Swap rule necessary? Hex, Havannah

19 replies. Last post: 2013-09-03

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Swap rule necessary?
  • SimonF at 2013-08-20

    How big is the first player advantage without swap rule in Hex? Can I beat someone with 200 more ELO-points if I have the first move?

  • Tasmanian Devil at 2013-08-20

    You can beat him with 24% probability even if he is allowed to swap. ;-)

    Seriously though, the advantage probably does not correspond to a fixed rating difference. Like in go, a strong player would normally be able to make better use of the advantage than a weaker player.

  • SimonF at 2013-08-20

    I’m ranked around 1750 at the moment, how large would the difference be for me? I’m just looking for an order of magnitude estimate :)

  • Tasmanian Devil at 2013-08-20

    I really have no idea, sorry. :-)

  • Carroll ★ at 2013-08-20

    It depends what your first move would be and how big the grid, what would you play on hex13x13?

    I guess a 2000 player would beat a 2200 player more than 90% of the time with the advantage of starting.

  • SimonF at 2013-08-20

    Interesting, do you think the advantage is smaller on large boards? Isn’t the middle hex known to be the strongest first move?

  • Tasmanian Devil at 2013-08-20

    The advantage is of course bigger on small boards. On 5x5, an extremely simple algorithm gives a win every time for the first player. On 19x19 I would be pretty sure to lose against a top ranked player even with a first move advantage.

    The middle hex is a natural first move without swap but not necessarily better than all others.

  • David J Bush ★ at 2013-08-20

    Without swap or some other balancing opening protocol, Hex would be much less interesting. I am confident that any of the top ten 13x13 players could win virtually 100 percent of the time against any opponent if given the first move handicap. Not that any strong player would agree to play the losing side. No one would have crossed the 2300 rating mark, and there would be fewer strong players playing here in the first place.

    The advantage of the first move is so strong, there are many first moves which would win easily without swap. The central hex cell is not necessarily any stronger than many other first moves.

    The smaller the grid, the more important each move is, especially in the opening. So certainly, the first move advantage is more pronounced on smaller grids.

  • shalev at 2013-08-30

    The advantage is certainly smaller on larger boards, yes.

    My personal estimate is that the first move advantage is worth maybe 300 ELO on a 13x13 board. This is just a guess though. I would say the advantage is significantly larger for 11x11 boards.

  • lazyplayer at 2013-08-30

    In general what people said here seems ok. Playing first without swap gives a big advantage especially on smaller boards.

    About center, it is one of the strongest moves in the small boards, like 11x11, but it is not the easiest to play on larger board, and it is not even entirely surely that it is winning on large boards like 19x19..

    On 11x11 the typical trap against center opening is this: http://www.trmph.com/hex/board#11,f6f8e8d3g4f7e7g5f5d10 (white is winning).

    If you come to www.iggamecenter.com you can play without swap rule vs me on 11x11 and see yourself... :)

  • Art Duval at 2013-08-31

    @lazyplayer: I think the center is a winning move in larger boards, though I must admit I don’t have any experience with 19x19. In order for it to be a winning move, you do have to play better than Black did in your “typical trap” game. Black’s real problem there is not the opening move in the center, but the complete lack of imagination, or any moves that serve two purposes. For instance, Black’s second move should be something like h8 instead of e8.

  • David J Bush ★ at 2013-08-31

    It’s a trap!

  • lazyplayer at 2013-09-02

    It is just a trap indeed! I’ve found it interesting because it is one of the very few things white can try to do to win against center.

    I also have no experience with 19, my impression that center becomes weaker with board size comes from comparing 13 to 11 and 11 to even smaller. Anyway it is very difficult (but maybe interesting9 to formalize even an informal argument for (or against) this.

  • shalev at 2013-09-03

    Thanks for the trap lazyplayer! I don’t play much 11x11, so I’ve never seen it before.

    The center move does become weaker on larger boards, but I doubt it ever gets weak enough to stop being a winning move. Notice that the opening moves used by experts in 19x19 are all along the sides of the board (due to the swap rule, of course). This implies that central moves are too strong.

    I would even conjecture that any move in the (n-4)x(n-4) center section of any nxn board is a winning move.

  • lazyplayer at 2013-09-03

    Shalev, another curious observation is this: moves that are too strong in human vs human matches may be in fact losing in perfect play vs perfect play matches.

    I think this is so because when second player (the one playing with a stone less than the other) can win, he needs to be very accurate with his moves...

    But anyway i agree with you that it is really hard to argue center or center zone is losing at some board size! :)

  • lazyplayer at 2013-09-03

    For example, in Go the perceived right komi does depend on the strength of the players... i think something similar is at work in Hex.

  • hyperpape at 2013-09-03

    Lazyplayer: that’s disputed, and no one argues the effect is really that large.

  • lazyplayer at 2013-09-03

    hyperpape, what’s disputed? that in Go newbies should play with lower komi?

  • lazyplayer at 2013-09-03

    By the way, it seems Tasmanian Devil had already said all i’ve said... only thing i’ve to add then is that i agree with him... :)

    I’ve also some thoughts on one game by SimonF, but i’ll wait its end before (maybe) commenting on it...

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