Book Transcription

Introduction

The game of Backgammon, which possesses a happy mixture of skill and chance, is deservedly popular among lovers of games.

Its derivation is a vexed question, both as to whence it came, and how it acquired its present designation. “La Maison des Jeux Académiques” abandons its origin as a desperate problem; and Dr. Henry claims its name as a Welsh compound, from “bach,” little, and “cammon,” battle.

On the other hand, Bishop Kennett and Strutt derive it from the Anglo-Saxon, viz., from “bac,” back, and “gamone,” a game; that is to say, a game where players are exposed to be sent back.

Perhaps this cavalier treatment of the etymology of the game may not be considered a sufficient offering to the antiquarian; yet as our readers for the most part will be desirous of becoming practical Backgammon players, all the space at our disposal will be used for their enlightenment and instruction, in preference to attempting the solution of problems of such little practical value.

From Chaucer we gather that the early name for Backgammon was “Tables,” and at this time the game was played with three dice (or more generally with two dice and an imaginary six supposed to have been thrown on the third), and all the “men” commenced their journey home, starting from the Ace point in the home table of their adversaries.

If this method of placing the men is compared with that now in vogue, it will be seen that such a long game had to be considerably shortened, and this was effected by placing all the men except two in various stages of forwardness towards the goal.

Backgammon has always been considered a particularly respectable kind of amusement, quite fitting for country rectors, and not derogatory to the dignity of even higher functionaries of the Church.

“It is only persons of consequence,” writes an old French writer, “who play at Backgammon, and those only who are the most quick-witted, ready, and watchful can ever thoroughly master it.”

In this opinion of the faculties necessary for a true appreciation of the game, at least in its scientific aspect, we most cordially agree; but one of the chief charms of this game is, that it can be played with equal gusto by those who laugh to scorn the idea that such a game of chance can possibly require any skill, or that probabilities or odds can have anything to do with the matter, as by those scientific ones who know Hoyle by heart, and delight in all the technicalities of the game.

Description of the Game.

Backgammon is played by two persons, with two boxes and two dice, upon a square or quadrangular board or table, on which are figured twenty-four points, or flèches, of two colours, placed alternately.

The board is divided into four compartments, two inner and two outer ones, each containing six of the twenty-four points. The players are each provided with fifteen men or counters, the one set black and the other white.

In the diagram given above, one player is supposed to sit where White is written, facing his opponent, Black, at the opposite side.

The compartment to White’s left hand is his “Home,” and the one to his right hand is his “Outer” table. In like manner the compartments to Black’s right and left hands are his “Home” and “Outer” tables respectively.

In all diagrams throughout this article the Home and Outer tables are supposed to be as shown here.

The usual custom among Backgammon players is to play towards the light, e.g.; the lamp or window, according to the time of day at which they may be playing; consequently it is by no means compulsory or even necessary to play into the left-hand tables, as shown in the diagram, and the table to White’s right might be his “Home” table, but then of course the position of the men would have to be altered.

It may be remarked that the tables of each player are numbered from 1 to 12; 1 to 6 representing the points in the “Home” table, and 7 to 12 the points in the “Outer” table of each player.

In order that the phraseology used throughout this article may be understood, it is necessary to explain that the points 1 to 6 will be hereafter spoken of as the Ace, Deuce, Trois, Quatre, Cinque, and Six point respectively.

The points marked “Seven” will be called the “Bar points,” and the other points by their respective numbers.

Now to arrange the board for a game.

If it is decided to make the left-hand tables the “Home” ones, White will place two men on his adversary’s Ace point, five men on his adversary’s 12th point, three upon his own 8th point, and five upon his “Six” point. Black’s men will be placed in corresponding order, in a position directly opposite. The position that the men should be placed in, is shown in the diagram.

The game consists in moving the men from point to point, according to the figures on the dice thrown, out of the adversary’s Home table into his Outer table, across into the player’s Outer table, and then over the bar into the player’s Home table.

This process is called “Carrying a man or men.”

The board having been dressed, the next step is to decide which player has the right to play first.

To settle this question each player throws a single die; he who throws the higher number wins, and may, if he chooses, adopt and play the joint number of the preliminary throws, or he may throw again with two dice.

A player on throwing his two dice should call out the numbers shown on the face of the dice, calling the higher number first. Thus, if the numbers 6 and 1 appear, he should call Six Ace, and then move one of his men to an unoccupied point, technically called an “open” point, or to one already occupied by his own men at the distance shown by one or other of the dice, and then moving another man (or the same man, further on, if he think proper) to another open point indicated by the number of the second die. This completes the move. For instance, if he throws Six Ace, he may play any one man seven points, or one man one point and another six points.

