QUAX
Copyright (c) 2000 Bill Taylor
QUAX is a two player strategy game played on any square board. The author suggests 11x11 (as usual, smaller is more tactical, larger more strategic).
- PIE RULE - One player drops one stone on the board. The other chooses who starts.
- MOVE - On each turn, each player must do one of the following actions:
- Drop a stone into an empty cell.
- Connect two friendly stones diagonally adjacent, if it does not cross another connection.
- GOAL - Wins the player that connect his to two opposite edges (horizontal for Black, vertical for Red).
A connecting example The black stones are connected. The red stones cannot be connected directly.
Race to connections If it's Black turn he wins by playing at cell [1]. If it's Red he must play at [1] and have a powerful threat to win at cell a10, where Black must drop a stone to continue his attack.
Quax is available on Richard Rognlie's email server.
Some words from the author:
The main diagonal lines have a similar role to the critical lines in TwixT.
One tactic has become clear:
A Tesuji Black dropped the marked stone. There's nothing Red can do about it. Black is sure to be able to slide down one side or other, and the 2-chain prevents any double-cut moves.
Play between the author & page-owner suggests a lot of early moves are best played on the "same-coloured" cells
I'm surprised no-one else seems to have thought of Quax before! I guess they just didn't think of a "diagonal crossing" as being a move; even though it is identical to play on the Archimedean 8/4/4 board:
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Connection games seem to be getting names ending with X, (Hex, TwixT), we thought that "Quadrangular Hex" could be usefully shortened to "Quax", which is also the noise made by the winner as he puts in the killing move! :-)
A small puzzle (from Bill Taylor) solution Black started. Who wins?
A sample game d3 f5, f8 h8, g6 f7, g3 f3, f2 e2, e3 e2f3, f4 g4, f4g3 h3, g5 f5g4, h4 g4h3, g7 e8, Black resigns
check the cells coordinates by pointing the mouse over them!
Two other games:
- d3 e6, c6 c8, h6 h8, f7 f9, e9 e8, d8 g9, c7 e10, c9 d9, c9d8 c4, d5 Red resigns
- c3 e5, f3 h3, g5 i6, h4 i4, i9 g7, f8 g9, g8 h8, h7 i7 Black resigns
The earliest reference to this game is a post in r.g.a at Dec 18, 1992, using another name: Link.
This game, LINK, is very similar to TWIXT, mentioned here several times.
I imagine it is more slow-moving than twixt, however.
It is a game I invented some while ago, though never played. Doubtless it has
been independently invented many times. It is an attempt to create a game
close to the connection game, HEX, but played on an orthogonal board. It is
essentially the same as hex, but to ensure a result, (no ties), there is a
twixt-like move available, whereby one may connect two diagonally adjacent
cells of one's own color, instead of a regular placement move.
I have never played it, as I say; but if anyone is interested in trying an
email game, I would be very keen.
Naturally, rule 1, board size, is open to negotiation; and I would suggest
a three-move equalization (described here earlier) would be suitable
to counteract the obvious first-move advantage.
RULES OF LINK
=============
1. It is played on an orthogonal 8x8 board, by two players, black & white.
2. Black has first turn. At each turn a player may EITHER put a counter of his
own color in any vacant square; OR connect two diagonally adjacent counters
of his own color with a bar of his own color, PROVIDED that such a bar does
not cross over one of the opposite color.
3. The winner is the first player to complete a path of stones between his
own two edges of the board: north-south for black, east-west for white.
A path is a sequence of stones each of which is either orthogonally
adjacent to its predecessor or connected to it by a bar.
=============
. O X . I hope the rules are suitably unambiguous, and not too long-winded.
/ It should be clear there is an unlimited supply of counters and bars
X X O . available. A bar may not be placed if either end is vacant.
\ \
. O X O The diagram here shows a completed game on a 4x4 board. Black has a
won with a 4-counter 2-bar path. Black has played 7 moves and white 6.
. O X .
There's a reimplementation of Quax, from 2004, called Stymie by Randall Bart.
The main difference is a more complicated rule about how many moves each player can make. In fact, so complicated that I don't understand the wording (or the logic). So, let me just copy-paste it from http://www.gamerz.net/pbmserv/stymie.html:
Two players, Vert and Horz, take turns placing pieces of their colour on the board. Vert plays first and places a single V piece on any empty cell as the opening move.
