Imagine a simple gote with Black's move achieving the count 1 or White's move achieving the count -1. (Exercise: put this on the board.) The initial position has the count 0.

Modern endgame theory: each move gains 1, which is the move value.

Traditional endgame theory: the move value is 2. Gains were neglected but if we considered them, we would find that they are inconsistent with the move value.

Thank you, gonna buy your book for more studies ^^

I've got both Antti Törmänen's Rational Endgame and Robert Jasiek's Engame 2 - Values. But I am still completely confused with the theory in them.
I can understand what happens with double gote moves, but the rest is still above me.

I’d say I don’t actually have much practical experience in the endgame. Many of my games are decided by resignation. I guess I could think about move values before then, but I’m too busy trying to read variations.

Then again, maybe I’m just making an excuse not to learn the math.

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be immersed

How about reading the books slowly and taking your time? Endgame evaluation is not like most other go theory but we must learn its own conceptual framework from scratch. If you find simple gote easier than other types of local endgames, this may be because simple gote depends on only two follow-up positions while other types depend on more. Understanding more can be more difficult than understanding two so be patient with yourself.

The purpose of the math is to make reading easier.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Personally, I don't think it makes reading easier; more like it dispenses with reading in favor of 'preparing' the endgame before the game begins in the form of analyzing and remembering particular formations and their values. I'm starting to believe that this is the way to go about it, given how complex some positions can be. If I got it correctly, Antti seems to share this sentiment when talking about finding the compromise between precise counting and managing time during tournament games. Calculating and manipulating a tree of formation-value pairs during a match doesn't quite strike me as natural.

Precise calculation of average values of complex positions is for analysis. During play I do not recommend that amateurs strive for more accuracy than ¼ pt., as a rule. Yes, situations do arise where the players can recognize that a very small difference matters, or may matter, and can do the math over the board. If precise calculation mattered much, you would not see so many math mistakes in endgame texts, Tormanen's and Jasiek's books being exceptions. But if the calculations did not matter, you would not see them in endgame texts at all.

Besides, there is more to endgame math than calculating average values.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

If values are very different, the larger ones are obvious and calculation is not needed. If values are similar, calculation is necessary to decide them. This is often so because there are many local endgames and similar values can occur easily.

I have often reflected whether approximation might be useful for rather similar values but I have almost always come to this conclusion: It takes more time to verify that an approximation is correct, applicable and does not create mistakes in decision-making than it takes time to calculate precisely. If approximation rounds to, say, 1/4 and allows 1/4 point mistakes, this is unacceptable because they are too large by far as they can accumulate over the very many endgame moves. Verifying which rounding to the nearest 1/4 is correct is hard. Rounding to integers might be feasible concerning time-consumption but is totally useless imprecision whenever similar values are involved. Instead of searching excuses allowing approximation, it is better to practise correct calculations with fractions and accelerate them.

There are situations for which values replace reading and others for which values very greatly simplify reading. Reading does not become superfluous but, in general, values very much accelerate reading.

EDIT: The middle game is different. Endgame values or positional judgements can often be rounded to, say, 1/2 because many other imprecise aspects, such as fighting or influence, also have an effect on decisions. However, when everything compared is local endgames characterisable by values, then approximation is dangerous.