To the Editor of the St. James’s Gazette
Sir,—I am honoured by the attention such an authority as “Cavendish” has given my letter on Lawn Tennis Tournaments, and hope you will afford me space for a brief reply.
He says “the primary object is to give the 1st prize to the best man,” but that it is “a matter of comparatively small concern” to give the 2nd to the 2nd best. Why so wide a distinction between them? Is it fair that the one should be certain of his prize, while the other has only an even chance of his?
Again, he says that, under my system, “the prize-winners could easily be predicted, and the interest of the whole meeting would suffer.” Is he not ignoring the “chances of the board,” where the element of luck enters largely, even under my system? The man reputed best is by no means certain of the 1st prize: many things may prevent his playing best. Also, does he find that the interest of a rifle-match suffers, because he who makes 2nd score is certain of getting 2nd prize?
Again, he thinks the present system “entices” 2nd-class players to enter more than mine would. Let us see what he and I, representing the two systems, would say to players before a tournament of 32 with three prizes. (We may assume that every one hopes to play at least up to his reputation.)
To the man reputed 2nd best, he would say, “If you play up to your reputation, your chances are—of the 2nd prize, one half; of the 3rd, 1-4th; of getting nothing, 1-4th;” whereas I should say, “If you do so, you will get the 2nd prize.” Here undoubtedly I make the best bid.
To the man reputed 5th best, he would say, “If you play up to your reputation, your chance of a prize is about 1-4th; and even if, by great luck and painstaking, you play 2nd or 3rd best, it never rises above a half;” whereas I should say, “I admit that, if you only play up to your reputation, you will get nothing; but, if you play 2nd or 3rd best, you are certain of the proper prize.” Thus he offers a chance of 1-4th, where I offer nothing; and of a half, where I offer certainty. I am inclined to think that here also I make the best bid.
I agree with him that “all popular games have, and must have, an element of luck.” This is true of all games—whether of pure chance, e. g. pitch-farthing; or of pure skill, e. g. chess; or mixed, e. g. whist. My proposal is to make Lawn-Tennis Tournaments a game of pure skill, instead of being mixed: but this would not destroy, what he thinks necessary, “some hope, even in the breast of a second-class player, of success through fortune, if not through skill.”
He says the logical conclusion of my proposal, to make a match consist of games, is to make it consist of strokes. I admit it, but think that would be going too far.
He thinks a match consisting of games would be uninteresting, so soon as one of two even players got a little ahead, while under the present system “a lucky game on one side is often balanced by a lucky game on the other side.” And why should not the being ahead on one side be balanced by a lucky game on the other side? Suo sibi gladio hunc jugulo.
I believe that a system of handicapping, such as is usual in races, would be a much more satisfactory way of equalizing players, and thus giving all a reasonable hope of winning a prize, than the present lottery-system. But in any case I protest against the present absurdity of excluding a man, who has been beaten only once, from all further competition in a tournament with more than one prize.
May I add a few words in reply to “Corrigenda,” whose letter, in MS., you have kindly sent me? He thinks I am estimating too highly the chance of its happening that the players should be paired “in order of merit,” because I have not allowed for the rule “that the players draw for their oponents (sic) every time:” and he calculates that, with 16 players, the odds against this event are 21 to 1. Let me remind “Corrigenda” that I spoke of it as “an extreme case:” the odds against it, I do not mind admitting, are more than 21 to 1: how much more, I do not feel bound to say.
He also says that the absurdity I pointed out in scoring matches, where A wins twelve games to ten and yet loses the match, could never happen, because one must “always” win six games, not three, to win a “set.” I think that for “always” we should read “always in Corrigenda’s experience;” but I gladly accept a correction which strengthens my case so much. If he, who wins six games, wins a set; and he, who wins three sets, wins a match; than a player may actually win 27 games to 18, and yet lose the match!—I am, Sir, your obedient servant,
Charles L. Dodgson.
August 3.