investigation, has proposed and solved the following problems. 1. To find at piquet the probability which the dealer has for taking one ace or more in three cards, he having none in his hand. He concludes from his computation, that it is twenty-nine to twenty-eight that the dealer takes one ace or more. 2. To find at piquet the probability which the eldest has of taking an ace or more in five cards, he having no ace in his hand; the answer is two hundred and thirty-two to ninety-one, or five to two nearly. 3. To find at piquet the probability which the eldest hand has of taking an ace and a king in five cards, he having none in his hand; the answer is, the odds against the eldest hand taking an ace and a king are three hundred and thirty-one to three hundred and fifteen, or twenty-one to twenty nearly. 4. To find at piquet the probability of having twelve cards dealt to, without king, queen, or knaves, which case is commonly called cartes-blanches; the odds against cartes-blanches are seventeen hundred and ninety-one to one nearly. 5. To find how many different sets, essentially different from one another, one may have at piquet before taking in; the answer is, 28,967,278. This number falls short of the sum of all the distinct combinations, by which twelve cards may be taken out of thirty-two, this number being 225,792,840; but it must be considered that in that number several sets of the same import, but differing in suite, might be taken, which would not introduce an essential difference amongst the sets.