BACK Bone, or SPINE. See Anatomy, no. 30.
the manege, and among farriers. A horse's back should be straight, not hollow, which is called faddle-backed: horses of this kind are generally light, and carry their heads high, but want in strength and service. A horse with a weak back is apt to stumble.
In the French riding-schools, to mount a horse a dos, is to mount him bare-backed without a saddle.
BACK-GAMMON, an ingenious game played with dice, upon a table, by two persons.
Manner of playing the game. The table is divided into two parts, upon which there are 24 black and white spaces called points. Each adversary has 15 men, black and white, to distinguish them; and they are disposed of in the following manner: Supposing the game to be played into the right-hand table, two are placed upon the ace point in the adversary's table, five upon the fix point in the opposite table, three upon the cinque point in the hitherto table, and five on the fix point in the right-hand table. The grand object in this game is for each player to bring the men round into his right-hand table, by throwing with a pair of dice those throws that contribute towards it, and at the same time prevent the adversary doing the like. The first bell throw upon the dice is esteemed aces, because it stops the fix point in the outer-table, and secures the cinque in the thrower's table; whereby the adversary's two men upon the thrower's ace point cannot get out with either quatre, cinque, or fix. This throw is an advantage often given to the antagonist by the superior player.
When he carries his men home in order to lose no point, he is to carry the most distant man to his adversary's bar point, that being the first stage he is to place it on; the next stage is six points farther, viz. in the place where the adversary's five men are first placed out of his tables. He must go on in this method till all his men are brought home, except two, when by losing a point, he may often save the gammon, by throwing two fours or two fives.
When a hit is only played for, he should endeavour to gain either his own or adversary's cinque point; and if that fails by his being hit by the adversary, and he finds him forwarder than himself, in that case he must throw more men into the adversary's tables; which is done in this manner: He must put a man upon his cinque or bar point; and if the adversary neglects to hit it, he may then gain a forward game instead of a back game: but if the adversary hits him, he should play for a back game; and then the greater number of men which are taken up makes his game the better, because by these means he will preserve his game at home: and then he should endeavour to gain both his adversary's ace and trois points, or his ace and deuce points, and take care to keep three men upon the adversary's ace point, that in case he hits him from thence, that point may remain still secure to himself.
A back game should not be played for at the beginning of a set, because it would be a great disadvantage, the player running the risk of a gammon to win a single hit.
Rules for playing at setting out all the throws on the dice, when the player is to play for a gammon or for a single hit (A). 1. Two aces are to be played on the cinque point and bar point, for a gammon or for a hit. 2. Two fixes, to be played on the adversary's bar.
(A) The rules marked thus † are for a gammon only; those marked thus * are for a hit only. bar point and on the thrower's bar point, for a gammon or for a hit. 3. † Two trois, to be played on the cinque point, and the other two on the trois point in his own tables for a gammon only. 4. † Two dences, to be played on the quatre point in his own tables, and two to be brought over from the five men placed in the adversary's tables for a gammon only. 5. † Two fours, to be brought over from the five men placed in the adversary's tables, and to be put upon the cinque point in his own tables, for a gammon only. 6. Two fives, to be brought over from the five men placed in the adversary's tables, and to be put on the trois point in his own tables, for a gammon or for a hit. 7. Size ace, he must take his bar point for a gammon or for a hit. 8. Size deuce, a man to be brought from the five men placed in the adversary's tables, and to be placed in the cinque point in his own tables, for a gammon or for a hit. 9. Six and three, a man to be brought from the adversary's ace point, as far as he will go, for a gammon or for a hit. 10. Six and four, a man to be brought from the adversary's ace point, as far as he will go, for a gammon or for a hit. 11. Six and five, a man to be carried from the adversary's ace point, as far as he can go, for a gammon or for a hit. 12. Cinque and quatre, a man to be carried from the adversary's ace point, as far as he can go, for a gammon or for a hit. 13. Cinque trois, to make the trois point in his table, for a gammon or for a hit. 14. Cinque deuce, to play two men from the five placed in the adversary's tables, for a gammon or for a hit. 15. † Cinque ace, to bring one man from the five placed in the adversary's tables, for the cinque, and to play one man down on the cinque point in his own tables for the ace, for a gammon only. 16. Quatre trois, two men to be brought from the five place in the adversary's tables, for a gammon or for a hit. 17. Quatre deuce, to make the quatre point in his own tables, for a gammon or for a hit. 18. † Quatre ace, to play a man from the five placed in the adversary's tables for the quatre; and for the ace, to play a man down upon the cinque point in his own tables, for a gammon only. 19. † Trois deuce, two men to be brought from the five placed in the adversary's tables, for a gammon only. 20. Trois ace, to make the cinque point in his own tables, for a gammon or for a hit. 21. † Deuce ace, to play one man from the five men placed in the adversary's table for the deuce; and for the ace to play a man down upon the cinque point in his own tables, for a gammon only. 22. * Two trois, two of them to be played on the cinque point in his own tables, and with the other two he is to take the quatre point in the adversary's tables. 23. * Two deuces, two of them are to be played on the quatre point in his own tables, and with the other two he is to take the trois point in the adversary's tables. By playing these two cases in this manner, the player avoids being shut up in the adversary's tables, and has the chance of throwing out the tables to win the hit.
