I’ll just throw in a few random comments, FWIW. The OP poses a really great question. Today we have fantastic chess programs that can now play at a grandmaster level. We (humankind) created these programs, and yet we still don’t know the answer to the question. The reason these programs are so good, in a nutshell, is that they are a massive body of heuristics – a huge mish-mash of things that have been found to work well, rather than any singular particular achievement or algorithm. It has certainly helped that very fast computers have much greater width and depth of look-ahead than was ever possible before, but that’s only part of the answer.
I myself am quite a poor chess player, even though I manage some other intellectual feats of some moderate scope. I have no idea why. I have the memory capacity, the processing capability, yet I just can’t grasp the “big picture” to play decent chess.
One thing that may be of interest to some is Wolfpup’s Great Computer Chess Competition that I posted some time ago. It’s probably far more interesting to me and perhaps similar old farts in the comp sci business than to others, but it’s a match between the first really good and very famous chess program from the 60s, and a chess program that I have on my humble Amazon Fire tablet. The latter is called Shredder, and is quite well rated as a PC program. Anyway, the bottom line is that Shredder, on the humble tablet, beat the pants off what was once regarded as a magnificent mainframe computer chess program and a shining example of artificial intelligence.
I have to add also that I really love Shredder, because ironically it’s the only modern computer chess program that I can actually beat. That’s because it has a mode where it assesses your playing skill and it can fall back to handicapping itself to playing at about your level, including making stupid mistakes. It even has the audacity to rate my skill, which currently stands at 1505 Elo for all games played, and 1556 for the last 10 games (hey, I was rusty, and am improving!). But both scores are pretty poor, about two notches up from “novice”. But yet at the same time, if you crank up its playing skill, this thing can beat renowned venerable chess programs like MacHack, which was known for its aggressive tactics and often quick wins.
Anyway, just some random thoughts. I’m fascinated by chess and forever bummed out about my poor skills at it.