If the foul is not claimed the player continues to score, if he can. _=13.=_ After being pocketed or forced off the table the red ball must be spotted on the top spot, but if that is occupied by another ball the red must be placed on the centre spot between the middle pockets. _=14.=_ If in taking aim the player moves his ball and causes it to strike another, even without intending to make a stroke, a foul stroke may be claimed by an adversary. (See Rule Fifteenth.) _=15.=_ If a player fail to hit another ball, it counts one to his opponent; but if by the same stroke the player’s ball is forced over the table or into any pocket it counts three to his opponent. _=16.=_ Forcing any ball off the table, either before or after the score, causes the striker to gain nothing by the stroke.
Suppose a suit so distributed that you have four to the King, and each of the other players has three cards; what are the probabilities that your partner has both Ace and Queen? The common solution is to put down all the possible positions of the two named cards, and finding only one out of nine to answer, to assume that the odds are 8 to 1 against partner having both cards. This is not correct, because the nine positions are not equally probable. We must first find the number of possible positions for the Ace and Queen separately, afterward multiplying them together, which will give us the denominator; and then the number of positions that are favourable, which will give us the numerator. As there are nine unknown cards, and the Ace may be any one of them, it is obvious that the Queen may be any one of the remaining eight, which gives us 9 × 8 = 72 different ways for the two cards to lie. To find how many of these 72 will give us both cards in partner’s hand we must begin with the ace, which may be any one of his three cards. The Queen may be either of the other two, which gives us the numerator, 3 × 2 = 6; and the fraction of probability, 6/72, = 1/12; or 11 to 1 against both Ace and Queen. If we wished to find the probability of his having the Ace, but not the Queen, our denominator would remain the same; but the numerator would be the three possible positions of the Ace, multiplied by the six possible positions of the Queen among the six other unknown cards, in the other hands, giving us the fraction 18/72. The same would be true of the Queen but not the Ace. To prove both these, we must find the probability that he has neither Ace nor Queen. There being six cards apart from his three, the Ace may be any one of them, and the Queen may be any one of the remaining five.
_=SIX-HAND BRIDGE.=_ This is played by six persons, sitting with two card tables pushed together so as to make one. Each dealer sits at the long end of the table, the two dealers being partners. On each side of one sits a pair of adversaries so that the initial arrangement, if pair A had the deal, would be this:-- [Illustration: B C +-----+-----+ | 5 | 6 | | | | A |1 | 4| A | | | | 2 | 3 | +-----+-----+ B C ] Numbers are placed on the tables to indicate the positions to which the players shall move after each deal. The player at 6 goes to 5; 4 to 3; 3 to 2; 2 to 1, and 1 to 6. Each pair of partners, as they fall into the end seats, have the deal. If the dealer at either end will not declare on his own cards, he passes it, and the Dummy hand opposite him must be handed to the dealer that sits at the other end of the long table, who must declare for his partner. The usual four hands are dealt and played at each table, and scored as usual. Three scores must be kept, because there are three separate rubbers going on at once,--that between A and B; between A and C, and between B and C. If one pair wins its rubber against one of the others, three players will be idle at one end of the table for one deal, but then all will come into play again, for the next deal.
=_ Before playing, the throw must be announced by the caster, and if the throw is played as called it stands good, unless an error in the call is discovered before the dice have been touched for the purpose of putting them in the box again. _=9.=_ If a player moves a man a wrong number of points, the throw being correctly called, the adversary must demand that the error be rectified before he throws himself, or the erroneous move stands good. _=10.=_ If a man wrongly moved can be moved correctly, the player in error is obliged to move that man. If he cannot be moved correctly, the other man that was moved correctly on the same throw must be moved on the number of points on the second die, if possible. If the second man cannot be so moved onward, the player is at liberty to move any man he pleases. _=11.=_ Any man touched, except for the purpose of adjusting it, must be moved if the piece is playable. A player about to adjust a man must give due notice by saying, “J’adoube.
Whatever tricks they win are placed together, and the counting cards contained in them reckon for their joint account. The tricks have no value as such, except the last. _=Showing.=_ The winner of the last trick takes the stock, and each side then turns over its cards and counts the total value of the points won. The lower score is deducted from the higher, and the difference is the value of the game. If all 35 points are won by either side, they count double, 70. _=Scoring.=_ If the single player loses, he loses to both adversaries, and if he wins he wins from both. His score is the only one put down, and the amount is preceded with a minus or plus sign according to the result. If he secures 23 points, he wins 11; if he takes in 16 only, he loses 3.