24. * Two fours, two of them are to take the adversary's cinque point in the adversary's tables, and for the other two, two men are to be brought from the five placed in the adversary's tables. 25. * Cinque ace, the cinque should be played from the five men placed in the adversary's tables, and the ace from the adversary's ace point. 26. * Quatre ace, the quatre to be played from the five men placed in the adversary's ace point. 27. * Deuce ace, the deuce to be played from the five men placed in the adversary's tables, and the ace from the adversary's ace point.
The three last chances are played in this manner; because an ace being laid down in the adversary's tables, there is a probability of throwing deuce ace, trois deuce, quatre trois, or size cinque, in two or three throws; either of which throws secures a point, and gives the player the best of the hit.
Cautions, &c. The player must understand by the directions given to play for a gammon, that he is to make some blots on purpose, the odds being in his favour that they are not hit; but if it should happen that any blot is hit, as in this case there will be three men in the adversary's tables, he must then endeavour to secure the adversary's cinque, quatre, or trois point, to prevent a gammon, and must be very cautious of his fourth man's not being taken up.
He must not crowd his game at any time if he can help it; that is to say, he should not put many men either upon the trois or deuce points in his own tables, being the same as losing those men not having them in play. Besides, by crowding the game, and attempting to save a gammon, the player is often gammoned. His game being crowded in his own tables, the adversary has room to play as he thinks proper.
The following calculations will show the odds of entering a single man upon any certain number of points; and accordingly the game should be played.
It is necessary to know that there are thirty-six chances upon two dice, and the points that are upon these thirty-six chances are as follow.
| Points | |--------| | 2 Aces | 4 | | 2 Deuces | 8 | | 2 Trois | 12 | | 2 Fours | 16 | | 2 Fives | 20 | | 2 Sixes | 24 | | 6 And 5 twice | 22 | | 6 And 5 twice | 20 | | 6 And 3 twice | 18 | | 6 And 2 twice | 16 | | 6 And 1 twice | 14 | | 5 And 4 twice | 18 | | 5 And 3 twice | 16 | | 5 And 2 twice | 14 | | 5 And 1 twice | 12 | | 4 And 3 twice | 14 | | 4 And 2 twice | 12 | | 4 And 1 twice | 10 | | 3 And 2 twice | 10 | | 3 And 1 twice | 8 | | 2 And 1 twice | 6 |
Divide by 36 \( \frac{294}{288} \) and it proves, that upon an average the player has a right to 8 points each throw. The chances upon two dice calculated for backgammon are as follow.
| 2 Sixes | - | 1 | |---------|---|---| | 2 Fives | - | 1 | | 2 Fours | - | 1 | | 2 Trois | - | 1 | | 2 Deuces | - | 1 | | + 2 Aces | - | 1 | | 6 And 5 twice | - | 2 | | 6 And 4 twice | - | 2 | | 6 And 3 twice | - | 2 | | 6 And 2 twice | - | 2 | | + 6 And 1 twice | - | 2 | | 5 And 4 twice | - | 2 | | 5 And 3 twice | - | 2 | | 5 And 2 twice | - | 2 | | + 5 And 1 twice | - | 2 | | 4 And 3 twice | - | 2 | | 4 And 2 twice | - | 2 | | + 4 And 1 twice | - | 2 | | 3 And 2 twice | - | 2 | | + 3 And 1 twice | - | 2 | | + 2 And 1 twice | - | 2 |
As it may seem difficult to find out by this table of thirty-six chances what are the odds of being hit upon a certain or flat die, let the following method be pursued.
