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An interesting game played out between Wesley So and Levon Aronion1:

[title "Wesley So vs Levon Aronian"]
[fen "rn4k1/p2bP1b1/2q5/1pp2p1Q/2p5/8/PP3PPP/3R1RK1 w - - 0 1"]

So was in a far superior position according to the computer, but had only ~1 minute compared to Aronian's ~5 minutes.

Is there any established system for evaluating positions taking into account time for both players?

1 Link to game: https://www.chess.com/events/2021-magnus-carlsen-invitational-prelims/06/So_Wesley-Aronian_Levon

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    There is a subroutine which effects how much time a computer will think for the current move, but I've never seen this used in the evaluation function. It's an interesting idea to program the computer to try for traps when the opponent is low on time. – Mike Jones Mar 14 at 19:23
  • @MikeJones great point. Also, some winning positions require extreme precision, which can be time consuming if only because of the calculations/checking involved. (the So v Aronian game was like that, where So was winning, but needed to be very precise to convert the winning position, otherwise it would drop back to even, or he could have been back rank mated). On the position above, although he had 1 minute, he used right down to 5 seconds (!) before playing the subtle Rfe1. – stevec Mar 14 at 19:36
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Is there any established system for evaluating positions taking into account time for both players?

No, there isn't. This is for two main reasons:

  1. There is no objective measure for how time affects a player's ability to play any given position.
  2. Such evaluations would be useless. They would literally tell you nothing useful

Let me give an example from a game one of my clubmates (rated about 1800 at the time) played a few years ago in the UK National Universities Championships.

In the blitz section (3+2) in one of his games he reached a KBN vs K endgame with less than 30 seconds left on the clock. He knows that endgame (he has a strict coach who makes him learn that kind of stuff) and so blitzed out the win with plenty of time to spare on his clock.

I also have stronger clubmates (2100+), however, who don't know that endgame. They would never be able to mate in so little time. Give them 20 minutes on the clock and maybe they'd succeed. There have even been IMs who have failed with plenty of time on the clock.

Bottom line: even with as simple a position as this there is no way to provide a meaningful evaluation of the position that takes time into consideration.

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Time is implicitly added to any position analysis, but not in the way you would expect. All algorithms stop at either certain depth or time consumed, or memory, processor... consumed or the combination of these. It stops when it is predicted that it would need more time than what you have on your computer, some Web site server, or generally when it is obvious that the resource consumption will start increasing beyond acceptable level (for example exponentially). Sometimes it just stops as further depth analysis shows no promising result.

Then a computer will stop and give you the estimate.

That is how it is working. So the best way of mimicking your situation is to let computer play against itself with the time that you have. A computer is totally aware of the time left, and it will reduce analysis in order not to lose on time. But you cannot strictly evaluate the position based on that. The only way is to restrict the computer itself while playing.

Usually I do this more than once, but not too many times, in order to get some sort of feeling of what human would do in that position with the same time restriction. If you do a full analysis and this reduced analysis, you can almost always see that a computer is crippled, but not in the same sense as human. You need to play a little bit more around to mimic what human could come up with on short notice. You do get the feeling over what is not immediately visible and what line looks tempting, but it is generally wrong. Of course, it says to you nothing how human would play, it is telling you generally what you could expect a player to fall for if he is under pressure.

Computer and human play different game and reducing time has a quite different effect. Still, you can get some real feeling over how human would play a similar position if you let a computer play the same position couple of times (and try to erase its learning mechanism in between if there is such thing implemented).

Evaluation with time restriction is possible, and all computers in the world must restrict this. But it is not the same as restricting real time for a chess player.

What you need to do in order to get a feeling about the position complexity is to track computer analysis. More and longer it is jumping before reaching a stable evaluation, it is more likely that a position is complex for human to quickly analyze when under time constraint.

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