Thereafter players may place either:
1) One piece of their colour on any empty cell, or
2) Two pieces of the colour on an empty octagon and an adjacent empty square.If the opponent's last move was a singleton (not counting the opening move) then the current player may instead make a special three-piece move, occupying an empty octagon and two empty squares adjacent to the octagon or an empty square and two empty octagons adjacent to the square.
Bill also considered a variant where two friendly stones become diagonally adjacent, the corresponding connection is made immediately (except if the opposite cross-diagonal already exists). This variant is called Quickway.
Solution Black wins! Red best move is at [1]. There is no way to stop the Black chain (move 5 is a White connection between [1] and [3]).
This was posted in Nov 11, 2007 (an excerpt):
The current game belongs to the family represented by Mark Steere's "Crossway", and my own "Quax" and "Quadrex". It is most like Crossway, which I acknowledge in the name "Quickway", while keeping the Qu- motif, as for QUadrangular-connection games.
The games are all essentially the same, one side has to connect the north and south edges, the other the east and west edges, by orthogonal paths of stones, alternately placed. Like Hex.
The differences arise by how to treat a "Cross-cut", "Stymie" or "Impasse". e.g.
More specifically, how to treat . . . .
the situation where 3/4 of . X O .
a stymie has occurred... . , X .
. . . .
* In Quadrex, the 4th point (,) is automatically filled as X;
* In Quax, the 4th point may be played, then resolve cross-cuts by allowing either player to use a turn to mark in a diagonal, (these may not cross).
* In Crossway, the 4th point (,) is forbidden to O,
* In Quickway, the diagonal connection between the 2 X's is filled in automaticaly, and the 4th point (,) may be filled by either.
So Quickway is a kind of cross between Quax and Crossway, in that the final board will look very like a Quax game, but the "Hane" shown at the above right is a guaranteed connection for X.
As far as playing goes, I expect it is most like Crossway; the new game is just a variant of it. Although the diagonal connection between the X's is not marked in Crossway, it is effectively there. Most games would be identical, with a very rare case of where O might want to fill that 4th point for some other reason. It seems more natural to me to allow him to do so.
As I say, I think this may be the final member of this family, in that Mark and I seem to have covered every case of what to do with a 3/4 stymie, regarding the status of the diagonal connection and also the status of the 4th point.
status of fourth point
imposed allowed forbidden
________________________________
Diagonal: | | | |
auto | quadrex | quickway | crossway |
|__________|__________|__________|
requires | | | |
move |(quadrex) | quax |(crossway)|
|__________|__________|__________|
Very cute!As always, a swap option on the 2nd half-turn is required for equalization, and the size of the board is a parameter. The same size should suit both Crossway and Quickway, which as I say are almost identical. So...
QUICKWAY
========
Played on a square quadrangular board of arbitrary size.
Players alternately place one of their stones (an unlimited supply) on any free cell of the board. Once placed, a stone is not moved.
The goal is for one player to connect the north and south edges by an orthogonal path of stones (perhaps augmented by diagonal lines), and the other is to connect east and west.
When stones of the same colour occur on diagonally adjacent cells, the corresponding diagonal line is automatically filled, unless it would cross over a previously marked diagonal.Also check a subsequent post from Nov 5, 2008 (which comes with a long thread).
Another variant played by Bill Taylor and Joćo Pedro Neto was called Torax, using an auction mechanism:
1. Initially both players, alternatively, plays one or more blocks (white stones), or else adopt Blocker (play as White).
2. After adoption, the other player (Black) starts the alternating moves. Play continues as in Quax.
3. The game ends when Black has made a connected global loop in any direction (vertical, horizontal or diagonal); or until this is impossible.So, Blocker starts with great disadvantage, which means it makes sense to place several white stones, before Blocker starts to be on a balanced position.
