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beyondCritics

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If your code may be compiled, to use the Intel x87 numerical coprocessor, an important issue is the so called "excess precision": Different values on chip can collapse after being rounded and stored to their memory locations, invalidating previous comparisons. Spilling can happen unexpectedly. Note that Intel calls the x87 "legacy"

Statistical clueless amateurs found something they did not like, but of course were unable to convert their suspicions into something sound. They do not even think about it. Nevertheless a big sensation was anounced. I am tired of this.

However when “few enough” pieces remain on the board (in the endgame), the number of possible game states is small enough that it’s possible to brute force solve the game from each state by enumerating all possible moves and resulting states so as to find the absolute optimal move for any given board position

You can basically never do that, even in the endgame, since you get always exponential blow up! Furthermore with less pieces on the board, they hamper each others movement less, therefore the branching factor really goes down only slightly. If you want to compute all mate-in-n positions, you discover the theoretical values in tiers, by unmoving each tier twice: If you know all mate-in-0,...,mate-in-n positions, unmove the mate-in-n set for the defender and filter out results, where he can avoid moving into the union of the known tiers. Then unmove for the attacker, to find mate-in-(n+1). Repeat until convergence. Repeat the whole process for the left over positions, to find more theoretical values.

It is terrible to lose a relative in young age. But at least 80% percent of all heart diseases are known to be fully avoidable. The risk factors are known for ages and as matter of fact every adult is fully responsible to care for his own health. The right thing to do, is to watch out for a healthy diet.

Bruce helped the young athlete understand his movements in a way that seemed to decelerate time. “Bruce showed me how to harness some of what was raging inside me and summon it completely at my will. The Chinese call it chi; the Japanese, ki; the Indians, prana—it is the life force,” he said. “I was quite amazed to find, after working with Bruce, that when I really had my presence of mind, when I did control my life force, that’s what I saw, things coming at me in slow motion with plenty of time to get out of the way.

Seemingly we are learning here something new about Bruce Lee, that outside observers can't understand, most notably western ones. This decelaration of time also happened to me two times spontaneously, when I was attacked on surprise, hence I believe this verbatim. In both cases, that got me plenty of time, to decide what to do and was able to save myself without a scratch. However it never occurred to me,that that had something to do with my Chi force...

0.9999 ≊ 1 1 year ago

The explanation is, that the number is _not_ the infinite string of characters, but the sum of the scaled digits of the string. This sum is defined as the limit of the partial sums. In Germany, you can understand this in high school.

It's one of the single biggest misconceptions ever, it gets repeated endlessly

FM Roese here (best DWZ 2399). I agree, figuring or even conjecturing that Fischer overlooked 30.g3 is totally insane. However he also did not saw the theoretical draw, this strikes me even more off. He never opened up about his idea, so in all likelihood he calculated something very stupid.

if you plug it into an engine, it shows an equal evaluation

They criticized this argument rightly, but many basically repeated your mistake in the process of doing so. All engines use some evolved adaption of iterative refinement, be it either "Iterative deepening" (of an alpha beta search) [1] or "UCT" [2]. If you post computer evaluations you should at the very least give the reported nominal search depth and the engine name and version, otherwise you are just asking for trouble. On computer chess fora [0] they often post the whole log file bluntly.

[0] https://www.talkchess.com/

[1] https://www.chessprogramming.org/Iterative_Deepening

[2] https://www.chessprogramming.org/UCT

Facility score may IMHO be understood as some statistical measure of tactical involvement. It has really nothing to do with the established and important concept of weakness in chess, which looks at significant static features of a position. For example in the position from figure 1, white's pawns on the queen side are all weak, especially c4. Also the black squares around the white king are weak. After 1...exd4 these weaknesses are pronounced sharply. Considering fragility score, I see nothing that points towards these weaknesses. a4 and b6 are not attacked, hence ignored. c4 is attacked once and defended once, but there is no trajectory over it. Weak squares are not considered. If we look at the knight D4, it's BC score may tell us, that after taking it with a pawn, which can be done in two different ways, the bishop e3 is hanging, hence we gain a tempo, which is significant, also f3 is weaker (noise) and bishop e6 is not under pressure any longer. Hardly something which convinces to identify the key moment, but may be useful in a statistical sense. Nevertheless it appears to be an oversold complexity measure.