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Inspired by a recent video where Magnus Carlsen was surprised that the engine thinks his position was a draw. Even top players may find a position considered winning can actually be drawn with perfect play, but is too hard to defend in practice, but that doesn't mean their evaluation is unjustified. Conversely a weak player like myself may find it hard to convert what engines think is a big advantage because I can't find the only winning move(s).

I'm interested in finding a way to make engine evaluations also show how hard it is to find the best move sequence for a given position, for example whether most reasonable-looking moves according to common principles are playable, or if only one/a few moves (especially if counterintuitive ones) can win or defend the position. And by extension, how difficult it will be for the opponent to defend against a candidate move that I can make, not just how objectively good it is with perfect play (kind of like the "dark forest where 2+2=5" idea. And possibly how easy it is to play a wrong move as well, for weak players like me :)

Even if it's as simple as adding some grey area in the evaluation bar to show difficulty or likelihood of keeping/losing an advantage, but possibly much more sophisticated than that. I'm willing to try writing some software if none are available.

Similar questions may have been asked before but no good solution seem to be given: Are there any engines that present evaluations based on probability of finding moves?

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  • The more important question is: what is the mathematical criterion (not objectively, because it won't be possible, but something you will have to choose anyway if you're gonna write this algorithm) for saying that a move is hard to find or a position is hard to unravel? Commented Jun 3 at 9:31
  • One more comment: an AI expert who was interviewed by Levy Rozman on the "5 levels of difficulty" video says that he's very interested in making AI's that think like human chess players - the other task, that of stronger and stronger engines, having got a bit boring. That would help with finding out what moves are natural to human minds and what are not. Commented Jun 3 at 9:38
  • @ChrisSanders I'm no expert but I think a move is hard to find if it doesn't seem to achieve any obvious or short-term goal according to simple principles that a human player can easily memorize and tactical analysis within a shallow depth, and a position is hard if the best moves (for you and/or opponent) are hard to find and there are many more or equally reasonable-looking moves possible that are worse such that it's unlikely to choose a good move if one has to guess. The principles to memorize can be rules like don't hang pieces or castle in the opening, or simple visual patterns. Commented Jun 3 at 13:36
  • @ChrisSanders Slightly more advanced rules may include how to play certain endgames, or concepts like pin or fork. There are so many patterns and rules I don't even know that a top player may not be able to remember one under pressure, and humans have limited memory/attention and accuracy during analysis as well so that needs to be taken into account, like how many pieces do you have to keep track of and how many different follow-up moves do you have to consider and what happens if you miss some, in addition to depth. Just from my experience as a beginner, I'm sure others have better ideas. Commented Jun 3 at 14:01

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