BILLIARD HANDICAPS

WE have on several occasions been asked to explain the system on which handicaps should be made, and must confess that the ignorance displayed by the questioners has ofttimes been so great that we somewhat despair of being able to render ourselves intelligible. There is, however, a good maxim in instructing stupid children, that teachers should always bear in mind, and that is, that if they fail to make themselves understood, the fault is theirs and not their pupils. Now, in making a billiard handicap there has too often been one important fallacy apparently running through the minds of all alike, who have got bewildered over the subject. It is sometimes a consolation to find that there are others quite as stupid as ourselves, and our correspondent will perhaps be pleased to hear that a well-known professional ran his head against the self-same post of difficulty in writing on the subject of handicaps as he has.

But to render ourselves intelligible to the general public, we will at once explain the difficulty to be as follows.

We will suppose A, B, and C to be three billiard players, and that A can give B 10 points in 100, and also that B can give C 10 points in 100. How then should they be handicapped in a game of 100 up? The ready answer is, why of course A starts at scratch, B gets 10, and C 20, and probably the asker of the question is thought to be uncommonly stupid for asking anything so simple. However, the handicap, supposing the original points given— viz., A gives B 10, and B gives C 10, to be correct —would be unjust.

As perhaps the best method of rendering this point obvious would be to take a rather extreme case, we will suppose the case of three players who play in a ratio of, Cook, a first-rate amateur, and a very bad player. Now Cook could give the amateur 50 points in 100, and this amateur could give the bad player likewise 50 points in 100. Yet it is manifestly absurd to handicap these players as we did in the previous case—viz., making Cook start at scratch, the amateur receive 50, and the bad player 100. Now if we consider this last case for one moment, we shall see the secret of making a handicap. When we say Cook can give 50 points in 100, we simply mean that he on the average will score 2 while the other scores 1. Again, the amateur will score 2 while the bad player scores 1.

Therefore while Cook scores 100 the amateur will only score 50; but while the amateur scores 50, the bad player will only score 25; the handicap therefore should be—Cook scratch, the amateur 50, and the bad player 75.

Let us now apply this method to our former case. A gives B 10 in 100, therefore A can score 100 while B will only make 90; in other words, A scores 10 to B's 9. Again, B gives C 10 in 100, therefore B scores 10 to C's 9. What then should be the handicap? A of course starts at scratch, B of course receives 10; but what does C receive? Not 20, for he has to play B a game of 90 up and not 100 up. And as B can score 10 to his 9, it follows that while B is making 90, or nine tens, C will only make nine nines, or 81. For the handicap therefore to be fair, C should receive only 19 points instead of 20.

Now of course this difference of one point practically amounts to nothing. But then it is the system that we wish to explain.

Suppose we take this handicap. We suppose a good amateur player can give another 30 in 100, who in his turn can give 20 in 100. If we make the handicap 500 up, and simply handicap these men as scratch, 30, and 50, we commit a gross injustice, and probably make the limit man win to a certainty. The middle player, who can give the worst 20 in 100, can only score 10 to his 8; but if they play, as they would in the handicap, a game of 70 up, in which the middle player gives 20 in the 70, he will, in order to win, be obliged to score 7 to his opponent's 5; or, in the one case, 25 to 20, and in the other case 28 to 20. When, therefore, the game is made a long one, and the players are incapable of making particularly large breaks, the difference is considerable.

We have often heard it observed that a long game is in favour of the best player, and that consequently if a man can give another 15 out of 50, he can give him rather more than 30 in 100. This is, however, a fallacy depending on the fact that as a rule the giver of points has what is known as "a little in hand." All billiard players know that when two persons play, one giving points, the giver of points is always the favourite in the betting. Now it is obvious that if one man giving another 15 in 50 has say 5 to 4 the best of it, should he give 30 in 100 the odds on him would be more than 5 to 4.

The principle is somewhat akin to the fact, that should in any game the chances be slightly in favour of one player—never mind how slight, say 1,001 to 1,000—if they continue playing an infinite number of games, the chance of the one winning is reduced to an absolute certainty. Just so in billiards, if a player can give a trifle more than he does give by increasing the length of the game, the odds become greatly increased in his favour.

It should, however, be borne in mind that the better the players the longer must the game be made in order that any result may be arrived at.

Suppose two players like Cook and Taylor were to play a game of 50 up, the result would be a toss up. Again, were Cook to play a good amateur a game of 21 up even, the odds on Cook would be only slight, whereas if they play 1,000 up the odds would be 100 to 1.

In modern handicaps among professional players where the game is 500 up, each game may be made in one break, consequently the number of points that each one receives influences the result in but, comparatively speaking, a slight degree, If Taylor and Stanley meet in a match of 500 up, if 5 to 4 is laid on one man, the betting would scarcely alter by one making a break of 20. In making a handicap, therefore, among professional players, splitting hairs, like giving one man 100 points and another 110, is simply irritating to the players themselves without benefiting the receiver of most points. There should be some limit fixed in the number of points that separate the players; just as in an auction it is ridiculous when a man has bid £100 for another to bid £100 0s. 6d. If two men capable at times of scoring three or four hundred off the balls, are considered so nearly equal that one is considered only 20 points better than the other, it would be far better to put them level than to make a distinction between the two, the only result of which is to excite angry feelings in the mind of the receiver of points, which probably does his game more harm than the points do good.