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opening. Games in which a rout of the defensive position occurred were seen only where the
opening was seriously misplayed. Most importantly, no adversary openings were found which
could produce a positive score in a series of games starting from the same opening position.
All games seen to date demonstrate the difficulty of attacking the standard position. The
defense is so compact and coherent that it resists all attacks. There are practically no weaknesses
that can be exploited. Even if some lines are found where serious weakness can be provoked,
strong responses will be found: there will always be other sequences of the standard opening to
counter effectively, or we can move into one of the large number of close variants.
All the close variants are almost as strong as the Beginner s Game, and some of them may
even be stronger, when responding to particular adversary openings. The large number of
possible lines, all retaining the basic character of the standard opening, insures that the opening
will be able to resist any opposing play, while retaining its basic form.
On the offense, there is always a wide range of options present. The open field in front of
the position makes almost all the pawn moves playable. The pieces all have good relocation
squares, and are ideally placed to support the pawn advances. Various queen placements and
castling options exist as well. The attacking potential of the Beginner s Game has been
demonstrated in almost every single game played with it. It seems to be a natural consequence of
the standard opening that it always uncoils into strong attacks.
Can other B-systems openings be refuted? Certainly some will prove useful only in defined
contexts, because they contain forward placements that can t always be supported, or because
other members in the system are more effective in developing along given lines. The
Beginner s Game is probably the most generally playable of all the B-system openings. But many
Can It Be Refuted? Is It Optimal? 123
other new openings in the system will prove to be valid against most lines of adversary play, and
so worthy of inclusion in a revised compendium of chess openings.
It is almost certain that the close variants of the Beginner s Game are valid: their similarity
to the standard opening virtually guarantees it. They may be considered as part of an overall
system of play, but each one is also a valid opening in its own right. Among the more distant
variants, there are many examples of generally playable openings, even if many others are
suitable only against certain conventional openings, or against other B-system openings.
In summary, it is highly unlikely that the Beginner s Game, its close variants, and many of
the better distant variants of the B-system will ever be refuted.
Optimality:
In the early days of wild excitement after the discovery of the Beginner s Game, the author
staggered about considering the consequences if it should prove to be optimal - it would mean
that the game of chess was in fact a puzzle waiting all along to be solved. There s a real possibility
that it is so. If there is such a solution, the first eight moves of it have likely been found.
There are various possible definitions of optimality. The strong definition is that it is
always possible to win or draw using the opening. This type of optimality is extremely hard to
prove, given the immense number of possible games, even from an advanced starting position. A
simpler, more operational definition would be that the opening results in the largest percentage of
wins (and draws) in play at master level between players with similar ratings.
The author feels confident that the Beginner s Game will prove optimal in the operational
sense. Experience in play will soon put this hypothesis to a test. Proving optimality in the strong
sense is another question altogether.
If an optimal opening according to the strong definition does exist, it is likely to have the
characteristics of the Beginner s Game. Principal among these is use of the same opening for
black and white, and ability to confront any adversary with a standard deployment. The existence
of a small and well defined set of related variants, such as the close variants of the B-system,
would also likely be a part of an optimal system. These variants offer some flexibility in
responding to those few situations in which an adversary could possibly develop an advantage.
A true test of strong optimality would require the compilation of millions of games, with
extensive research into lines that put the standard opening in difficulty. The vast majority of
these games could be generated by computer, but still with significant human participation. The
Beginner s Game was not found by a computer, and the best defenses to it may not be found by a
computer either. A real test of strong optimality can only be done with massive experimentation;
but even a limited experiment would furnish an excellent indication of operational optimality.
With highly specialized chess playing programs alone we should be able to come very
close to a definitive response to the question of strong optimality. The participation of many
experts would still be necessary: not only expert players, but also designers and analysts capable
of modifying and improving these programs. Any competent group that decides to dedicate
themselves to this research will certainly find a receptive audience for their findings.
With even a modest amount of organization, it should be possible to collect and build
databases of games generated by players of this system. The chess playing community could be
enlisted to research advanced positions, and submit results for compilation. Using large game
databases, we can identify problematic lines, and begin pruning the move trees. With the
participation of a large number of interested persons, it should be possible to obtain a very
reliable response to the question of strong optimality.
Because the entire process is one of gradually approaching absolute certainty, research
into the optimality of the Beginner s Game may go on for many years. And if the final answer is
affirmative, it doesn t mean the end of chess, or even the end of chess as it has been played until
the present. It does mean the end of the real competition between humans and computers. They
will finally be unbeatable, as has always been predicted. But this shouldn t conceal the triumph of
the human over the computer, because most of the moves of their lookup game will have been
taught to them by humans. Moreover it was humans who invented, built, and programmed them!
The author ventures the following odds on the possible results of strong optimality:
White can always win or draw: more than 1/2
Black can always win or draw: about 1/2
In all this discussion we have not considered what is probably the best practical definition
of optimality: that the greatest number and variety of players can adopt the system and
immediately improve their game. Under this definition the Beginner s Game is definitely optimal!
The X series Experiments
The author ran a controlled experiment with the Beginner s Game to see how strong it is. A
series of 200 games was generated, played by the computer from the ninth move onwards, using
different personalities . Two thirds of the games used classical defenses, invented by the
computer. The other third of the games used strong custom defenses, such as those described
previously, invented by the author. Both sides had equal computing time, of 20-30 minutes.
The results of this experiment are impressive: the Beginner s Game won 58% and drew 28%
of the games. Results with black were almost as good as with white. Another experiment showed
that, using this system, a beginner can play at master level thru the first 12 moves! Although far
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