Hoyle's Games Improved

in this manner, because, by laying an ace down in your adversary's table you have a probability of throwing deuce-ace, trois-deuce, quatre-trois, or six-cinque, in two or three throws: in any of which cases you are to make a point, which gives you the better of the hit; and observe by the directions given in this chapter, that you are to play nine chances out of the thirty six in a different manner, for a single hit, to what you would do when playing for a gammon.

SOME OBSERVATIONS, HINTS, AND CAUTIONS.

1. By the directions given to play for a gammon, you are voluntarily to make some blots; (the odds being in your favour that they are not hit; but should that so happen, in such case, you will have three men in your adversary's table; you must then endeavour to secure your adversary's cinque, quatre, or trois-point, to prevent a gammon, and must be very cautious how you suffer him to take up a fourth man.

2. Take care not to crowd your game, that is, putting many men either upon your trois or deuce-point in your own table; which is, in effect, losing those men by not having them in play. Besides, by crowding your game, you are often gammoned; as, when your adversary finds your game open, by being crowded in your own table, he may then play as he thinks fit.

3. By referring to the calculations, you may know the odds of entering a single man upon any certain number of points, and play your game accordingly.

4. If you are obliged to leave a blot, by having

recourse to the calculations for hitting it, you will find the chances for and against you.

5. You will also find the odds for and against being hit by double dice, and consequently can choose a method of play most to your advantage.

6. If it be necessary to make a run, in order to win a hit, and you would know who is forwardest, begin with reckoning how many points you must have to bring home to the six-point in your table the man that is at the greatest distance, and do the like by every other man abroad; when the numbers are summed up, add for those already on your own tables (supposing the men that were abroad as on your 6 point for bearing), namely, six for every man on the six, and so on respectively for each; five, four, three, two, or one, for every man, according to the points on which they are situated. Do the like to your adversary's game, and then you will know which of you is forwardest and likeliest to win the hit.

OBSERVATIONS AND DIRECTIONS FOR A LEARNER TO BEAR HIS MEN.

1. IF your adversary be greatly before you, never play a man from your quatre, trois, or deuce-points, in order to bear that man from the point where you put it, because nothing but high doublets can give you any chance for the hit; therefore, instead of playing an ace or a deuce from any of the aforesaid points, always play them from your highest point; by which means, throwing two fives, or two fours, will, upon having eased your six and cinque points, be of great advantage: whereas, had your six-point

remained loaded, you must perhaps be obliged to play at length those fives and fours.

2. Whenever you have taken up two of your adversary's men, and happen to have two, three, or more points made in your own table, never fail spreading your men, either to take a new point in your table, or to hit the man your adversary may happen to enter. As soon as he enters one, compare his game with yours; and if you find your game equal, or better, take the man if you can, because it is 25 to 11 against his hitting you; which being so much in your favour, you ought always to run that risk, when you have already two of his men up: except you play for a single hit only, and playing that throw otherwise gives you a better chance for the hit, then do not take up that man.

3. Never be de'erred from taking up any one man of your adversary by the apprehension of being hit with double dice, because the fairest probability is 5 to 1 against him.

4. If you should happen to have five points in your table, and to have taken up one of your adversary's men, and are obliged to leave a blot out of your table, rather leave it upon doublets than any other, because doublets are 35 to 1 against his hitting you, and any other chance is but 17 to against him.

5. Two of your adversary's men in your table are better for a hit than any greater number, provided your game be the forwardest; because having three or more men in your table gives him more chances to hit you, than if he had only two men.

6. If you are to leave a blot upon entering a man on your adversary's table; and have your choice where, always chuse that point which is the most disadvantageous to him, To illustrate

this, suppose it is his interest to hit or take you up as soon as you enter: in that case leave the blot upon his lowest point: that is to say, upon his deuce, rather than upon his trois, and so on, because all the men your adversary plays upon his trois or his deuce points are in a great measure out of play, these men not having it in their power to make his cinque point, and consequently his game will be crowded there and open elsewhere, whereby you will be able also much to annoy him.

7. Prevent your adversary from bearing his men to the greatest advantage, when you are running to save a gammon; suppose you should have two men upon his ace point, and several others abroad; though you should lose one point or two in putting the men into your table, yet it is your interest to leave a man upon the adversary's ace-point; which will prevent him bearing his men to his greatest advantage, and will also give you the chance of his making a blot, that you may hit. But if, upon calculation, you find you have a throw, or a probability of saving your gam mon, never wait for a blot, because the odds are greatly against hitting it.

CASES SHOWING HOW TO CALCULATE THE ODDS.

1. SUPPOSE your table made up, and that you have taken up one of your adversary's men, who has so many abroad as require three throws to put them in his table; it is then about an equal wager that you gammon him. Because, in all

probability, you will bear two men before you open your table, and when you bear the third man, you will be obliged to open your six or cinque point; in that case it is likely that your adversary must take two throws before he enters his man in your table, and two throws more before he puts that man into his own table, and three throws more to put into his own table the men which he has abroad, in all seven throws: and as you have twelve men to bear, these probably will take seven throws in bearing, because you may twice be obliged to make an ace, or a deuce, before you can bear all.

N. B. No mention is made of doublets on either side, that event being equal to each party.

The foregoing case shows it is in your power to calculate very nearly the odds of saving or winning a gammon upon most occasions.

2. Suppose you have three men upon your adversary's ace point, and five points in your table, and that the adversary has all his men in his table, three upon each of his five highest points, what is the probability for a gammon ?