Twixt - Recently Updated Pages

Puzzle 1

twixter — Tue, 24 Nov 2009 23:01:11 CST

There is no abstract available for this page revision.

15x15 grid

twixter — Tue, 24 Nov 2009 22:59:57 CST

The format here is a 15x15 grid with four border rows, 13x13 common area. The player to move should have border rows on the top and bottom. This player is referred to as either vertical or the color of those border rows. The object could be player to move and win, or player to move and draw. Standard Twixt rules apply with link removal, not PP rules. The number of horizontal versus vertical pegs should be equal, or horizontal could have one peg more.

Puzzles

twixter — Tue, 24 Nov 2009 22:49:03 CST

There already is an excellent Twixt puzzle site at http://www.ibiblio.org/twixtpuzzles/ with an interactive Javascript board. But the format there is restricted to 12x12 quarter board sections of a larger board. Wetpaint might be a home for other size grids, or puzzles which include all four border rows instead of just two, or puzzles where finding the key move is not enough to claim a solution, or perhaps for Twixt variants such as diagonal border lines.

Solved boards

maraca — Thu, 13 Aug 2009 08:03:13 CDT

At which board size is the first spot that leads to a draw if both players play perfect (size > 5x5)? Is such a starting move existing at all? These are some of the interesting questions behind this topic, let's see if we can find out...

< 3x3

Impossible because the corners aren't part of the game.

3x3 to 5x5

Draw: At 3x3 and 4x4 there isn't even an existing connection, that means even with the help of the opponent we can't win. 5x5 is the first little challenge. These games result in a draw because 'X 'can't connect to the top (and of course the same is valid for the mirrored position to come down), so the right answer for '1' is '2':
. * * * .
* 1 X * *
* * * 2 *
* * * * *
. * * * .

6x6

1 = win for white (up-down). 2 = win for black. 0 = draw. Top left corner without first column:
2 2
1 1
1 1

7x7

TODO

Twixt wetpaint usage and maintenance discussion

twixter — Fri, 20 Feb 2009 05:26:25 CST

There is no abstract available for this page revision.

The Mousetrap

Kd_Hoffmann — Mon, 27 Oct 2008 10:40:49 CDT

Often you will have the situation that you can attack a defending peg either on one or the other side.
Attacking on the strong side gives you a local breakthrough, the weak side can easily be defended by your opponent.

Nonetheless it might be a good idea to start your attack on the weak side and put some cheese into the mousetrap.

In the diagram above Blacks 4.i12 (weak side) can easily be defended - but Black continues attacking on that side as long as he can threat to break through without a defensive reaction from White.

But now, as late as possible, the mousetrap snaps and Black catches the mouse with 14.i18 on the strong side leaving White with a huge disadvantage (see diagram below).

White cannot break through on the left bottom side, e.g. 15.e17 16.f21 -/+ (Achilles Defense) or 15.e18 16.e20 -/+ (Medcalf Defense).

On the right side of the board White has only left the rows 'k' to 'w' but the whole range of lines '1' to '24' for the remaining match.
Black otherwise has a lot of possibilities with much shorter ways thanks to his earlier mousetrap strategy.

Conclusion: Be careful when you smell some cheese. It might be healthier for you to continue attacking your opponent somewhere else on the board!

Some examples for mousetraps (including the above example):

Maxims for moves

alhensel — Mon, 29 Sep 2008 18:47:48 CDT

In Twixt the first move is so very powerful that black is given the option of swapping. To avoid giving black a powerful first move, white should play a very weak move. D-3 and D-22 are good examples. If you play black and your opponent plays a strong move *always* swap as your first move.

mryan asks: If white wanted to make a strong first move, but instead makes a poor move to avoid black taking the move, and thus on blacks first move black goes where white wanted to go, I see black in the strong hole no matter what white does.Would it be better for white to make a medium move and if black took it, white could then make that killer first move, and if black declined the swap, wouldn't white now have a better first move than if he had made a weak move? Please help me understand mryan9810c

That's exactly right, mryan: the first move should be medium: neither too strong, nor too weak. What Steven is alluding to above is the fact that the first move is such a strong advantage, that a good medium move will look very weak to a new player. Thanks to the way ladder chases work out, a move like 1.d3, way off in the corner, turns out to be medium, although it may seem very weak the first time you see it. Even 1.c3 is pretty even-handed. -Alan

The most common defensive strategy is to play directly ahead by 2 pegs or 4 pegs. Beware of playing 3 pegs directly in front of your opponent. It only works well under specific conditions. More than 4 pegs may allow your opponent to setup bridges. Too close and he may go right past you.

Strategy changes as you get farther from the middle. Blocks that work in the middle will not work close to the border. Blocks that work well close to the border, may not work in the middle. The cardinal lines are your guidelines as to when to change strategy. The most basic strategy to keep in mind is to play between your opponent and his border whenever that is feasible.

Playing between your opponent and one of his other pegs is risky, especially if you can't see an absolute block. Always think twice or even thrice about trying this strategy.

Another good strategy is to try to place your line parallel to your own board edge when you can. This gives you multiple points of attack making your opponent work harder to decide where to block.

Finally, try to find a way to create 2 paths to your border. Again this makes it more difficult for your opponent to block.

These guidelines for Twixt moves contributed by Steven Medcalf and reflect the author's personal opinions about Twixt play.

----

The following maxims are contributed by Alan Hensel.

A good defense is the best offense. Learn to block. Defensive tactics are important to understand early, because they make it easier to make sense of opening moves. And the person with better opening moves will grab the upper hand early, and end up in a good offensive position. (This is an intentional twist on the typical saying, "a good offense is the best defense". Please don't edit it back! -awh)

Play the whole board. Local battles are very tempting. Resist. Keep your mind on winning the war. The player with better holistic thinking gives himself more choices, and the advantage. When your opponent gives you a narrow alley and a broad alley, don't go down the narrow alley.