The player may observe in the table that what are thus marked are,
| + 2 Aces | - | 1 | | + 6 And 1 twice | - | 2 | | + 5 And 1 twice | - | 2 | | + 4 And 1 twice | - | 2 | | + 3 And 1 twice | - | 2 | | + 2 And 1 twice | - | 2 |
Total 11
Which deducted from 36
There remains 25
So that it appears it is twenty-five to eleven against hitting an ace upon a certain or flat die.
The above method holds good with respect to any other flat die. For example, what are the odds of entering a man upon 1, 2, 3, 4, or five points?
Answer.
To enter it upon for against for ag.
| 1 point is 11 to 25 | Or about 4 to 9 | |---------------------|-----------------| | 2 points 20 - 16 | 5 4 | | 3 - 27 - 9 | 3 1 | | 4 - 32 - 4 | 8 1 | | 5 - 35 - 1 | 35 1 |
The following table shows the odds of hitting with any chance, in the reach of a single die.
To hit upon for against for ag.
| 1 is - 11 to 25 | Or about 4 to 9 | |-----------------|-----------------| | 2 - 12 - 24 | 1 - 2 | | 3 - 14 - 22 | 2 - 3 | | 4 - 15 - 21 | 5 - 7 | | 5 - 15 - 21 | 5 - 7 | | 6 - 17 - 19 | 8½ - 9½ |
The odds of hitting with double dice are as follow.
To hit upon for against for ag.
| 7 is - 6 to 30 | Or about 1 to 5 | |----------------|-----------------| | 8 - 6 30 | 1 5 | | 9 - 5 31 | 1 6 | | 10 - 3 33 | 1 11 | | 11 - 2 34 | 1 17 | | 12 - 1 35 | 1 35 |
How to find out the odds of being hit upon a six, by the table of thirty-six chances.
| 2 Sixes | - | 1 | |---------|---|---| | 2 Trois | - | 1 | | 2 Deuces | - | 1 | | 6 And 5 twice | - | 2 | | 6 And 4 twice | - | 2 | | 6 And 3 twice | - | 2 | | 6 And 2 twice | - | 2 | | 6 And 1 twice | - | 2 | | 5 And 1 twice | - | 2 | | 4 And 2 twice | - | 2 |
Which deducted from 36
There remains 19
By which it appears to be 19 to 17 against being hit upon a six.
The odds on the hits.
| 2 Love is about | 5 to 2 | |-----------------|-------| | 2 to 1 is | 2 1 | | 1 Love is | 3 2 |
Directions for the player to bear his men. If a player has taken up two of the adversary's men, and happens to have two, three, or more points made in his own tables, he should spread his men, that he either may take a new point in his tables, or be ready to hit the man which the adversary may happen to enter. If he finds upon the adversary's entering, that the game is upon a par, or that the advantage is on his own side, he should take the adversary's man up whenever he can, it being 25 to 11 that he is not hit; except when he is playing for a single hit only; then, if playing the throw otherwise gives him a better chance for it, he ought to do it.
It being five to one against his being hit with double dice, he should never be deterred from taking up any one man of the adversary's.
If he has taken up one of the adversary's men, and should happen to have five points in his own tables, and forced to leave a blot out of his tables, he should endeavour to leave it upon doubles preferable to any other chance, because in that case the odds are 35 to one that he is not hit; whereas it is only 17 to one but he is hit upon any other chance.
When the adversary is very forward, a player should never move a man from his own quatre, trois, or deuce points, thinking to bear that man from the point where he put it, as nothing but high doubles can give him any chance for the hit. Instead of playing an ace or a deuce from any of those points, he should play them from his own five or highest points, so that throwing two fives, or two fours, his five and cinque points being eased, would be a considerable advantage to him; whereas had they been loaded, he must have been obliged to play otherwife.
It is the interest of the adversary to take up the player as soon as he enters. The blot should be left upon the adversary's lowest point; that is to say, upon his deuce point rather than upon his trois point, or upon his trois point rather than his quatre point, or upon his quatre point preferable to his cinque point, for a reason before mentioned. All the men the adversary plays upon his trois or his deuce points are deemed lost, being greatly out of play; so that those men not having it in their power to make his cinque point, and his game being crowded in one place and open in another, the adversary must be greatly annoyed by the player.
If the player has two of the adversary's men in his tables, he has a better chance for a hit than if he had more, provided his game is forwarder than that of his antagonist's; for if he had three or more of the adversary's men in his tables, he would stand a worse chance to be hit.
