Another human-generated puzzle Dots and Boxes

16 replies. Last post: 2015-03-30

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Another human-generated puzzle
  • al_ef13 at 2015-03-29

    Player 2 to move and win:,f3h9k8j9g8h5f7g4f1j5d9d5e6e2g2i4h3k2j3k4e8f9d11b9a8

    This position occured in my recent game with purgency:

    In the game I quickly played 22.k6, which is losing, but there is a better option.

    Probably this puzzle is not very hard for experienced players, but for a novice player like me the position is quite complex. I did not find the win without computer.

  • William Fraser at 2015-03-29

    I believe that you linked to the wrong game.
    The correct one is

  • al_ef13 at 2015-03-29

    Yes, you are right. Sorry for confusion.

  • purgency at 2015-03-29

    1. Hm, 22.k6 was the most intuitive response but I guess it’s not necessary to play it since it’s still possible to prevent the chain at the top by sacrificing and aim for one chain in case player 1 would play i6.
    4. Well, I honestly don’t see any kind of intuitive logic that can be applied here. This is pretty much just about counting imo, so instead of playing k6 it’s probably the best to prepare for the endgames that are likely to appear and try to determine the value.
    7. If k6 is played and the quad at the left doesn’t create an earmuff (which is unlikely) we will get an endgame with value:
    9. v(4L+n-4L+m); 3 <= m <= 5; 4 <= n <= 6,
    11. where 4L is the Quad, n-4L the dipper with chain-length n and m the length of the chain at the top.
    14. v = 0 is a win for player 2, v >= 2  is a win for player 1 and if v = 1 it all depends on the small chains.
    17. If we could just turn the value into 0 this would be an easy win but unfortunately we can’t since both n and m shift the value by one as they in- or decrement and we can only influence either n or m on our next move. So that’s not easy at all and I guess this puzzle is pretty hard for anyone. One may be able to narrow down the options for m by taking into account that some of the moves at the top can’t be played due to i6 e.g. 22.h11 doesn’t work due to i6 so as an effect we can probably ignore the options with m = 5.
    20. v(4L+4-4L+3)=1
    22. v(4L+5-4L+3)=0
    24. v(4L+6-4L+3)=1
    26. v(4L+4-4L+4)=0
    28. v(4L+5-4L+4)=1
    30. v(4L+6-4L+4)=2
    32. v(4L+4-4L+5)=1
    34. v(4L+5-4L+5)=0
    36. v(4L+6-4L+5)=1
    39. (calculating this is especially annoying in this game since the rule of thumb which tells us to open loops first and then chains, can’t be applied to endgames with dippers which would make this easier)
    42. We can see that with n = 6 the value is either 1 or 2 which is bad while lower values exist for n = 4 and n = 5 so it might be smarter to play something that turns the dipper short rather than long.

      Well, I think this is as far as simple logic can get you while certainty in being victorious can only be assured by solving the position brute force.

      PS: I didn’t see the winning move either.

  • purgency at 2015-03-29

    That’s some weird formating, what the hell happened there o.o?

  • al_ef13 at 2015-03-30

    purgency, thank you very much for your analysis!

    I have several remarks.

    First, we shouldn’t ignore the options with m=5, because h11 can be played by P1. Say, if P2 makes some 22nd move in the southwest, then 23. h11 would force 24. k6. And after that P2 doesn’t want a 2-chain in the southeast. This observation already cuts some moves from consideration by P2.

    Second, I guess the calculations of the loony endgame values can be made a bit simpler. E.g. if v(4L-n+4L+m)=0 for some n and m, then changing either n or m by +1 or 1 would give the value 1. Moreover, I think it’s not that hard to generalize the results of  the paper to the sums of isolated chains, loops and (possibly double) dippers. However, I guess I will not do that in the near future, since I already have a number of papers to be written :)

    Third, in some situations we should consider the possibility for P2 to sacrifice a box to make the loony endgame value to be 0, of course if after that he gains 2 from the short chain battle. Also, a surprising point is that in some situations P1 can play f5,
    sacrificing 2 boxes but considerably changing the loony endgame value.

    And a general remark about such endgames. For me, the ideal winning move (it it exists, of course) is the one that makes all possible loony endgame configurations to be winning. For example, in this position
    the ideal winning move is 21. c2 (and I guess the only winning move), after that I can just play non-sacrificing moves until the short chain battle.