No player may play beyond his “Ace” point, or on to any point in the possession of his adversary, i.e., a point on which there are two or more men belonging to the adversary; that is, he cannot play a six from his “Six” point, or an ace from his adversary’s 12th point, but he may play a seven to his Six point from adversary’s 12th, because his Bar point is open, although his 12th is in possession of the adversary.

If either player should throw Trois Ace, and play two men to his Cinque point, one from his 8th, and the other from his “Six” point, he would be said to “make a point.” Did he, on the other hand, play one man from his adversary’s 12th to his own 9th previously unoccupied, he would be said to have “left a blot”; that is, he would leave one man alone on a point.

If the same number is thrown with both dice, it is called “Doublets,” and the player is entitled to double what he throws. For instance, if a player throws doublet sixes, he is entitled to play 24 points, and in any of the following ways — (a) one man 24 points, (b) one man 18 points, and the other 6 points, (c) one man 12 points and two men 6 points each, (d) two men 12 points each, (e) four men 6 points each, provided, as before stated, he does not go beyond his Ace point nor play on any point occupied by his adversary. Should, however, all the points indicated by the throw of the dice be covered by the adversary’s men, the moves are lost. Let us take an example: quatre doublets are thrown, and the first fourth point from all the player’s men is occupied by at least two men belonging to the adversary; in this case the move is lost, although the eighth, twelfth, and sixteenth points be uncovered.

The players play alternately throughout the game.

A player must play, so as to complete his whole throw, if possible.

Thus, if a player threw Six Quatre, and the men were so placed that he could play either six points or four points, but not both, it would be optional which he played; but if by playing the quatre first he could play the six afterwards, he would be obliged to do so.

Blots.

When, during the progress of the game, a single man is left on a point, it is called a “Blot,” and is exposed to be taken by the adversary, who generally endeavours to “hit” it, by bringing one of his own men to that point. When a man is thus captured, it must be removed from the table and placed upon the bar, — i.e., the division joint of the board, — and the player to whom it belongs cannot move again until he has “entered his man.” This can only be effected by throwing a number, which entitles him to enter his man on a point, unoccupied by the adversary, in the adversary’s home table, playing it as if from a point off the board adjoining and beyond the adversary’s Ace point.

Towards the end of the game, when most of the points in the hostile home table are “covered,” — i.e., have two or more men on each, — it becomes difficult to enter; but a man that has been “hit” must remain on the bar until the exact number required is thrown, or until more points are exposed by the adversary having played some of his men up or borne them off the board. When all six points are blocked, it is of course useless for the player, to whom the captured man belongs, to throw, and his adversary throws alone, and plays continuously until a point is left open, on which the captured man can enter.

“Hitting a Blot” frequently adds extreme variety and interest to the game.

If, during the course of the game, every point upon which a man could be moved is covered by the adversary’s men, the player’s men are compelled to remain in in statu quo, and the adversary proceeds. If one man only can be played, it must be played.

No player is compelled at any time to hit a blot, if he can play without touching the point on which the blot rests.

For example, suppose a player throws Six Trois, and wishes to play a man situated three points away from a blot. If he can play the six first and the trois afterwards, he is not compelled to take up the blot.

Bearing.

As soon as either player has brought all his men into his “Home” table, he must begin to take them off the board, which, in the technical language of the game, is called “bearing” his men.

For every number thrown a man is removed from the corresponding point, or, if the player prefers it, may be played up; if it is impossible to play up a man, the man must be “borne.” Should the highest point on which a player has a man be lower than the number he throws, men must be taken from the highest point occupied. Thus, if he throws a cinque and has no man on his Six or Cinque point, but has one on his Quatre point, he must bear that.

Again, should a player throw Six Ace, and have only one man on his Six point, he may, if he chooses, play up an ace from his Six point, and bear the Six from his Cinque point.

If, on the other hand, a low number is thrown, and the corresponding point hold no men, they must be played up from a higher point, thus, if double aces be thrown, and there are no men upon the Ace point, four men must be played up from the higher points, or a less number played up and taken off.

Doublets have the same value as in the earlier stages of the game.

In bearing, should the adversary be waiting to “enter” any of his men which have been hit, care should be taken to leave no “Blot,” or uncovered point. Should a blot be left and captured by an adverse man, the man so captured must be entered in the adversary’s home table, and carried home, before its owner is entitled to bear another man.

Scoring.

The player who bears all his men first wins a “Hit” or single game, provided his opponent has borne off one or more of his men.

But if a player has borne all his men before his opponent has borne any, that player wins a “Gammon,” equivalent to two games or hits.

