First moves and swapping Hex, Havannah

35 replies. Last post: 2003-11-03

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First moves and swapping
  • Marius Halsor at 2003-05-06

    I was wondering if anyone cares to share their opinion on what the appropriate first move should be? And also, if anyone think there are openings to which the reply should be something other that the center (and why, of course). Personally, I feel that the center is so valuable that I am willing to open b2 to get it. I do not usually swap b2 openings either (although – you never know :) ). Does anyone have any statistics on how much they have lost/won with different first moves? I hope you strong players are willing to discuss this issue, so we other hexplayers could learn something :)

  • jjjklj at 2003-05-06

    i think that b2 is a weak opening move. even on even sized boards where there is no center piece i think b2 should not be swapped. as far as a second row fair move, i am not really sure what the correct move is, but as you probably already know, i’ve been toying with d2. i’ve played a lot of 10x10 games at playsite, and i’ve had better luck not swapping b2, and also not swapping a3, but david thinks a3 is strong. i think you just have to play different openings and see where you think the balance is. if you think occupying the center space is very important, than you may want to play stronger first moves, so they will be swapped. i personally don’t think the center space is quite so important on 13x13 because it’s so far from both edges.

  • michael at 2003-05-06

    As mathematician i know of the rigourous proof mr Nash himself gave after “inventing” the game of hex...it says what most players know, that the first player has a forced win, the bad part is that no one knows the winning strategy (for higher than 7x7 boards, heard sthing about the 8x8 being solved, but i’m not sure of that). Anyway apart from not knowing the winning way...it looks to me that the first player has a sure advantage in the game, therefor i’d always swap, even if the move looks bad i.e a move at the side, so the opponent moves in center (note that i’m not a hex-player, just a mathematical approach). Any comments?

  • jjjklj at 2003-05-06

    i’m pretty certain that there are moves that should not be swapped. you say that 7x7 has been solved, see if it is possible for the first player to win moving b2, or a1...

  • ypercube ★ at 2003-05-06

    I haven’t checked it but I would bet 10 euros that b2 wins at 7x7. I would also bet (but without the 10) that b2 wins at 13x13. If you think I am wrong try playing against david with b2.

    pandelis

  • ypercube ★ at 2003-05-06

    The <a href="http://www.littlegolem.net/jsp/tournament/tournament.jsp?trnid=hex.rt.2003.8.24> 8.24 hex rated tournament is now officially called the <a href="http://www.littlegolem.net/jsp/tournament/tournament.jsp?trnid=hex.rt.2003.8.24> b2 tournament since 4 of the 5 games have started with b2 ! (1 game pending)



    pandelis

  • jjjklj at 2003-05-06

    i would try that, but i have a feeling david wouldn’t swap b2...and i have beaten him with him swapping b4...but we’re just human, we can’t be expected to play perfectly

  • jjjklj at 2003-05-06

    sorry, i played d2, not b4, it was b4 after he swapped it...

  • ypercube ★ at 2003-05-06

    Correction:
    The 8.24 hex rated tournament is now officially called the b2 tournament since 4 of the 5 games have started with b2 ! (1 game pending)

    pandelis

  • ypercube ★ at 2003-05-06

    Yes, of course, I have also beaten David once. And lost so many others. What I meant to say is that David (or a highly rated player) would win more games than lose if he were to play b2. I suppose he feels that way too, since he prefers a3 that is a “weaker” move. Weaker in the sense that if a3 wins for the 1st player then b2 wins also. Which is another conjecture of course.

    Pandelis

  • ypercube ★ at 2003-05-06

    As of myself, I prefer playing on the perimeter and have tried many moves, a2, a3, a4, a5, ... and b1, c1, d1, ...
    I prefer the a2 and a4 moves.

  • jjjklj at 2003-05-06

    another thing, i don’t believe that a3 is weaker than b2, in fact i believe a3 is stronger than b2, but i feel that neither of them should be swapped...i think david agrees with me on everything except that he thinks a3 should be swapped...please let us know what you do think, david, because i may have something wrong

  • michael at 2003-05-06

    I was wrong in my previous note; saying that there is a winning strategy for first player, doesn’t mean that every opening move wins...it could be the case, but it isn’t necessary. Using the swapping rule now implies that the 2nd player has the sure win, because either he swaps a winning opening move, or doesn’t swap a losing opening move.

