Interesting Game Dots and Boxes

2 replies. Last post: 2005-03-10

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Interesting Game
  • Knox (Computer) at 2005-03-04

    I thought it might be nice if people occasionally posted
    some good games with commentary. To start this off, I’m
    posting the game between Knox and Oord2000 from the current
    championship (3rd, level 1). In this game, both sides made
    a premptive sacrifice. In fact, there were three premptive
    sacrifices in the game as well as three one-box sacrifices.
    All of the sacrifices except possibly a relatively early
    one-box sac were the best plays.

    <table CELLPADDING=5 BORDER=0>

    <tr ALIGN=LEFT><th WIDTH=120>Knox<th WIDTH=120>Oord
    Click Here

    1. e3-f32. e4-f4


    Position after 2nd move


    3. a4-b44. a3-b3


    Position after 4th move


    5. d3-d46. c3-c4


    Position after 6th move


    7. d4-e48. b3-c3
    9. c4-d4


    Position after 9th move


    <td COLSPAN=3>
    Since Knox wants an even number of long chains, it
    sacrifices one box to divide up the board into an even
    number of regions. As a practical matter, Knox can
    apply nimstring (a way to get “control”) when the board
    divides up quickly so Knox should do well here.

    10. c3-d3, d2-d3
    <td COLSPAN=3> The majority of responses win at nimstring.
    Knox has almost no means of discriminating between
    various moves that win at nimstring. It will prefer
    winning nimstring moves that break up quads and avoid
    those that create them. Also, it prefers free moves to
    those that give away boxes. For the next three plays,
    the choice was simply random among the free winning
    nimstring moves. [If Knox is losing nimstring, it will
    play the move with the fewest free responses that win at
    nimstring.]

    11. e4-e512. c4-c5


    Position after 12th move


    13. f1-f214. d1-d2


    Position after 14th move


    15. e2-e3

    <td COLSPAN=3>I was able to get the perfect play
    results from here on out via D. Wilson’s analysis program.
    Right now oord is winning by a single box.
    16. d1-e1


    Position after 16th move


    <td COLSPAN=3>Now Knox is winning by 1 box!
    This turned out to be the critical error as Knox kept
    the 1 box advantage throughout the rest of the game
    (both sides played perfectly from here on out!). Any
    of the following moves would have won by 1 box with perfect
    play: a4-a5, a5-b5, b5-c5, b6-c6, c6-d6, a2-a3, b2-b3,
    a2-b2, b2-c2, b1-b2, b1-c1, c1-c2, c1-d1. Instead of
    extending the chain with d1-e1, oord needed to try to
    establish the correct parity in the rest of the board.

    17. d5-d6! (Don’t ask me why!)
    Knox switched from nimstring mode to search mode here.
    It turned out to be the perfect time to switch because
    this moves loses at nimstring! Curiously, Knox evaluated
    the game as being in oord’s favor. Strangely,
    every response by oord now loses by
    exactly one box with perfect play.

    18. b5-b6
    19. c5-c6


    Position after 19th move


    <td COLSPAN=3>
    Now Knox correctly evaluates the game as being 1 box
    in its favor. Any of a4-a5, a5-b5, d6-e6, e5-e6, e6-f6,
    or f5-f6 would also have won by 1 box.

    20. b2-b3


    Position after 20th move


    <td COLSPAN=3>
    I didn’t expect this. c1-c2 creating a 4’th chain seems
    like such an obvious response. But oord must have already
    planned to meet c1-c2 by sacrificing this chain. Instead
    of b2-b3, I was thinking he would sac 1 box with c2-c3.
    The winning response to this (after taking the box) is a2-b2.

    21. c1-c2
    <td COLSPAN=3>
    Necessary as it is the only way to win. Knox can now see
    to the end of the game. Hence, it already “knows” it is
    going to win by at least 1 box.

    22. b2-b3


    Position after 22nd move
    — A nice pre-emptive sac.
    <td WIDTH=120>23. b2-c2, c2-d2, c1-d1, a1-b1
    <td COLSPAN=3>
    The take-all/leave two decision is not an easy one.
    Leaving two loses by 1 box though this is far from
    obvious. After taking the entire chain, the long
    chain parity in the rest of game favors oord. Knox
    is going to have to eventually make a return pre-emptive
    sacrifice to win this game. The two winning choices
    after taking the chain are to either sac the three
    chain in the top-central or (Knox’s choice) to play
    one of the equivalent moves a1-a2 or a1-b1 which threaten
    to create a fourth chain.

    24. a2-b2


    Position after 24th move

    <td COLSPAN=3>
    This one box sac is necessary to stop Knox from
    creating a fourth chain and hence, stops Knox
    from switching the parity to its favor.

    25. b1-c1, e1-e2


    Position after 25th move

    <td COLSPAN=3>
    Since the parity is in oord’s favor, Knox must make
    a premptive sac on this 4-chain or on the 3-chain
    at the top-middle.
    <td WIDTH=130>26. d2-e2, d3-e3, e3-e4, f3-f4, d5-e5


    Position after 26th move

    <td COLSPAN=3>
    The take-all and the leave two options both lose by
    1 box! If you take all, then you should either sac
    the 3-chain (as oord just did) or play a5-b5. If you
    leave two, then the opponent should take these two
    and either offer the 3-chain or play a5-b5. It seems
    strange that a5-b5 is just as good as the premptive
    sac — the premptive sac seems necessary in both cases
    because the parity is not what is wanted.

    <td WIDTH=120>27. d4-d5, c5-d5, c6-d6, a5-b5


    Position after 27th move

    <td COLSPAN=3>
    Taking all is necessary. Knox wants two more chains
    while oord wants one. The chain in the upper-left
    cannot be stopped while the one in the upper-right
    cannot be forced. Hence, oord is going to get his
    one long chain (of length 4) and he will take this
    at the end. But to stop the chain in the upper-right,
    oord is going to have to sac 1 box. But Knox’s a5-b5
    creates a second short chain in the upper-left so that
    Knox will get two more boxes in the short chain swaps.
    These three boxes plus the two that Knox is ahead by
    are just enough to overcome oord’s final 4-chain.

    28. e5-f5
    29. f4-f5, f5-f6


    Position after 29th move

    <td COLSPAN=3>
    It’s all over now. Just count up the boxes in
    every other chain to determine how many more boxes
    you are going to get. Knox wins 13-12.



  • oord2000 at 2005-03-10

    Great Analysis. Too bad i lost, but i’m glad i found some nice moves.

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