Tab. I Day IV (e). J and R must be paired together, though they have a common superior.

Tab. I. Day IV (e). M is First-prize-man.

Tab. I. Day V (m). R and f must be paired together, though they have a common superior. J is `odd man'.

Tab. II. Day V (m). R is now the only man with one superior, and is therefore Second-prize-man.

Tab. I. Day V (e). J and f contend for the Third prize.

If this Tournament were fought by the present method, the 4 Prize men would be C,M,V,f: f would get the 2nd prize, and C and V the 3rd and 4th: i.e. the 5th best man would get the 2nd prize, and the 14th and 11th best the other two.

5. An equitable system for scoring in matches.

In order to make `matches' more equitable, I propose to abolish `sets' and make a `match' consist of `games'. Thus instead of `best of 11 games = set; best of 5 sets = match' (i.e. he who first wins 6 games wins a set; he who first wins 3 sets wins a match), where a player may win with as few as 18 games, and must win with 28, I would substitute `he who first wins 28 games, or who gets 18 games ahead, wins the match.' I therefore propose as follows: `For a whole-day, he who first wins 28 games, or who gets 18 ahead, wins the match: for a half-day, he who first wins 14 games, or who gets 9 ahead, wins the match.'

TABLE I. (Pairs.)
I.(e)II.(m)(e)III.(m)(e)IV.(m)(e)V.(m)(e)
A}*A}C}*C}C}M}M}*R}*J}*
B}C}*G}M}*V}*f}f}f}f}
C}*EM}*VJ}*J}*J}J}
D}G}*R}f}*a}V}R}*
E}*J}V}*A}L}R}*
F}M}*Y}J}*g}*g}
G}*P}a}G}R}*
H}R}*f}*L}*c}
J}*S}A}*R}*
K}V}*E}S}
L}W}J}*Y}
M}*Y}*P}a}*
N}a}*L}*g}*
P}*c}Q}T}
Q}f}*S}*c}
R}*g}W}
S}*B}*Z}
T}D}c}*
U}F}*g}*
V}*H}B}
W}*K}F}
X}L}*T}*
Y}*N}d}*
Z}Q}*h}
a}*T}*
b}U}
c}*X}
d}Z}*
e}b}
f}*d}*
g}*e}
h}h}*

TABLE II. (Superiors.)
I.(e)II.(m)(e)III.(m)(e)IV.(m)(e)V.(m)(e)
A...C...J(M)
BA(C)g()
C.........MV(f)
DCB(A)
E...GA(C)
FE(G)T
G......CL(M)
HGF(E)
J...M............R...Pr.III.
KJL(M)
LM.........g(f)
M..................Pr.I.
NPQ(R)
P...RJ(M)
QR...L(M)
R......M............Pr.II.
S...V...R(f)
TS(V)...g
UVT(S)
V.........f...J(M)
W...YS(V)
XWZ(Y)
Y......Va(f)
ZY...c(V)
a......f...J(M)
bad(c)
c...a(f)...R
dc(a)(f)
efh(g)
f..................MRJ
g...f.........R(M)
hg(f)d

6. Concluding remarks.

Let it not be supposed that, in thus proposing to make these Tournaments a game of pure skill (like chess) instead of a game of mixed skill and chance (like whist), I am altogether eliminating the element of luck, and making it possible to predict the prize-winners, so that no one else would care to enter. The `chances of the board' would still exist in full force: it would not at all follow, because a Player was reputed best, that he was certain of the 1st prize: a thousand accidents might occur to prevent his playing best: the 4th best, 5th best, or even a worst Player, need not despair of winning even the 1st prize.

Nor, again, let it be supposed that the present system, which allows an inferior player a chance of the 2nd prize, even though he fails to play above his reputation, is more attractive than one which, in such a case, gives him no hope. Let us compare the two systems, as to the attractions they hold out to (say) the 5th best Player in a Tournament of 32, with 3 prizes. The present system says, `If you play up to your reputation, your chance of a prize is about ¼th; and even if, by great luck and painstaking, you play 2nd or 3rd best, it never rises above a half.' My system says, `It is admitted 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, the one system offers a chance of ¼th, where the other offers nothing; and a chance of a half, where the other offers certainty, I am inclined to think the second the more attractive of the two.


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