Here are some matches:
a b c d e f g h i Bill Joao | _Bill__JoaO_
--------------------------------- ---------- | 11. b5 e7
. . . . . O _X O . 1. c3g7 b3h7 | 12. g5 h5
_/ | 13. h4 i4
. . . X _O _X _O . . 2. b7h3 adopt | 14. i5 d5
_/ _/ _/ | 15. c5 c6
. O O O _X _O _X O . 3. e5 e2 | 16. d4 d5e4
_/ _/ _/ | 17. d4e3 f3g2
. . . X _O X O X_ O 4. f2 f3 | 18. g1 h1
_/ \_ | 19. h9 f1
. X X _O X . X O X 5. e3 e4 | 20. f2g1 f9
_/ | 21. a7 a6
O . O X . . . . X_ 6. f4 g4 | 22. i6 i7
_ \ | 23. i6a7 a8
X _O . . O . O O O 7. d2 d3 | 24. h4i5 i9
_/ | 25. d6 c6d5
O X . . . . . . . 8. g3 d3e2 | 26. b8 a8b7
| 27. resign
. . . . . O . X O 9. e3f2 e4f3
--------------------------------- 10. f4g3 g2
a b c d e f g h i Joao Bill
--------------------------------- ----------
O . O . O . O O . 1. c3g7 a1i9 10. c1 h4
. . . X . X . . . 2. i8 h89 11. h1 b4
. . O . X . O . O 3. i7 h7g89?? 12. i3 resign
. X . . . . . X . 4. adopt e5
. . . . X . X . O 5. g3 e3
. . . . . . . . . 6. e1 g5
. O . . . . O O O 7. i5 a9
. . . . . . O O O 8. b7 f2
X . . . . . O O O 9. g1 d2
a b c d e f g h i Bill Joao
------\_------------------------- ----------
O X _O . . . O . X 1. c3g7 h7 11. a8 i8
_/ 12. i7 a7
X O_ X X X . . . . 2. h8 g8 13. i7a8 b8
\_ 14. b9 a9
. X O O O X _O X . 3. adopt e5 15. a8b9 c9
_/ 16. c1 f3
. . . . . O_ X . . 4. g3 g4 17. e3 d2
\_ 18. d3 c2
. . . . X X O_ X . 5. g5 h3 19. b2 b3
\_ 20. b2c3 b1
. . . . . . X O X 6. f4 f5 21. c1b2 a2
22. c1b9 e2
X . . . . . O O O_ 7. f4g5 g6 23. g3f4 resign
_ \_ 24.
O_ X . . . . O O X 8. h6 h5 25.
\_ 26.
X O_ X . . . . . . 9. g5h6 i6 27.
\_ 28.
10. g1 i1 29.Another variant is QuikQuax, a 2008 variant by Bill Taylor. Same as Quax except:
- 134* progressive sequence,
- As soon as a diagonal pair appears, it automatically gets a diagonal join
- The moves in each sequence must be in different quadrants
Here's some sample matches:
| Jo| Bx__
a b c d e f g|h i j k l m n ==================================
. . . . . . . . . . . . . . 1. .. .. .. e6 .. i5 i10 e10
. . . . . . . x . . . . . . 2. f7 i7 g10 l10 e3 m6 g8 h8
. X x . x . o . . . . . . . 3. g3 h7 j8 f9 f5 h2 g12 h12
. o . o x x . . x x x . X . 4. g6 j5 e8 l12 c10 g5 h5 k9
. . . o o x x x x o x o . . 5. e5 k7 l8 f11 e4+ e12 k5 k11
. . . . o . o . . o o o x . 6. d4+ l9 k6+ d9 c3 c12 k13 j4++
__. . . . . o . o o . o . . .__7. l13 l5+ d11 b4 b3 m4 d12 m12
. . . . o . x x . o . o . . 8. resign
. . . o . o . . . . x o . . 9.
. . x . x . o . x . . o . . 10.
. . . o . o . . . . x . . . 11.
. . x X x . x x . . . o X . 12.
. . . . . . . . . . x o . . 13.
. . . . . . . . . . . . . . 14.
a b c d e f g|h i j k l m n
|
| Bo| Jx-
a b c d e f g|h i j k l m n ==================================
. . . . . . . . . . . . . . 1. .. .. .. d4 .. e10 i10 j4
. . . . . . . o . . . . . . 2. d6 m6 c10 l10 f6 l3 c12 l13
. . . . . . o . . . . x . . 3. l4 h8 g7 d10 k4 g5 i8 d9
. . . o . X . o . x x o . . 4. h10 b8 e7 h4 f7 j7 f11 h11
. . . . . . x . X . . . . . 5. g3 h6 h9 f12 j6 f13 h13 c7
. o . o . x . o . x . . o . 6. h2 b6 d13 h12 f4 i5 e12 i12
__. . x . o x o . . x . . . .__7. resign
. o . . . . . o x . . . . . 8.
. . . x . . . o . . . . . . 9.
. . o o x . . o x . . o . . 10.
. . . . . x . x . . . . . . 11.
. . x . X o . o X . . . . . 12.
. . . o . x . x . . . x . . 13.
. . . . . . . . . . . . . . 14.
a b c d e f g|h i j k l m n
|