2019-05-31 last update, 2019-05-31 first day, Robert Jasiek

Endgame Study


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.


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.


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.


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.