When a player is running to save the gammon, if he should have two men upon his ace point and several men abroad, although he should lose one point or two in putting his men into his tables, it is his interest to leave a man upon the adversary's ace point, because it will prevent his adversary from bearing his men to the greatest advantage, and at the same time the player will have a chance of the adversary's making a blot, which he may chance to hit. However, if a player finds upon a throw that he has a probability of saving his gammon, he should never wait for a blot, as the odds are greatly against his hitting it, but should embrace that opportunity.
How to calculate the odds of saving or winning the gammon. Suppose the adversary has so many men abroad as require three throws to put them into his tables, and at the same time that the player's tables are made up, and that he has taken up one of the adversary's men; in this case, it is about an equal wager that the adversary is gammoned. For in all probability the player has bore two men before he opens his tables; and when he bears the third man, he will be obliged to open his five or cinque point. It is then probable, that the adversary is obliged to throw twice before he enters his men in the player's tables, twice more before he puts that man into his own tables, and three throws more to put the men which are abroad into his own tables; in all seven throws. Now the player having 12 men to bear, he may be forced to make an ace or a deuce twice before he can bear all his men, and consequently will require seven throws in bearing them; so that, upon the whole, it is about equal whether the adversary is gammoned or not.
Suppose a player has three men upon his adversary's ace point and five points in his own tables, and that the adversary has all his men in his tables, three upon each of his five highest points. Has the player a probability of gammoning his adversary or not?
For bearing three men from his 6th point is
Carried forward
From his 4th point
From his 3rd point
From his 2nd point
In all 60
Bringing his three men from the adversary's ace point to his five point in his own tables, being 18 points each, and making together
There must remain
It is plain from this calculation, that the player has much the best of the probability of the gammon, exclusive of one or more blots which the adversary is liable to make in bearing his men, supposing at the same time the throws to be upon an equality.
Suppose two blots are left, either of which cannot be hit but by double dice, one must be hit by throwing eight and the other by throwing nine; so that the adversary has only one die to hit either of them. What are the odds of hitting either of them? The chances of two dice being in all
The chances to hit 8 are 6 and 2 twice
5 and 3 twice
2 Deuces
2 Fours
The chances to hit 9 are 6 and 3 twice
5 and 4 twice
2 Trois
For hitting, in all
Chances for not hitting, remain
So that the odds are 25 to 11 against hitting either of these blots.
This method may be taken to find out the odds of hitting three, four, or five blots upon double dice; or blots made upon double and fingle dice at the same time. After knowing how many chances there are to hit any of those blots, they must be added all together, and then subtracted from the number 36, which are the chances of the two dice, and the question is solved.
A critical case for a Back-game. Suppose the foregoing to be played by A, and that all his men are placed as usual; B has fourteen of his men placed upon his adversary's ace point and one man upon his adversary's deuce point, and B is to throw. Who has the best of the hit?—Answer: A has the best of it, gold to silver; because if B does not throw an ace to take his adversary's deuce point, which is 25 to 11 against him, A will take up B's men in his tables either singly or to make points; and then if B secures either A's deuce or trois point, A will put as many men down as possible, in order to hit, and thereby get a back-game. It is evident that the back-game is very powerful; consequently, whoever practises it must become a greater proficient at the game than he could by any other means.
Another critical case. Suppose A to have five men placed upon his five point, as many upon his quatre point, and the same number upon his deuce point, all in his own tables. At the same time, let us suppose B to have three men placed upon A's ace point, as many upon A's trois point, and the same number upon A's cinque point in his own tables, and three men placed as usual out of his tables. Who has the best of the hit?—Answer: The game is equal, till B has gained his cinque and quatre points in his own tables; which if he can effect, and by playing two men from A's cinque point, in order to force his adversary to blot by throwing an ace, which should B hit, he will have the best of the hit.
A case of curiosity and instruction; in which is shown the probability of making the hit last by one of the players for many hours, although they shall both play as fast as usual.—Suppose B to have bore 13 men, and that A has his fifteen men in B's tables, viz., three men upon his five point, as many upon his cinque point, three upon his quatre point, the same number upon his trois point, two upon his deuce point, and one upon his ace point. A in this situation can prolong it, as aforesaid, by bringing his 15 men home, always securing six close points till B has entered his two men, and brought them upon any certain point; as soon as B has gained that point, A will open an ace, deuce, or trois point, or all of them; which done, B hits one of them, and A taking care to have two or three men in B's tables, is ready to hit that man; and also he being certain of taking up the other man, has it in his power to prolong the hit almost to any length, provided he takes care not to open such points as two fours, two fives, or two fixes, but always to open the ace, deuce, or trois points, for B to hit him.
