To find the best move, the dream of any chess player, chess engines are used extensively. Nowadays, the most popular chess engine is Stockfish. Many chess players, including top chess grandmasters consider Stockfish "the best chess player of the world." We, humans, are not considered the best chess players anymore.
Today is March 9, 2023. If you go the download section of Stockfish: https://stockfishchess.org/download/ You can find that the current version is Stockfish 15.1.
It is my understanding that a better proccessor can find better results in small amount of time because it can perfom calculations faster. However, my doubt is for infinite analysis without a specific time limitation. Like for example, a faster car can arrive to a destination faster, but at the end both will arrive to the same destination, unless we are talking about a space trip.
In my experience as a chess player, after you arrive with Stockfish analysis to a depth of 60, there are only insignificant differences. I consider that after a depth of 60, we arrive to something similar to the mathematical concept of asymptote or maybe more appropiate would be the concept of limit. Of course, I would like to learn if my understanding is correct. That is the reason behind this question. I am limiting this question to Stockfish to reduce the complexity of this question. What can you tell me about it?
I am asking to assume that the first analysis is performed with a Windows machine equiped with the best processor available, using the version for faster processors, version AVX2. While the second analysis is performed in a Windows machine equiped with an older processor using the version for older processors, version POPCNT. I am using only the Windows operating system, again, only to reduce the complexity of the question.
My understanding is that while the slower processor will stay at depth=60, but the faster processor will go further (maybe depth=70) but for practical purposes there will not be difference because both would have arrive to the same destination, asymptote or mathematical limit.
To support this idea, we have evidence that correspondence chess games end in a draw most of the time. To challenge this idea, we find that the chess rating of correspondence chess players is not equal. All the correspondence chess games are collected in several databases. So, we have what in statisics in called a representative sample.