If the loser still have one or more men in his adversary’s “Home” table, or waiting to enter, when the winner has borne all his men, the latter is considered to have won a “Backgammon,” provided that the loser has not previously borne a man.

A “Backgammon” is usually held to be equivalent to three hits or games, although sometimes, by agreement, it is reckoned as a quadruple game.

But if a player have one of his men taken up, after he has borne one or more men, he cannot lose more than a “hit,” even though he have not carried his man out of the adversary’s “Home” table when the game is won.

It will be seen by Table No. 2 that the most advantageous throw at the outset of game is doublet aces, as it blocks the “Bar point,” and secures the “Cinque point,” so that the adversary’s two men cannot move if he throw either quatre, cinque, or six. This throw of doublet aces is sometimes conceded to inferior players, at the commencement of a game, by way of odds.

As the main object of a player consists in bringing his men into his home table, all throws that contribute towards that end, and prevent the adversary from doing the same with regard to his men, are advantageous, and vice versâ.

During the progress of the game, it should he the endeavour of a player to block up or detain a part of his opponent’s men, and to prevent his adversary from re-entering such of his men as may happen to be taken up.

Illustrative Game.

The first part of an illustrative game will now be given to render the above explanation more complete. The game is not played on scientific principles, but merely to show our readers the ordinary moves of the game.

The players are supposed to sit, and the men to be placed as in the diagram given above (Fig 35). The players throw to decide who commences, and White wins the throw.

White 6.1	secures his Bar point.
Black 5.1	plays one man to his Bar point.

This may appear to be a risky move on the part of Black, considering that he is offering a blot to his antagonist, but as will be seen in Table No. 3, the odds are slightly against being hit at the distance of six, when the fifth point is occupied. Should the blot not be taken up, Black will probably be able to cover it next move and greatly improve his position.

White 4.2	plays from adversary’s Ace point, and takes up blot.
Black 4.3	enters on Quatre point and secures it.
White 6.5	secures adversary’s Bar point, and plays Cinque to own 8th.
Black 6.3	play one man from adversary’s Ace point.
White 3.1	takes up blot and plays an ace to own Bar point.

Here White might have played a safer game by making his Cinque point, and thereby attempting to block up the two black men.

Black 5.3	enters at Trois point and plays cinque from adversary’s 12th.
White 2.1	makes his own Cinque point.
Black 5.3	makes his own Trois point.
White 2.2	plays two men from adversary’s Bar to adversary’s 11th point.
Black 6.2	plays one man from adversary’s Trois to adversary’s 11th point.

Black might have taken up the blot, but he would be foolish to give up his adversary’s Quatre point (an advantageous position) for the sake of sending back a man to enter a comparatively open table.

White 6.1

plays one man from own 10th to Trois point. The game will now stand as in Fig. 36.

The Average of the Throws.

Before commencing the tactics of the game, it is desirable that the reader should become acquainted with the following data, which will aid him considerably in settling doubtful points of play.

Firstly, let us consider what number of points can reasonably be expected to be thrown, one throw with another. This can be made clear in a very simple manner. All throws possible are as follows: —

To this has to be added 42, because doublets count double the number of points shown on the face of the dice. Consequently the whole number of points is 294.

Now it will he readily seen from the above table that there are 36 different throws, and 294 divided by 36 show that eight is a reasonable number of points to expect for each throw on the average.

Secondly: if a player wishes to know how often in 36 throws he can expect to throw an ace, all he has to do is to count the throws in the first column and add the top row of the other columns, and he will be able to decide at a glance that an ace can be thrown in 11 throws out of the 36, and consequently he has 11 throws in his favour, and 25 against him, or roughly, over 2 to 1 against.

In the same way the other numbers can be seen, but perhaps not quite so readily.

The general rule for finding in how many ways any particular number can be thrown, either on one of the dice or by adding together the numbers on both, is as follows: neglect the two columns in which the number wanted is placed, and examine the left-hand corner of the table cutoff by these columns for any throws, whose sum make up the number wanted; then add the numbers of throws so found to 11, which is the number known to exist in the neglected columns.

For instance, to find the number of ways of throwing four: —

Search the left-hand corner cut off by the 4th column and the 4th row, in which will be found, 1.1, 1.3, 2.2, 3.1; consequently there are 11 + 4 ways of throwing a four, i.e., 15 in favour and 21 against, or roughly 4 to 3 against.

The Tactics.

1.  At the commencement of a game at Backgammon, the principal objects you should have in view are, firstly, to secure your own or your adversary’s Cinque point, or even both; secondly, when those points are secured, to play a pushing game, and endeavour to gammon your opponent.