  • ypercube ★ at 2003-05-06

    Computers might help us answer some questions about openings in hex if they manage to solve the games up to 10x10 or 15x15 (in 10, 20, 50 years ?).
    Here’s some questions/conjectures :

    1. b2 wins for 1st player in all sizes
    Could be answered if it was found that at say 11x11 its a loss for the 1st player. Which means that the question could be answered only if the answer is negative and it’s on a small size. If the answer is positive no computer would help us.

    2. for every move (b2, d2, d3, c6, whatever) there is a board that its a loss for the 1st player.
    Computers might help us in this if they could solve several sizes and then only giving us hints that this is correct.

    Pandelis

  • ypercube ★ at 2003-05-06

    You are right Michael. In fact it has been proven that a1 is a loss in all sizes >= 2 .

  • Taral at 2003-05-06

    There are a few things that have been proven:

    a1 is a losing opening move on sizes 2 and greater.
    b1 is a losing opening move on sizes 3 and greater.
    If a2 is a winning opening move, then b2 is also a winning opening move.

  • Marius Halsor at 2003-05-06

    I’m happy this subject got so many replies :-) First to Michael: Since it is proven that the first player should win without the swap rule, one can easily deduct that the second player should win WITH the swap rule (provided, ofcourse, that he plays perfectly). Yper, to your second question: If the moves are defined as a certain distance from the edges, there might be that there is always a board in which that move would be losing (although it’s not certain). However, if it’s defined as being a certain distance from the center, that’s definitely not the case. And tray: Do you really feel that a3 is stronger than b2? Wow. I surely don’t feel that. Does anyone else agree with Tray on this issue? I’d definitely not swap a3.

  • Ryan at 2003-05-06

    I agree with Tray that a3 is stronger than a2, I have since stopped playing a3(I used to open every game with it). After playing David in a few 10x10 games where he swapped my a3... he showed me there are a few plusses to it besides a direct connect from a ladder on the second row. I am in search now of a new opening and am glad this forum is addressing it.

    Since there is the swap option, you can say the ‘best’ move would be the most neutral one, a move that doesn’t give either player too much advantage. What do you think that may be? Jason has been opening with j3 in 10x10, and have seen it a bunch on Kurnik. Anybody have any thoughts on that one?

  • David J Bush ★ at 2003-05-06

    My nose has been rubbed in the fact that I am clueless about Hex openings. I just go with what has worked for me, and try to stay away from what hasn’t worked. I would probably swap 1.B2, but if I get beaten up that way I would probably change my mind, if I can’t find any other reason for the loss. I don’t understand this fascination with 2.G7 (the center cell). It’s an okay move, but there are usually plenty of other possibilities. If I didn’t swap 1.B2, I might play 2.E6 for example, which sits on two “diagonals” which lead to B3 and B12, and therefore makes efficient use of the board, or so it seems.

    Perhaps more important than an openings database, is an understanding of the tactical patterns and strategic concepts that opening theory is based on.

  • jjjklj at 2003-05-07

    i have a question for everybody...has anyone ever played a game with b1 or b2 where the game could have been different at all if they had b1 instead of b2 or b2 instead of b1? i’m sure there are subtle differences, but i can’t recall ever playing a game where it made a difference whether it was a2 or b2

  • jjjklj at 2003-05-07

    that was supposed to be a2 or b2, not b1 or b2

  • jjjklj at 2003-05-07

    yes, i really feel that a3 is stronger than b2, but this is based on the games i’ve played on 10x10...the only real use i’ve found for b2 is as a 2nd and 3rd row ladder escape, but a3 is pretty powerful although when it’s used, it often complicates games...a3 can be used as a “defensive” stone because it blocks the opponent a little farther toward the center than b2 does, although when this happens, it usually just results in a ladder going horizontal from left to right along the top...this is what makes it complicated. i’ve played many games on 10x10 with both a3 and b2, i used to open every game with a2 or b2, then i moved to a3 or a9 once i decided that a2/b2 was too weak if my opponent didn’t swap. i now think that a2/b2/a3 should not be swapped, and a9 (a12) should be swapped, but i don’t have enough games with that opening to really feel strongly about it...and as for jason’s opening with m3 or m4....i have no idea what to do about those....

