I recently analyzed alternative lines for this puzzle on chess.com.

[Event "French Championship"]
[Site "Val d'Isere FRA"]
[Date "2002.08.23"]
[Round "5"]
[White "Almira Fyodorovna Skripchenko"]
[Black "Laurent Fressinet"]
[Result "1-0"]
[SetUp "1"]
[StartPly "4"]
[FEN "4q3/4nkbr/pp1P1r1p/3Np1pP/P5P1/1B3P2/1P6/3R1RK1 w - - 0 35"]

1. d7 Nxd5 2. Bxd5+ Kf8 3. dxe8=B (3. dxe8=R+ Kxe8) (3. dxe8=Q+ Kxe8) 3... Kxe8

Now the nature of the promotion is immaterial (no pun intended), as 3... Kxe8 is inevitably the best reply by Black. The resulting positions are identical and winning for white.

However, the chess.com engine gives (slightly) different evaluations for each of those alternatives, and these differences seem nontrivial.


Notice how the top continuations are identical in each case. Indeed, for 3. dxe8=R+ and 3. dxe8=Q+, then 3... Kxe8 is the only legal move. Thus, each of these two lines must legally converge to one identical position, and they should evaluate identically.

Even for 3. dxe8=B, there is a dramatic dropoff from 3... Kxe8 to other alternatives, which are practically beneath consideration.


So the question remains: why are the evaluations not identical?


I have read that certain underpromotions evaluate more favorably. An opponent might refrain from taking a piece valued less than the queen, or one that delivers no check; this new piece facilitates a faster checkmate. However, no checkmate is imminent here.

  • 1
    You say "Notice how the top continuations are identical in each case" but all I see are that the first 9 moves in the main continuations are identical. Presumably once you reach depth 20 in those variations, there are slight deviations near the end making up the slight difference in evaluation. Feb 17 at 18:55
  • 1
    @NoseKnowsAll But those continuations converge immediately at 4.; especially 3. dxe8=R+ Kxe8 and 3. dxe8=Q+ Kxe8, which have only one possible continuation. Since each continuation begins at an identical position, there should be no deviation for these two in particular. Indeed, unless the engine chooses candidate moves at random, the top continuations will remain identical to arbitrary depth, so the top positions at depth 20 will be identical positions: identical continuations from the original identical position.
    – Greg
    Feb 17 at 19:41
  • 1
    As a programmer, the ordering suggests that the difference lies in a quirk of evaluation in which losing a Queen is rated more negatively than losing a Rook (likewise Bishop). Feb 17 at 19:45
  • @L.ScottJohnson I suspected something of the sort too, or at least a corollary: that winning while mobilizing less material scores higher. However, when I try to replicate it, I sometimes find 3. dxe8=Q+ Kxe8 as the top line. It's inconsistent, and in some cases, the evaluations are identical; but it's the unidentical cases that bug me, because they're all evaluating what amounts to an identical position at 4.. Especially in the cases of 3. dxe8=R+ Kxe8 and 3. dxe8=Q+ Kxe8, which share only a single legal continuation that leads to only one possible position at 3.
    – Greg
    Feb 17 at 19:48
  • The answer in chess.stackexchange.com/questions/25278/… seems to give some possible reasons.
    – D M
    Feb 21 at 10:49


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