2.  The next best point, after the Cinque point in the home table has been secured, is the Bar point, as by securing it you prevent the adversary running away, if he throws doublet sixes.

3.  When your Cinque and Bar points are secure, you should prefer to make your Quatre point in your home table in preference to the 9th point.

4.  These points being gained, you will have a fair chance of gammoning your opponent, more especially if he is very forward. In order to do so, however, it will be necessary to vary your game according to circumstances. Suppose your opponent’s home table is very ragged, it will be your interest to open your Bar point, in order to oblige him to come out of your home table with a six, in which case he will leave two blots. Then, if your men are properly “spread,” — i.e., not crowded on any one or more points, — you may not only catch the man which your opponent brings out, but will also have a fair chance of taking up the man left behind. But if your adversary has a blot in his home table, it will then be advisable for you not to make up your home table, but leave a blot in it; and if you are taken up, you will have a probability of getting a third man, which will render a gammon exceedingly probable.

5.  If you are not particularly desirous of winning more than a “Hit,” you should endeavour to gain either your own or your adversary’s Cinque point; and if you fail in this, by being hit by your adversary, who is also more forward than you are, you should play a bold game. Thus, place a man upon your Cinque or Bar point, and if your opponent fails to hit it, you may then “cover “ — i.e., place another man on the man already there — the blot yourself, and play a forward game instead of a back one.

If, on the other hand, the blot is taken up, a back game must be resorted to, and the more blots offered and taken up the better.

It should be your endeavour, when playing the back game, to gain your adversary’s Ace and Deuce points or Ace and Trois points, and you should be particularly careful to keep three men on your adversary’s Ace point, in order to have it in your power to hit a blot, and at the same time keep possession of this very important point.

6.  We will now give a table, showing the best way of playing any throw at the outset of the game.

In the above tables it is shown how to play certain throws differently, according as the player desires to play for a “Hit” or a “Gammon.” It may occur to some of our readers that all players desire a gammon in preference to a hit. That is doubtless true; but no player should thus early in a game risk a hit, in order to win a gammon, except under the following circumstances: Suppose A and B are two players (contesting a rubber of three games), and A has already won the first game. Here B especially desires to win a gammon, and thereby the rubber, whereas A has only to win a hit to secure the rubber. Consequently B has to play a more risky game.

7.  If it appear inadvisable to spread your pieces, endeavour to escape with one or other of your distant men.

8.  When compelled to leave a blot, you should do so where there is the least chance of its being hit by the adversary.

Table No. 3 shows the odds against being hit on any point at every possible distance from the adversary.

It may be noticed that the preceding table differs from any other already given in books of reference on this game in two respects; namely, (1) it includes the last five long ranges; (2) it gives the odds of being hit on a Twelve as being 11 to 1 instead of 35 to 1. The latter was an error originally made by Hoyle, and carelessly followed by all subsequent writers.

It will be obvious that 33 to 3 or 11 to 1 is correct, when it is considered that there are thirty-six ways in which two dice can be thrown, and doublet six, doublet quatre, and doublet trois will all hit a twelve, namely, if two of the first, three of the second, or all of the third are used. Twenty-four can only he played under the following conditions. Doublet Six is thrown; the thrower must have a man up, and the Six point in his adversary’s table must be vacant. Then the man will be entered and brought home to Ace point. It is merely included to render the table complete.

Backgammon players may justly urge, if a mistake has so long existed about the Twelve, how can they be sure this table is correct?

The reply to any such question is as follows: — If the second row of figures in the “Exact Odds” column is added up, it will be found to make the total of 114. Again, each doublet (of which there are six) will hit four separate points, and each of the other throws will hit three separate points. For example, “Quatre Trois” will permit a man being played to 3rd, 4th, or 7th points distant from its previous position.

Six sets of doublets (hitting 4 points each) touch 24 points. Thirty other throws (hitting 3 points each) touch 90 points, making 114, which corresponds with the total obtained from the preceding table.

No throw, therefore, has been forgotten; and it is almost incredible there should be two errors still, when all writers agree about the table’s correctness as far as the first eleven numbers are concerned.

9.  Table No. 3 may be summed up thus: — If a blot must be left within six of adversary, leave it as near as possible; but if a blot must be left more than six points distant from adversary, leave it as far away as possible, with two exceptions — eleven is safer than twelve, and seven more advantageous than eight (see Problem No I). The table only gives the danger of leaving one blot; consequently, if two or more blots are left, the risk of being taken up is of course increased. On the other hand, if any intervening points are in the possession of the player leaving the blot, the odds are decreased.

