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.
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.
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
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
basic arithmetic calculations and pairwise value comparisons.
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
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.
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
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
accidental calculation mistakes in endgame evaluation. If we consider
a local position with several follow-up positions in
reading, we must determine and recall several statuses while
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.
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.
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.