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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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