or Picket, a celebrated game at cards, much in use throughout the polite world.
It is played between two persons, with only 32 cards; all the duces, threes, fours, fives, and fixes, being set aside.
In reckoning at this game, every card goes for the number it bears, as a ten for ten; only all count 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 define 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, i.e., 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 suit he has most cards of; and reckoning how many points he has in that suit, if the other have not so many in that or any other suit, he tells one for every ten of that suit. He who thus reckons most is said to win the point.
The point being over, each examines what sequences he has of the same suit, viz., how many tierces, or fe-
quences of threes, quartes or fours, quintes or fives, six- emes, or fixes, &c. For a tierce they reckon three points, for a quarte four, for a quinte fifteen, for a fixieme sixteen, &c. 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, i.e., 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 over, they 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, e.g., three aces, has all his others made good hereby, 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 suit; and the highest card of the suit wins the trick. Note, un- less 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 that he who plays last does not reckon for his cards unless he wins the trick.
The cards being played out, he that has most tricks reckons ten for winning the cards. If they have tricks alike, neither reckons anything. The deal being fin- ished, and each having marked up his game, they pro- ceed 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 that can reckon 30 in hand by carte-blanche, points, quintes, &c., without playing, before the other has reckoned anything, reckons 90 for them; and this is called a repique. If he reckons above 30, he reckons to many above 90. If he can make up 30, part in hand and part play, ere the other has told any- thing, he reckons for them 60. And this is called a pique. Where the name of the game. He that wins all the tricks, instead of ten, which is his right for winning the cards, reckons 40. And this is called a capot.
Mr de Moivre, who has made this game the object of mathematical investigation, has proposed and solved the following problems: 1. To find at piquet the prob- ability which the dealer has for taking one ace or more in three cards, he having none in his hand. He con- cludes from his computation, that it is 29 to 28 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. Answer: 232 to 91, or 5 to 2, 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. Answer: the odds against the eldest hand taking an ace and a king are $331$ to $315$, or $21$ to $20$ nearly.
4. To find at piquet the probability of having 12 cards dealt to, without king, queen, or knaves, which case is commonly called cartes-blanches. Answer; the odds against cartes-blanches are $1791$ to $1$ nearly.
5. To find how many different sets, essentially different from one another, one may have at piquet before taking in. Answer; $28,967,278$. This number falls short of the sum of all the distinct combinations, whereby 12 cards may be taken out of 32, this number being $225,792,840$; but it must be considered that in that number several sets of the same import, but differing in suit, might be taken, which would not introduce an essential difference among the sets. The same author gives also some observations on this game, which he had from an experienced player. See Doctrine of Chances, p. 179, &c. M. de Monmort has treated of piquet in his Analyse des Jeux de Hazard, p. 162.