Chess for Beginners

Category: calculation

  • Think Like a Chess Engine

    In Kotov’s great book “Think Like a Grandmaster” he taught the average chess player the inner workings of how a chess master thinks about a position by creating a tree of candidates and then proceeding along the tree. While there is much to learn from Kotov’s work, I have always been facinated how computers can evaluate positions and how their positional play is derived from these material evaluation algorithms. I believe that the way chess engines derive material evaluations might help the lower rated amateur improve their evaluation skills.

    Below is a combination of the Crafty chess engine algorithms as well as Larry Kaufman’s material evaluation processes which is used by the Rybka engine.

    Pawns

    Pawn = 1

    isolated pawn penalty based on file:
    a-pawn : -.12
    b-pawn : -.14
    c-pawn : -.16
    d-pawn : -.20
    e-pawn : -.20
    f-pawn : -.16
    g-pawn : -.14
    h-pawn : -.12

    Doubled pawn (and not also isolated) penalty of -.12 plus add isolated pawn penalty

    Backward pawns -.06 penalty +.04 bonus for attack on backward pawn on semi-open file.

    Pawn advance in center +.04 / rank increasing to about +.08 / rank in the endgame
    Development

    Rook pawn is worth 15% less than a regular pawn (.85 of a pawn) (L.Kaufman)

    Knights

    Knights = 3.25
    Centralized knight: +.30
    In outpost : +.08

    Unpaired knight is worth approximately 3.14 pawns (worth less) (L.Kaufman)

    Bishops

    Bishops = 3.25
    Bishop in endgame +.10
    Bad bishop : -.04
    Corner bishop : 0.0
    Center bishop: +.3
    Attacking / good bishop: +.18
    Attack against King: +.05

    The Bishop Pair

    Bishop pair: +.50  Bishop pair is worth .50 more if not pieces exist to exchange them (L.Kaufman)

    Bishop pair is worth less than .50 a pawn when most or all of the pawns are on the board, and more than .50 pawns when half or more of the pawns are gone (L.Kaufman)

    If you have the bishop pair, and your opponent’s single bishop is a bad bishop (hemmed in by his own pawns), you already have full compensation for 1 pawn (L.Kaufman)

    Unpaired bishop is worth approximately 3.14 pawns (worth less) (L.Kaufman)

    Rooks

    Rooks = 5
    Attacking on open-file: +.20
    One semi-open file: +.10
    On open-file: +.14

    Rook and Bishop is better than the Rook and Knight. (L.Kaufman)

    Queen

    Queen = 9.75

    Queen and Knight is slightly better than Queen and Bishop

    King
    Centralized in opening: -.24
    Centralized in endgame: +.36
    On open file in opening: -.23
    No adjacent pawns: -.08

    Special Cases

    Hanging pieces: -.10

    Exchanges favor the side with a material advantage

    Minor pieces lose their value as the endgame approaches

    In endgames with no other piece the bishop is worth about 2.5 and the knight 2.25 with other pieces the minors are worth about 3.25

    Rooks gain value as the endgame approaches

    Note: I have modified the Crafty point values to reflect the Kaufman values.

    Resources

    Evaluation of Material Imbalances in Chess

    GNU Chess Positional Heuristics

    http://chessprogramming.wikispaces.com/Evaluation

    http://www.chessvariants.com/d.betza/pieceval/index.html

  • Connecting the Dots in Chess

    I have made an observation while solving puzzles, that I feel will improve my tactical puzzle solving skills, and might have direct application during actual games.

    When solving a tactical puzzle of intermediate to advanced level I either:

    1. Have no clue how to go about solving it and get it wrong.

    2. Have multiple ideas that look promising, but after further analysis don’t win {usually end up playing one of the two and get the answer wrong}.

    3. Solve the puzzle correctly.

    This post is going to focus on solving the 2nd category above. I have found that you will get many more puzzles correct by combining ideas that arise by analyzing different candidate moves. Unfortunately, by not making a link between the two, or forgetting about your first idea when looking at the second, I mainly fail to connect the dots and only after reviewing the correct answer do I see that I had been on the right track and would have answered correctly  if I had combined my candidates.

    You might want to solve this puzzles on your own before reading the answers below taking into account your thought process while doing so and then see if you encountered the same issues as I did.

    Here’s the first position we will look at:


    White to move and win

    The first candidate that came to mind was 1.Bb6 attacking the Queen. I analyzed the response 1…Nxb6 2.axb6 Qxb6 which loses a pawn for White and the Black Queen lives on. So I abandoned this candidate and looked for a better move.

    I then found that Qh6 looked promising and I began to analyze 1.Bh5 with the idea of Bh8 and then getting my Queen to h6. But I soon found that 1.Bh5 was a slow since it allows 1…Kh7 and White is out of gas. What I missed, and where I think there is room for improvement, is if I would have combined both moves. Attacking the Black Queen with 1.Bb6 with the idea of freeing the diagonal for my Queen to get to h6 with mate was the winning combination and one I failed to see by not connecting the dots.

    Let’s look at another example, and one which occurred right after I had attempted to solve example #1 above.

    White to move and win

    In this position quickly saw that both the White rook and Queen were attacking the Black d8 rook, and that there might be a tactical opportunity if the Queen were deflected from its defense. The candidate that came to mind was 1. b4 but after further analysis I saw that the Queen could seek shelter by moving to 1…Qc7.  The other candidate that stood out was 1.Qf6+ but the King can easily get out of the way with 1…Kg8 and there aren’t enough White pieces in the vicinity to force the issue. The third candidate I analyzed was attacking the undefended bishop with 1.Qe7 but I found that the bishop can get out of harms way via 1…Bc8. If I would have combined the two ideas or even looked a few ply deeper  I would have found the answer 1.Qe7 attacking the bishop and preventing the Queen from seeking shelter at c7 after deflecting her with b4. 1…Bc8 2.b4! and Black resigned.

  • The Sixth Ply

    Before we get started let’s define what a ply is in chess:

     A ply is a half move and a move is equivalent to 2 ply or a turn by each player. For example,  1. e4 is one ply and 1…e5 would be the 2nd ply, together these two plys make one move.

    Getting close to the truth of a chess position requires the calculation of a minimum of 6 ply (3 moves). The higher your rating the higher the ply calculation requirement increases since your opponent will be delving more deeply into the position than you. If you calculate anything less than 3 ply you are playing hope chess, since you are not forseeing your opponent’s responses. 

    Below is an assessment of how calculation skill correlates to one’s chess rating:

    0-1000 1 ply

    1000-1200 2-3 ply

    1200-1400 4 ply

    1400-1600 6 ply

    1600-1800 8 ply

    1800-1900 10 ply

    1900-2000 12 ply

    Stopping your calculations too soon can prevent you from finding the winning move. Many times the winning move comes after a series of seemingly unfavorable moves, and stopping your calculation too soon will prevent you from finding the best move in the position. At the same time, not looking deeply enough into your opponent’s moves will cause you to miss defensive opportunities against your opponent’s threats. (more…)