A critical game to play.—Suppose A and B place their men for a hit in the following manner: A to have three men upon the five point in his own tables, three men out of his tables upon the usual point, and nine men upon his adversary's ace, deuce, and trois points; that is, three upon each; and suppose B's men to be placed in his own and his adversary's tables in the same order. So situated, the best player should win the hit. The game being so equal, that in this case the dice should be thrown for. Now if A throws first, he should endeavour to gain his adversary's cinque point; this being done, he should lay as many blots as possible, to tempt B to hit him, as it puts him backward, and A thereby gains an advantage. A should always endeavour to have three men upon each of his adversary's ace and deuce points; because when B makes a blot, these points will remain secure, and when A has bore five, six, or more men, A yet may secure six close points out of his tables, in order to prevent B from getting his man home, at which time he should calculate who has the best of the hit. If he finds that B is foremost, he should then try to lay such blots as may be taken up by his adversary, that he may have a chance of taking up another man, in case B should happen to have a blot at home.
Laws of Backgammon. 1. If a man is taken from any point, it must be played; if two men are taken from it, they also must be played. 2. A man is not supposed to be played till it is placed upon a point and quitted. 3. If a player has only fourteen men in play, there is no penalty inflicted, because by his playing with a lesser number than he is intitled to, he plays to a disadvantage for want of the deficient man to make up his tables. 4. If he bears any number of men before he has entered a man taken up, and which of course he was obliged to enter, such men so borne must be entered again in the adversary's tables as well as the man taken up. 5. If he has mistaken his throw and played it, and his adversary has thrown, it is not in the choice of either of the players to alter it, unless they both agree to do so.
Back-Painting, the method of painting mezzotinto prints, pasted on glafs, with oil-colours. See Mezzotinto.
The art consists chiefly in laying the print upon a piece of crown-glas, of such a size as fits the print.
In order to do this, take your print and lay it in clean water for two days and two nights, if the print be on very strong, clofe, and hard gummed paper; but if upon an open, soft, spongy paper, two hours will sometimes suffice, or more, according as the paper is.
The paper or picture having been sufficiently soaked, take it out and lay it upon two sheets of paper, and cover it with two more; and let it lie there a little to suck out the moisture.
In the mean time, take the glafs the picture is to be put upon, and let it near the fire to warm; take Strasbourg turpentine, warm it over the fire till it is grown fluid, then with a hog's-hair brush spread the turpentine very smoothly and evenly on the glafs.
When this has been done, take the mezzotinto print from between the papers and lay it upon the glafs; beginning first at one end, rubbing it down gently as you go on, till it lie clofe, and there be no wind bladders between.
Then, with your fingers, rub or roll off the paper from the back-side of the print, till it looks black, i.e., till you can see nothing but the print, like a thin film, left upon the glafs, and set it by to dry.
When it is dry, varnish it over with some white transparent varnish, that the print may be seen through it; and then it is fit for painting.
The utmost care will be necessary in rubbing or rolling the paper off the print, so as not to tear it, especially in the light parts.
You may, instead of soaking your prints two days and two nights, roll them up and boil them for about two hours, more or less, according to the quality of the paper, in water; and that will render it as fit for rubbing, rolling, or peeling, as the other way.
This being done, and your oil colours prepared, ground very fine, and tempered up very stiff, lay on the back-side of the transparent prints such colours as each particular part requires; letting the master-lines of the print full guide your pencil, and to each particular colour will lie fair to the eye on the other side of the glafs, and look almost as well as a painted piece, if it be done neatly.
The shadows of the print are generally sufficient for the shadow of every colour; but if you have a mind to give a shadow by your pencil, then let the shadows be laid on first, and the other colours afterward.
In laying on colours in this kind of back-painting, you need not be curious as to the laying them on smooth. This is not at all requisite here, where the chief aim is only to have the colours appear well on the fore side of the print; and therefore the only care to be used in this work, is to lay the colours on thick enough, that its body may strike the colour of it plainly through the glafs.
Back-Staff, a name formerly given to a sea-quadrant. drant invented by Captain Davis: because the back of the artif is turned towards the sun at the time of observation. See Quadrant.
Back-Stays, of a ship, are ropes belonging to the main-mast and fore-mast, and the masts belonging to them; serving to keep them from pitching forwards or overboard.
Back-Tack, in Scots law: When a wadsetter, instead of possessing the wadset-lands, grants a tack thereunto to the reverfer for payment of a certain sum in name of tack-duty, that tack is called a back-tack.
Back-Worm. See Filanders.