Hex with pass Hex, Havannah
6 replies. Last post: 2003-11-17Reply to this topic Return to forum
Taral at 2003-11-13
I thought of a new variant of hex. It’s like conventional hex, except that the players are allowed to pass. At the end of the game the winner gets an amount of points which equals one plus the number of times he passed during the game.
This version can be used for example in matches over several games, or in handicap games.
In a handicap game the stronger player can give the weaker a komi of, say, 1.5, in which case he has to pass once before he can complete his winning path.
I guess that in most games between experienced players there will no passes.
David J Bush ★ at 2003-11-13
That might work, but perhaps better would be an initial handicap of N stones, similar to Go. If the stronger player has to pass, it would probably be in his/her best interest to make all the passes at the start, otherwise the handicap would probably be even greater. That means the weaker player gets to choose how to place the initial extra stones, which is a very strong handicap. Better to place the initial stones in specific patterns, to control the amount of handicap given.
You almost certainly know this, but row handicapping is not feasible in Hex. If the board becomes a rhomboid instead of a rhombus, the player with shorter distance to cross has an easy win, even if the other player goes first. This has been proven on any board of dimensions N by M where M>N. Twixt is superior to Hex in this regard. :-)
Tim Shih at 2003-11-14 hi, interesting discussions here by Taral and David. How about the following 3rd option: (let me use the 9x9 board as our example, and N is the maximum number of moves for the better player to claim the victory)
Two equal-strengthed players: N=81 (if swap was taken, then N=82)
David against a beginner: N = 21 (something like that)
If David cannot form a solid continuous chain in 21 moves, then he loses.
When handicapped games are played, there can be many kinds of possible arrangements. The essence of the handicapping is:
* such that the weak player has a chance to win,
* such that the strong player is sufficiently challenged.
Once I played ping pong with a right-handed pro. He used his left hand to hold the paddle, and still defeated me.
Once a Go pro played a handicap game. The rule was that he was requirerd to win EXACTLY two points. no more, no less. Gee, that is challenging, don’t you think? :)
Dvd Avins at 2003-11-16
David, wouldn’t a rhomboid be a 3-dimensional analog of a rhombus? As I learned it, the shape you refer to is a parallelogram.
David J Bush ★ at 2003-11-17
A rhomboid is a parallelogram with two sets of unequal sides. A rhombus is a parallelogram with all equal sides. 3-dimensional objects usually have “hedron” at the end, so maybe you are thinking of a rhombohedron?
Dvd Avins at 2003-11-17
“Hedron” is the 3D analog to the suffix “gon”, in that it refers to the faces of an object just as “gon” refers to the sides. But ellipsoid, for instance, refers to a shape created by spinning an ellipse about a central axis.
I thought that in geometry “oid” was specific to that kind of 2D>3D transformation, but now I guess, as in general English, it just means 'sort of like a..." without specifying in what way it is like the root word.