10.  When compelled to leave a blot, choose a point which is more likely to be covered next throw than one which is less likely, even if the chance is slightly greater of being hit on the point chosen. For instance, leave a blot seven away from an adversary in preference to one nine away, if the point chosen is more likely to be covered, or more valuable when covered. Notwithstanding that it is 6 to 1 against being hit on a nine and 5 to 1 on point chosen.

11.  In the rules for playing any throw at the outset of the game, variations are pointed out which are to be followed when it is all important to win a gammon, and you are recommended to make some blots chiefly on your Cinque point. The odds are only 7 to 5 against your man being captured, and if your adversary succeeds in hitting it, your tactics must be changed; you must give up all idea of a gammon, and go in for securing a Cinque, Quatre, or Trois point of your opponent, and be careful how you suffer him to take up a fourth man.

12.  When the numbers shown on the face of the dice are not available to make points, let them be used to make preparations for securing points; spread your men so that you may reasonably hope to make a point the next throw; but do this only while the adversary’s table affords temptations in the shape of blots, or at any rate facilities of entering any man that may be taken up.

13.  Never make two or more blots in your home table, even when your adversary has left it; for this reason, your adversary will immediately play a bold game, and you will be powerless to prevent his placing his men to the best advantage, because owing to the blots in your table you will fear to take him up.

14.  It is frequently good play to take up a blot of an adversary and leave one of your own in its place, if he cannot hit you, except with double dice — i.e., by throwing a number over six, — as it is 5 to 1 against his doing so. If playing only for the hit, and you have already two of your adversary’s men up, you should avoid even this risk.

15.  Beware of “crowding your game” at any time — i.e., getting a long string of four or five men on any point, — but more especially is this to be avoided on the Deuce and Trois points in your home table. Such men are practically useless, and the struggle has to be carried on by stragglers, perhaps at a distance from home, and certainly at a disadvantage.

16.  If you have two or three captives and an indifferently furnished home table, hurry your men forward, so that you may be enabled to make points, and take your adversary up as soon as he enters.

17.  If you crowd your game in attempting to save a gammon or to win a hit, you frequently defeat your own object: your adversary, finding you are becoming cramped and have an open table, leaves blots, and otherwise plays his game to the greatest advantage to himself.

18.  When your opponent has secured his Cinque and Bar points, linger no longer than you can help in his power, or you may be hemmed in.

Back Game.

19.  At the commencement of a game or rubber do not play for a “back game” — i.e., exposing of blots unnecessarily, and otherwise waiting for the opponent to make blots, — because by so doing you play to a great disadvantage, and run the risk of losing a gammon in order to win a hit.

20.  If you are obliged to leave a blot, upon entering a man in your adversary’s table, and have it in your choice to select one of two, always choose that point which is the least advantageous to him.

For example, let us suppose it is your opponent’s interest to take you up, immediately you enter. In that case you should leave the blot on his lowest point; that is to say, on his Deuce rather than on his Trois point, and on his Trois in preference to his Quatre point. All the men the adversary plays upon his Trois and Deuce points are deemed as lost, being in a great measure out of play; and consequently his game will become crowded on those points and open elsewhere, which may enable you to annoy him more than you otherwise could.

21.  There are two principal reasons for playing a back game. (1) If your adversary has been throwing very high, and is in consequence so forward, that you have no chance of winning a hit unless you can obtain a good home table and hit a blot of your adversary, then the best policy is for you to leave blots for him to take up, and retain your two men in his home table as long as possible.

(2) If you are so hemmed in your adversary’s table that escape is practically hopeless; in such a position at once leave blots, as four men securing two separate points in your adversary’s table, especially should they happen to be his Quatre and Deuce points, will sorely annoy him, and render his home decidedly uncomfortable, even if not quite unbearable.

22.  From these hints on back play two obvious conclusions may be drawn: firstly, it is advisable to block your antagonist as soon as possible, in order to force him to play a back game, and thereby risk a gammon to gain a hit; secondly, you should never take up, unless obliged, blots purposely left by a skilful antagonist, as if it is good play on his part to leave blots, it cannot be to your advantage to take them up.

It should be clearly understood that the last hint refers only to blots intentionally left, and not to those exposed at some risk, which, if not hit, will in all probability gain a point hitherto open.

23.  When you have taken up two of your adversary’s men, and happen to have three or more points made in your home table, never fail to spread your men, in order either to make a new point in your table, or to be ready to hit the man your adversary may happen to enter. As soon as he enters one of his men you are to compare your game with his; and if you find his equal or better than yours, never fail to take his man up, if you have the opportunity, because the odds are in your favour against his hitting you.

This risk you ought to run, as having two men of your adversary up, you should not come to much harm, even if he should capture you.

