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

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.

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.

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.

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.