5

Let us say that two players are playing each other. The are supposed to be in the same level (You can take that as an equal longtime ELO). They might be playing blitz, or rapid. But suddently, one of them blunders a pawn. Too bad. But the guy with one less pawn has more time. Is he compensated?

So to clear this out:

Is there a formula, supposing that the pieces have the following values:

  • Pawn - 1
  • Knight/Bishop - 3
  • Rook - 5
  • Queen - 9

And that there is a time difference between both players.

Regarding all factors, so remaining time for both players, increment, is there a formula that calculates what a piece is worth in time?

Increment will be a very important factor to consider. Because increment can save you if you have a very small amount of time.

Also the results cannot be precise to the maximum. We will suppose that the position would be equal if the lost piece was suddenly there. So 0.00.

Please ask me in the comments if you need any extra details.

EDIT:

In the comments it was noted to me that a passed pawn position could be fatal. So I am adding this condition:

The position will be valued by an computer program as 1.00 if a pawn is lost, 3.00 if a knight/bishop is lost, etc. This is to limit the search to games where the win is still unclear.

  • 2
    Are you asking, “How much is a second of time on the clock worth in terms of pawns?” – Nick Sep 6 '14 at 13:31
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    As I said, if there was a pawn in an appropriate position, the position would be drawn. Maybe we can limit it to middlegame only. – MikhailTal Sep 6 '14 at 15:15
  • 4
    I don't think this question is answerable. It's not possible to relate a pawn to the number of seconds on a clock. – SmallChess Sep 8 '14 at 3:11
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    A possible answer vector: Get a computer to play itself, one side down a pawn up N minutes in time, and see for which value of N the advantage swings toward the side with one pawn. (It's probably more like the ratio than the absolute difference, but you see the point). A similar experiment could be done with humans if you had the time data, but the computer version seems like a good first approximation. – Cam McLeman Sep 8 '14 at 18:16
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    The comment you just made kind of highlights why this can't be answered. As the players get better, the time on the clock matters less and the pawn matters more. There is no one correct answer. – Cleveland Sep 8 '14 at 22:04
1

This question can hardly have an objective answer, as the time controls and the strength of the players both matter a lot while valuing material and time management. A partial answer would be given assuming a time control of 1 minute. For this time control, regardless of the strength of the players, we can safely say that on lost positions the knight is the most valuable piece (after the queen). This is stated many times by IM Daniel Rensch on his Bullet Brawl Series.

When the player possessing the knight has more time, this difference is accentuated as he may look for tricks and swindles to try to make his opponent blunder or even lose on time. The forking ability of the knight is what makes it such a good piece in bullet, as some times the fork occurs and the knight cannot even be captured after he wins one of the forked pieces. This advantage is almost completely nullified when there is some kind of increment, allowing the players to take their time and think a bit more about the position.

  • Well, while this is not a complete answer, I would say that this offers an interesting idea. With the increase of increment, the disadvantage is inversely proportional to its square. – MikhailTal Sep 21 '14 at 17:43

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