There is, however, an exception to the rule; viz., if you are content with winning a hit, and your playing that throw otherwise gives you a better chance for the hit, you ought not to take up the man, unless you can do so without risk.

Management of the Home Table.

24.  To enable a player to manage his home table properly, and to decide at a glance when his adversary’s table is in such a state as to justify a blot being left, we give the following tables: —

25.  If, when in possession of a captive, you are compelled to leave a blot (capable of being hit), leave it, if possible, so that it necessitates doublets being thrown, to enable the adversary to enter and hit the blot. This is equally the case, if you happen to have five points covered in your table; it is 35 to 1 against the adversary hitting you with any named doublet, and any other chance is but 17 to 1 against him.

26.  If you are only playing for a hit, you should take up only one or two of your opponent’s men, as a greater number is frequently more dangerous, without being more effective.

27.  Avoid, if possible, breaking up the Six or Cinque point in your home table, more especially towards the close of the game, as after having done so, even if you take up a man, you cannot hope to detain him long.

28.  There is frequently a doubt in a player’s mind whether at a certain period in a game he ought to run or stay in hopes of capturing his opponent. This point can be easily settled by reckoning which has the more forward game, you or your antagonist. The method of estimating your position is as follows: firstly, you should pair any man you and your adversary may have on equivalent points, that is on points directly facing each other; then calculate how many points are required to bear the unpaired man or men which are at the greatest distance from home, and do the same with every other of your men unpaired. Then make the same calculation with regard to your adversary’s men that are unpaired, and compare the totals; if you have at least ten points less than your adversary, you are presumably a throw ahead of him, and should run; if the difference is less than ten, you should be guided by the respective home tables. If on the other hand, you are ten points more than your opponent, you should play a waiting game, as long as possible, or until a high throw so changes the aspect of affairs, that you think wiser to run for the hit.

Carrying Men Home.

29.  When you consider yourself in danger of losing a gammon, in order to lose no point in carrying your men home, you should carry the most distant men to your adversary’s Bar point, that being the first stage; the next one is six points farther, viz., the twelfth point in your outer table; the next stage is to the Six point in your home table. This method is to be pursued till all the men are brought home, except two, when, by losing a point, you may often save your gammon, by putting it in the power of cinque or quatre doublets to do so.

Bearing.

30.  If your adversary be greatly ahead of you, never play a man up from your Quatre, Trois, or Deuce points, while you still have men on the Six point, because nothing but high doublets can give you any chance of success: for this reason, therefore, instead of playing an ace or deuce from the aforesaid points, always play them from your highest point; by which means the throwing of high doublets will, by easing your Cinque and Six points, prove of great advantage to you; whereas had your Six point remained loaded, you might probably have been obliged to play up the cinque or quatre doublets.

31.  Prevent your adversary from bearing his men to the greatest advantage, when you are running to save a gammon: suppose you have two men upon his Ace point, and several others in the two outer tables, though you should lose a little in putting the men into your home table, yet it is your interest to leave a man upon the adversary’s Ace point as long as possible.

This method of play will prevent your adversary from bearing his men to the best advantage, and will also give you the chance of his making a blot which you may hit. If, upon calculation however, you find there is a fair probability of your saving your gammon, never wait for a blot, as the odds are considerably against the double event of his being obliged to leave one and of your hitting it.

32.  Be over bold rather than over cautious; games are more often lost by excess of timidity than by rashness.

33.  Be careful to distinguish what prompts your adversary to leave blots; as, if he is playing a back game, you must avoid taking them up; and if he is playing a bold game, they should be taken up even at some risk.

34.  It may be as well for players to remember the two following facts, which may prove of practical value, and to leave more abstruse calculations alone.

It is just as likely that one of two blots 7 and 8 points respectively distant from an adversary will be hit, as one blot 2 points distant, the odds in each case being 2 to 1.

It is just as likely that one of two blots 7 and 9 points respectively distant from an adversary will be hit as one blot one point distant, the odds in each case being 25 to 11.

The Chance of Winning or Saving a Gammon.

35.  Suppose your home table is made up, and you have taken up one of your adversary’s men; further, suppose your opponent has so many men abroad, that he will probably require three throws to take them home.

It is about an even chance that you win a Gammon.

In all probability you will bear three men, before you open your Six or Cinque point, and he will take two throws before he enters his man, and two throws more before he puts that man into his home table; then the other men abroad will take three more throws, or seven in all.

You have twelve men to bear, which will probably require seven throws, as you will have to play up twice while bearing your men. No mention is made of doublets on either side, the chances of that event being equal for each player.

Again on the supposition that it takes nine throws to bear all your men, you will have a reasonable expectation of gammoning your opponent if he has six men on your Bar point and the rest in his home table.