    If there is no ideal winning move (like in this puzzle), then I should search for some balance, so that I can finally determine the loony endgame configuration to be in my favour. Probably also I should first consider the moves that are forcing, i.e. if my opponent plays something neutral, then on the next move I will be able to win. And of course, I should cut off the moves which allow my opponent to gain the initiative and decide the endgame configuration to be in his favour (like the move I played in the game :-)).

    I agree with you that this position requires some brute force search, but maybe one can acquire some tacit knowledge which would simplify the analysis. Like in chess, for high-rated players the calculations are usually not that hard, because they know subconsciously which moves are worth considering.

    Surprisingly, I’ve seen some games on this site between high-rated players, where much more simple endgame positions were misplayed. Is this because people pay more attention to improving in opening and middlegame stages?

  • al_ef13 at 2015-03-30

    Some strange strikethrough appeared in my message. Don’t know the reason.

  • William Fraser at 2015-03-30

    I’m pretty sure that strikethrough iscaused by “ - ” folllowed by an alphanum, followed by some text, followed by an alphanum followed by a “ - ”.
    So, you need to put spaces in strategic spots.   Here are some tests, followed by the same thing with z replacing :

    Testing 1

    zTesting 1z

  • William Fraser at 2015-03-30

    Oh, so I guess it can include carriage returns, and it works with any non-space character.  A few more scenarios:
    Testing- testing testing.

    Testing-testing testing-testing.

    Testingz testing ztesting.
    Testingztesting testingztesting.

  • Carroll ★ at 2015-03-30

    Syntax for textile strikethrough:

    So how can you write
    some text −2 ?

  • Carroll ★ at 2015-03-30

    It seems that is not a minus, what is the difference between hypen ‐ en-dash – and fullwidth hypen-minus &#xff0d; ?

  • Sean_Hettenbach at 2015-03-30

     c10 or e10 is winning I believe. 12-13 is the score I got. I love the in depth analysis, yet a simple count would suffice yes? Thanks for the puzzle al_ef! It was a good quick exercise for the mind!

  • Sean_Hettenbach at 2015-03-30

     "I agree with you that this position requires some brute force search, but maybe one can acquire some tacit knowledge which would simplify the analysis. Like in chess, for high-rated players the calculations are usually not that hard, because they know subconsciously which moves are worth considering."

    Oh and yes I always look at sacrifices first. That’s always the first thing I consider. I thought “Well there is a threat to second player of 2 chains forming, so lets see how a sacrifice in the top region would play out...” and after I played it out, there were no winning responses for first player, so... That is where I concluded my analysis!:)

    Here is a quick overview of what I did:,f3h9k8j9g8h5f7g4f1j5d9d5e6e2g2i4h3k2j3k4e8f9d11b9a8e10c10h11g10f11i10 - Simple moves to consider if player two is trying to win. (maximizing his box count),f3h9k8j9g8h5f7g4f1j5d9d5e6e2g2i4h3k2j3k4e8f9d11b9a8e10c10h11g10f11i10k6d1- Player one finishes the loop and player two attempts to extend his conjoining chain.,f3h9k8j9g8h5f7g4f1j5d9d5e6e2g2i4h3k2j3k4e8f9d11b9a8e10c10h11g10f11i10f5e4g6b5 - Here player one tries to sac the center boxes to split the regions, which player two responds with the simple play of b5

    Anything other than those responses and the move i6 is devastating as it creates a giant long chain that is absolutely winning for player two.

    Hope this helps you al_ef!

  • Sean_Hettenbach at 2015-03-30

    correction of the first analysis board "...if player two is trying to win" ----> "... if player one is trying to win"

  • al_ef13 at 2015-03-30

    Sean, thanks for the answer.

    In your variation,f3h9k8j9g8h5f7g4f1j5d9d5e6e2g2i4h3k2j3k4e8f9d11b9a8e10c10h11g10f11i10k6d1
    what will be your response to the simple 27. b5? The largest loony endgame value you can get is 2, making the long chain of length 6. But P1 is already 3 points ahead (not to mention that he will gain extra 2 in the short chain battle in this case). I guess this refutes the sacrifice 22. c10.


  • Sean_Hettenbach at 2015-03-30

    Dear goodness I am terribly sorry about the miss here!!! I jumped the gun like I said and concluded my analysis way to soon. This is why I love these types of threads, makes you learn to not be so quick right? Well, since I just made a fool of myself, I guess I can only give this position a proper analysis! You are correct, 22.c10 is not good at all!:D

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