  • jjjklj at 2003-05-07

    and i do agree with david that tactics are much more important than opening theory...even if you knew which opening was a forced win, would any of us know what to do with it??? probably not, i personally, just use intuition for the first 10 or so moves, once the position looks a little more managable i’ll usually analyze it a bit, but having a good feeling about position is much stronger in the beginning usually because it’s so difficult to predict your opponents moves early in a game.

  • dj at 2003-05-07

    I saw an A1 opening win. And the whole while the opener was getting ragged about how bad the A1 opening is. The thing is that A1 is only bad if the reply is b2 almost immediately. Any other reply leaves A1 as a possible keystone to a win.

  • Jan C. de Graaf at 2003-05-08

    Michael is correct in stating that the player having the option to swap should have a sure win at any sized/shaped board.

    The question is which openingmoves should be swapped and which not on which board sizes/shapes.

    I’m NOT a hex-player. It seems to me that HEX is a game of defense/attack patterns that keep growing larger and more complex until the edges of the board are involved. Do any good programs exist. With todays hardware 7x7 should be solvable, even with pretty dumb approaches. I hope/think that patterns showing up in 7x7 should enable a good program to play well on larger boards as well. Do any good (beyond-human) programs exist?

    Eventually my guess would be that distance between the middle of the board, the edge and the first hex can be formulized and tell us immediately the theoretical winner.

    Just the thoughts of a programmer that likes many games...

  • jjjklj at 2003-05-08

    there are programs, but none that as good as humans. hexy, six, and queenbee are the ones i know of. jing wang claims to have “solved” 7x7, 8x8, and 9x9. i haven’t read his papers, only played against his program at his website, but the computer always goes in the same place for the first move. therefore i have no idea if he has it solved for every opening or not

  • michael at 2003-05-08

    ying wang should let the player open, and use a swap option, that way we could check which openings should be swapped and which ones not up to 9x9 boards.

  • jjjklj at 2003-05-08

    oh, i forgot to mention, he has only 8x8 and 7x7 on the website, he claims he has 9x9 also, but hasn’t gotten it up yet

  • Marius Halsor at 2003-05-10

    I have a “follow-up” to the “what do we swap?”-question: Say you open b2 – or a2 or a3 for that matter – and your opponent plays the center: Would you then make your next move on the same side of the center as your opening move, or on the opposite side? Playing on the same side makes that half-board rather strong, but leaves the other open. Any thoughts about this, anyone?

  • David J Bush ★ at 2003-05-12

    After 1.A3 2.G7 there are plenty of continuations. I have frequently played 3.i7, and then if 4.i6 5.K5 looks fine to me. One player is starting with a strong central group, and the other player is like a guerilla sniping around the edges. These roles may very well switch later in the game. To be successful at Hex, you need to know how to play both roles- something I am still trying to learn to do.

  • Glenn C. Rhoads at 2003-10-02

    The following are the results for 7x7 hex.

    The following list of moves (and their symmetric equivalents) are
    the only loosing opening moves (without the swap option). I.e.,
    a perfect player would swap everything except the following moves.

    A1 through F1,
    A2, B2, D2, A3, and A5.

    For 8x8 and 9x9, the central hex(es) have been shown to be winning
    (without the swap option).

  • Kevin O'Gorman at 2003-10-02

    I wonder about this list of moves to swap at 7x7. Where
    does it come from? Some of it I know from Jing Yang’s
    published work on the D4 opening and the E3/C5 opening.
    I know of no other published work, and I’ve looked.

    Jing has pulled his papers from his own site, but there
    are still PDF’s around (and I have them). I don’t know
    if it’s Jing or someone else who’s solved the rest of
    that board.

    AFAIK, nobody has published results on larger boards, but
    there may be results awaiting publication. Does anyone
    know, or is this all rumor?

  • Glenn C. Rhoads at 2003-10-05

    The results come from a paper by Ryan Hayward. I don’t know if the
    article has appeared in print yet (I was a reviewer for the article) so if
    you want more details about these results, I suggest you email Ryan
    Hayward at the University of Alberta (you should be able to find the
    address at the University’s web site — Hayward is in the computer
    science department.)

  • ypercube ★ at 2003-10-07

    Any connection between Ryan Hayward and Ryan that plays at this site ?

  • Ryan at 2003-11-03

    I’m just regular old Ryan Sarkela =)

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