Endgame Study


Importance

Professional players say that the greatest weaknesses of amateur
players are tactical reading and endgame evaluation. This has also
been my observation. According to a frequently heard wisdom, becoming
strong at physical or mind sports requires effort and patience when
studying and practising. It is no coincidence that tactical reading
and endgame evaluation are our greatest obstacles because both aspects
require effort and patience.

In scored games, the endgame phase covers half of the game. Endgame
evaluation also affects many moves during the opening and middle game.
Many decisions cannot be solved by tactical reading but require
endgame evaluation. Quite a few other decisions require both aspects.
More than half of all moves greatly profits from endgame evaluation.

Development

Despite its extraordinary importance, less than 5% of the go
literature has studied endgame evaluation. Why? The reason cannot be
the required effort and patience because there are many books on
tactical reading. Since we play a scored game, we should not be afraid
of numbers. What then is the reason and why have many books on
traditional endgame evaluation had many calculation mistakes? The
reason is that the theory of endgame evaluation has been very
under-developed in comparison to its importance and go theory for
other aspects of the game.

Traditional theory of endgame evaluation has been inconsistent and
very insufficient. During the 20th century, mathematicians have
developed combinatorial game theory, infinitesimals and thermography
but application of these theories is often hard and impractical for go
players. We need a consistent, powerful and applicable theory: modern
endgame theory.

Modern endgame theory is consistent because its already calibrated
values can be compared to each other naturally. The theory is powerful
because it evaluates sequences, individual moves and positions, and
relates their values to enable advanced decision-making. Modern
endgame theory is well applicable with its basic arithmetic
calculations and pairwise value comparisons.

The theory has been developed by a few amateur players. Sakauchi
Jun'ei made some early contributions. Bill Spight has researched in
modern endgame theory since the 1970s. Besides earlier contributions,
Robert Jasiek has done full-time research and writing about the
endgame since 2016. Because such research requires formulation and
mathematical proving of theorems, professional players with different
skills could hardly contribute to the development of modern endgame
evaluation. However, once the theory is developed, its application is straightforward for amateur and professional players. Writing related
books remains difficult for they require very much more proofreading
than books on other topics.

Effort

When we use tactical reading to determine a status of connection or
life+death of a group or its moves, we invest the effort of first
assessing the statuses of the follow-up positions and moves.
Similarly, when we use endgame evaluation to calculate a value of a
position or its moves, we invest the effort of first calculating the
values of the follow-up positions and moves. Tactical reading and
endgame evaluation are combined to select the best move achieving a
desired status. For example, a group shall live while optimising the
endgame. However, as soon as several moves are available and different
local positions must be considered together, exhaustive 'reading and
counting' is too complex and we need endgame evaluation for our
decisions.

Do I hear a complaint that evaluation requires the effort of
calculation? We must always recall that becoming strong requires
effort and patience. Instead of complaining, we should welcome the
necessary effort for greatly improving our game. Now that we know the
truth, we can appreciate the calculations further below.

They are easy enough so what is the real effort? Like we have to avoid accidental mistakes in tactical reading, we must also avoid accidental calculation mistakes in endgame evaluation. If we consider a local
position with several follow-up positions in tactical reading, we must determine and recall several statuses while not confusing them.
Similarly, if we consider them in endgame evaluation, we must
calculate and recall several values while not confusing them.
Furthermore, we must know what values to calculate and which to
compare. With patience, we learn to assess more difficult positions
with more follow-ups.

Calculations

We determine the value of a position (its 'count'), the value of first
playing in a position (the 'move value') or the value of an individual
move (its 'gain'). We need positive numbers favouring Black and
negative numbers favouring White. For example, we express "White has 3
points" by the negative count -3. What is the count of a local gote
endgame position if the starting black player achieves 11 points or
the starting white player achieves -3 points? We calculate the average
of the two numbers: the count is (11 + (-3)) / 2 = 8/2 = 4 points.
Such calculations require brackets. We also need fractions because
division by 2 can create them. Suppose Black achieves 1 point or White
achieves 0 points. Let us calculate the average: (1 + 0) / 2 = 1/2.
This is the expected count of the initial position.

Which move value, 7 or 1/2, indicates the more valuable move? We
determine the answer by comparing the two numbers: 7 > 1/2. We choose
the move with the larger move value 7. Quite like we identify
different persons by their names, we identify different values by
their variables. A position has its count C and move value M.

Suppose a position has the count C = 4 and move value M = 7. The
starting Black achieves the resulting count C + M = 4 + 7 = 11.
Instead, the starting White achieves the resulting count C - M = 4 - 7
= -3. This negative number favours White. All we need is such basic
school mathematics.


Text as a webpage: http://home.snafu.de/jasiek/Endgame_Study.html

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