Engine depth during endgame

[Peperoni]

Hello,

I have noticed that forcing engines to play against each other with a given depth, during engames, they reach very fast the depth (so play very fast) even if there are a lot of moves to consider (for humans), is there a reason why?

[Dann Corbit]

When the board is sparse there are not nearly so many moves to compute.

[Ajedrecista]

Hello Richard:

I agree with Dann. Just to bring some numbers into the scene, perft can be useful as well as the number of unique positions. Please imagine the starting position with well-known numbers:

Code: Select all

rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

Plies     Perft(Plies)     Positions(Plies)
  0                  1                    1
  1                 20                   20
  2                400                  400
  3              8,902                5,362
  4            197,281               72,078
  5          4,865,609              822,518
  6        119,060,324            9,417,683
  7      3,195,901,860           96,400,335
  8     84,998,978,956          988,192,872

Then imagine the same with the longest loss of the side with more pawns in KQPPvKQP endgame:

https://syzygy-tables.info/?fen=8/8/P7/ ... _w_-_-_0_1

Code: Select all

8/8/P7/1q6/4P3/6Q1/p7/k4K2 w - - 0 1

Plies     Perft(Plies)     Positions(Plies)
  0                  1                    1
  1                  5                    5
  2                122                  122
  3              2,777                2,478
  4             53,927               13,905
  5          1,163,367               79,735
  6         23,058,437              376,367
  7        489,451,797            1,353,023
  8      9,984,707,331            7,135,215

The values of the KQPPvKQP endgame were calculated with JetChess perft counter. It depends on the endgame, but branching factors are key in the explanation. Those numbers are not meant to be understood as an axiom since usual engines do not perform brute force analysis (i.e. searching all the nodes). Engines prune but they prune in both positions and the search tree is usually narrower with less pieces on the board, hence searching deeper in the same amount of time.

Regards from Spain.

Ajedrecista.

[Peperoni]

Very useful information, thank you to both of you