Six men at the above-mentioned distance from home require nine throws at the average of 8 points a throw (see “The Average of the Throws”) to get them home. The above calculations will enable the more forward player to estimate roughly how much he ought to be ahead to have a chance of winning a gammon: and they will enable a player to judge when he is far enough ahead; as in that case he should refuse to take up a blot, if he incurs any risk by so doing.

36.  When a Set — i.e., three games up or the best of five — is played at Backgammon, the odds are as follows: —

When A has won 1 game, B none, it is 3 to 2 on A.
When A has won 2 games, B none, it is 3 to 1 on A.
When A has won 2 games, B one, it is 2 to 1 on A.

Problems.

The following few problems are given, as illustrating various points of interest in the game.

The first is a good instance of Backgammon foresight and good tactics.

No. I.

Suppose that all the points in both home tables are covered; also that A has one man to carry home, but that B is in possession of A’s Bar point, and lies in wait to catch A’s man. If A pass him, A will in all probability win the Hit.

Suppose also that A has the choice of running the risk of being hit by a seven or an eight; which of these two equal risks is it better for him to run?

The answer is, the seven, for the following reasons: Firstly — If B does not throw a seven, it is nearly two to one (actually 23 to 13) that by his next throw A will either take B up or pass beyond him.

Secondly — If A’s throw should happen to be under seven, and that consequently he cannot hit the hostile man nor pass beyond him, yet he may play that cast at home and run the same risk as before.

Whereas, on the contrary, had A left the blot upon the 8, he would have made a bad choice.

Firstly — Because if he should escape being hit by 8, yet he would then have only an even chance (actually 17 to 19 against) for either hitting B or passing beyond him.

Secondly — In case A’s second throw should happen to be “Six Ace,” he would be obliged to play within two or one of his adversary’s men, and his risk of being hit would be enormously increased.

No. II.

A has borne thirteen men, and has two men on his Deuce point to bear; B has thirteen men in his home table, and two men up. B has to throw, and to name the throws both for himself and A, but a blot is not to be hit by either player.

What throws must B name in order to save his Gammon?

B calls for himself doublet aces, whereby he enters two men upon A’s Ace point. B calls doublet aces for A, and consequently A can neither bear a man nor play one up.

Then B calls for doublet sixes for himself and carries one man home to his Six point, and the other he places upon A’s Bar point. B now calls six ace for A, so that A has still one man left to bear, and then B calls for himself doublet sixes, which enable him to bear two men and save his Gammon.

No. III.

Suppose the men to be placed as shown in the diagram, who has the better game, A or B?

A has, because he ought to play, if possible, an ace or deuce from B’s Ace point, in order to take possession of B’s Deuce or Trois point, or both, as occasion may offer; and since he is already in possession of B’s Quatre point, he may more easily bring these men away, if he finds it necessary, and he will also have a resting place by the convenience of that point, which at all times during the game will give him an opportunity of running for the hit or staying to worry B, if he thinks proper. Whereas B cannot so readily come from A’s Trois point.

No. IV.

With the men arranged as in the diagram, who has the better game, A or B?

A, because the Ace and Trois points in your adversary’s table are not so good as the Ace and Deuce points, because when you are bearing your men, the Deuce point often saves you from making a blot, which is almost certain to happen, if the adversary has possession of your Ace and Deuce points.

A should further endeavour to be hit as often as possible to keep his game backward, and for the same reason should refrain from hitting any blots, which B makes.

No. V.

Who has the better of the Hit, with the men in the position shown in the diagram?

It is anybody’s game; but the difficulty lies with B, who in the first place should endeavour to gain his Cinque and Quatre points; and when that is effected, he should play two men from A’s Cinque point, in order to oblige A to leave a blot, if he should throw an ace. Should B be successful in capturing one of A’s men, he will have the better of the Hit.

No. VI.

Where A and B shall both play as fast as usual, and yet A, who apparently is in a hopeless plight, shall make the game last probably for hours.

This is the nearest instance of a draw that is possible at Backgammon.

Suppose B to have borne thirteen men, and that A has taken up the two remaining men.

Furthermore, let us suppose A has fifteen in B’s home table; viz., three men on each of B’s four highest points, two on B’s Deuce and one on his Ace point.

A should proceed as follows: Let him bring his fifteen men home by 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 should leave a blot or blots in the advance of his column; which effected, B hits one of them, and A taking care to have two or three men in B’s home table, is ready to hit B’s man should it pass the barrier of A’s men. And as there is every probability that A will have the opportunity of taking up the other man, A has it in his power to prolong the game to almost any length, provided he takes care not to open such points as might be hit by one of the higher doublets, but on the other hand always to leave blots on the points nearest to B’s men.

