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Subject: THE INEXHAUSTIBILITY OF CHESS

Author: William Dozier

Date: 08:59:29 05/19/99


the Famous logician and ecionomist, the late JohnStuart Mill, tell us, in his
Autobiography, that at one oeriod of hhis life he was seriouisly tormented by
the thought of the exhaustibility of musical combination. The varios sounds, he
reasoned with himself, can be put togather only in a limited number of ways, of
which but a small proportion are beautiful. Most of these have been already
discovered, and there cannot be room for a long succssion of Beethovens and
Mozartz to strike out, as these have done, entirely new and surpassingly rich
veins of musical beauty. A similar doubt with regard to Chess has probably
crossed the minds of maney chess players. A little reffection and calculation,
however, will soon show th eir misgiving to be no less chimerical than was that
of Mill.
To estimate the actual number of ways of playinf even a very few moves is beyond
the power of cacualtion, but to get somthing of an approximation to that number
is very simple. Taking an average varation of the opening as usually practiced,
we find that the player has tewnty-eight, thirty and-three way of playing the
second, third and fourth moves respectively; twenty-nine,thirty-one thirty three
being corresponding nubers of the second player. Of course both players, on
their first move, have a choice of twenty moooves. On the hypothesis that the
nuvber of replies open at each move is always the same, whatever the preceding
moves may have been, and that the foregoing figures give those numbers, the
numbers, the number of possable ways of playing the first four moves only on
eachside would be 313,978,584,000. if then, then, anyone were to play without
cessation at the rate of one set a minute it wpild take hiim more than six
hundred thousands years to go through them all.It woud be difficult to say
whether the above number is in excess or defect of the true one, but perhaps we
may safely affirm that it is not likely to be out  more than 20 per cent either
way. When we bear in mijnd that the number of possable ways increases ffor maney
moves some thirtfold for each move added, it is plain that the number of ways of
playing the first twenty or thirty moves oneach side is so great as to utterly
trancend the grasp of the imagination. No doubt the tatio of the plausible to
the possible number of moves at every stage is small, but after every allowance
has been made for that fact, the varieties of play still remain enormous. In a
very rough way we may easly easily extend our survey, After the first four moves
in commom form of the Giuocc Piano opening, White has thirty-three possible
moves in the Evans Gambit he has a choice of thirty-two.moves. Let us assume,
then, for convenience of calculation, that for the nest six moves on each side,
after the firs four on eachside have been played, there is always achoice of
thirty different ways of playing, an hypothesis probably below rather than above
the actual fact. We this get by combinatin with the result give above, that the
number of ways of paying the first ten moves on each side
is(169,518,829,100,544,000,000,000,000,000).

On this basis, and cosidering the population of the whole world to be 148
Million (Levasseur's estimate), More than 217 billion of years would be nedded
to go through them all, even if every man,woman, and child on the face of the
globe
played with cessation for that vast period at the rate of one set per minute,
and no set were repeated.(These figures have not been changed since the
publication of the first edition, publised about the turn of the century-1960)

This paragraph was take out of Book_The Principles of chess/By James Mason./NYC.

Enjoy/Respectfully/William



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