Laws of the Game.

1. At the commencement of a game either player, before he makes his first throw, but not after, may require the board to be properly dressed.

2. If any player neglect to place all his men before making his first throw, he cannot afterwards rectify his error. If fourteen men are played with, there is no penalty, because it is a disadvantage.

3. No throw is to be considered a throw unless properly thrown. To constitute a proper throw, the dice must be cast from the box, and both of them must rest flat on the surface of the table in which they are thrown, without resting either against a man, the edge of the table, or each other.

4. All faulty throws must be thrown again; there is no penalty beyond this.

5. Should a die be touched while rolling, or before it has been called by the thrower, the player who is not at fault, may name that part of the throw, provided there is any dispute on the point.

6. After a player has called his throw, the dice may be taken up, and the player is bound by his call.

7. If a man or men belonging to a player are moved by him from any point, that man or men must be played, unless he previously declares he wishes to adjust it or them.

8. No man is considered to have been played upon any particular point until placed there and quitted.

9. A mistake cannot be rectified by a player, after his adversary has thrown, except by mutual consent.

10. The whole of a throw must be played if possible, but if only a part can be played, the thrower has an option which part.

11. If any man or men be borne by a player before he has entered a man taken up, which he was obliged to enter before he commenced to bear, such men so borne must be entered again in the adversary’s home table, as well as the man taken up.

12. In bearing, a throw does not represent merely the exact number cast, but is also valued thus: —

    A six can take off a man from the Six point, or a man from the highest point occupied.

    A cinque can take off a man from the Cinque point or a man from the highest point occupied, provided the Six point is vacant.

    And so on with other numbers thrown.

Russian Backgammon, or Tric Trac.

This variety of the ordinary game is much in vogue in Russia, Germany, and other parts of the Continent, and, as it is occasionally adopted in this country, and some of our readers may wish to be instructed in its peculiarities, it is necessary for us to mention it briefly.

It is played with an ordinary Backgammon board, men, dice-boxes, and dice, and is a game for two persons, who sit opposite to each other in the usual way.

The board is not furnished before beginning the game, but the men of both players are entered in the same table by alternate throws of the dice, and are moved in the same direction, viz., from any table chosen, on which they are entered, round the board to the home table.

If the upper right-hand table is chosen for entry, then the course of the men is as shown in the diagram; or should the table marked “Home” be chosen for entry, then they are moved in the opposite direction.

The lead having been determined as in the English game (“Description of the Game”), the winner may either play the two numbers thrown, or he may throw again with two dice.

A player, having thrown, may enter two men in the table of entry, or he may enter one and play it on. Say he throws Six Cinque, he may enter a man each on the Six and Cinque points, or he may enter a man on the Six point and play the cinque out of the table of entry.

But should a player be taken up, he is obliged to enter the captured man before moving any of his other men on the board. Thus, if Black holds the Six and Trois points when he has captured a White man, and White throws Six Trois, White cannot enter his men; and as he may not play any other men out of the table of entry, or from any other part of the board until he has entered the men, he loses the throw.

If doublets are thrown, the player is entitled and bound not only to play them as in ordinary Backgammon, but also to play the complementary ones on the opposite faces of the dice. Thus, if he throws Cinques, he must first use, either for entering or playing, four cinques and then the four deuces; he also has a second throw.

This privilege given to doublets is not, however, allowed to either player when he throws his first set of doublets in a game.

No player is allowed to play any of the complementary doublets until he has completely used the doublets thrown, and he is not entitled to another throw until he has played the doublets thrown and the complementary ones.

If a player throws Deuce Ace, he is entitled to play any pair of doublets and their complements, which he may choose; and he is entitled to this even though he has not thrown doublets before. In that case, the fact of having thrown Deuce Ace does not entitle him to the privileges or doublets the first time he throws them.

Among some players it is customary, if a player cannot play the whole of his throw, or any part of it, for his adversary to he called on to play. But should the adversary in playing open a point, enabling the first player to play, the latter is bound to complete the throw as far as possible; but if, after the adversary has played, the first player is unable to play, the adversary again continues.

For instance, if a player throws doublet sixes and is only able to play two of them, he calls on his opponent to play a six; and then, if the caster is able to play the fourth six, he continues with doublet aces; and, if he can use them all, he is entitled to another throw.

But if the caster cannot continue with the fourth six, he calls on his opponent to play it, and the caster in this case forfeits his right to the second set of doublets and another throw.

If neither player can play any part of or complete a throw, the remainder of it is lost, and in case of doublets or Deuce Ace, the caster does not throw again.

In all other respects the game is similar to ordinary Backgammon.

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