Make double threats. This applies from the late opening moves to the end of the game. The winner of the game is often the last person to make a credible double threat. Spread your double threats; a widely separated double threat is the hardest to defend against.

Go left by going right. You can often use a threat of going one way around your opponent, even if it's obviously not going to work, to make it possible to go the other way around. Also called the mousetrap.

Almost sometimes counts. For example, where you see the opportunity to play a beam (0-4), a 1-4 gap is often also worth considering. (On the other hand, sometimes Twixt can be very unforgiving.)

A dashed line is better than a dotted line. A dashed line is often even better than a solid line, especially when forming parallelograms, because it can make the end of the line harder to block.

When winning, simplify. When losing, make chaos. And when playing against an opponent stronger than yourself, take him off the beaten path quickly, if you can, to deprive him of familiar patterns.

Learn to see the best moves quickly. Don't think you can just think harder or spend more time to make up the difference. You're staring down a combinatorial explosion. Someone who is seeing the best 2 moves each time can look 3 moves ahead more easily than someone who is seeing the best 3 moves each time can look 2 moves ahead (2^3 < 3^2). Therefore a good heuristic/intuitive sense of what looks like a good move is very important.

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Forced moves are a very powerful tool in TwixT, if you use them right. One example already mentioned here is the mousetrap, but you can expand this tactic. Every move that forces the opponent to play in a certain area if he doesn't want to lose the game or get a very weak position is considered to be a "forced move" in this text.

The most important thing to gain the maximum profit out of a forced move is timing. Look how the game may develop and decide when to use your ace in the sleeve. Thus it appears, that the order of your moves is very important too.

Warning: be always aware of the consequences of a forced move. For example an often used counter is to place a peg with 4 holes difference towards the opponent's border (means towards your border, if used against you), this makes the path to one side safe and increase the power to the other side. Of course this works only in specific situations and forced moves don't have to be at the border, they can be spread over the whole board.

Here a short forced move guide for intermediate TwixT players:
1. Look for forced moves
2. Look for their consequences (advantage for you or opponent, following forced moves, ...)
3. Decide how / when you want to use them (when you get the most profit, which order, ...)
4. Check if the one you maybe want to play later is still "alive" after your opponent's move
5. Always keep in mind, the opponent could play forced moves too...
6. Forced moves can be very powerful, but remember they are only one of many ingredients of a succesful TwixT tactics mixture.

Forced move example (move 14 and nearly all following moves): little golem game 891661.

These guidelines for Twixt moves are contributed by maraca and reflect the author's personal opinions about Twixt play.

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Some terms related to "forced moves" are "sente" (Go terminology for the concept) and "cascade attack" (making a series of threats against the gaps in your opponent's line, which he can easily close up, in order to set up a real threat.)

Twixt Maxims bear a striking resemblance to Go Proverbs. Here's one that also applies to Twixt:

"Your opponent's good move is your good move. It may often be useful to think about what your opponent would like to play if it was his move. If it is a good thing for your opponent to get something, it is a good thing for you to stop him from getting it. To stop him from playing on a point, you can play there yourself. Note that your move need not always be exactly the same move as he would have played. Rather, it often is a move in the same general area."

Twixt related Web links

artyomch — Thu, 25 Sep 2008 19:49:59 CDT

Playing Twixt in the Web:

igGameCenter - real-time multiplayer board games (including Twixt).
Little Golem - free turn-based online board games
The K2Z server to play Twixt in Realtime for free
On Richard's PBeM Server you can also play turn-based Twixt for free.
Download a Twixt package for Zillions of Games (non-free software). More screen shots and info are here. This is not a server, just a way for two people to play over the Net in real time.

Twixt software:

A JavaScript Twixt Board by Alan Hensel
Jtwixt, a game database manager and analysis tool (does not play Twixt)
T1 and T1j programs that play Twixt on your computer, by Johannes Schwagereit

Twixt puzzles:

40 Twixt Puzzles by Alex Randolph
Interactive Twixt Puzzles by Alex Randolph and Alan Hensel (based on the JavaScript Twixt Board)
Some full board puzzles by Martin Windischer

Twixt instruction:

Introduction to Twixt rules, puzzle articles, annotated games
A collection of articles in html format, annotated games, instruction, and puzzles
Annotated games from the Little Golem 13th championship first league tournament
Some basic corner battles by Martin Windischer
Twixt related information by the Spielekreis Hiespielchen (in German language, edited by Klaus Hußmanns (as far as I know))

Twixt general information:

Alan Hensels Twixt First Move Statistics
Twixt page on BoardGameGeek with pictures, comments, lots of info, links
Wikipedia Twixt page, rules, variants, and further links

Twixt commented games elsewhere:

TwixtPP games from LittleGolem's 13th and 14th championship
commented by György Csizmadia, Alan Hensel, David J Bush, Tim Shih and others.

Link Removal

twixter — Fri, 29 Aug 2008 09:57:12 CDT

Why remove a link?

The most common reason for removing a link or links is to avoid a draw.

White to move here should play i5, as indicated, removing the G5/H7 link (or, using Alan's notation, the G'6 link) and then double linking from G6 to H3. White could optionally play H4 instead of i5, but either way, the G'6 link should be removed so that white can have a contiguous chain of links connecting both border rows.

Computer programs on Twixt

ab_ab — Wed, 13 Aug 2008 15:52:04 CDT

As for Go, it is hard to write a program for Twixt although the rules are quite simple. The number of possible moves is large and judging a board position is fairly difficult. For these reasons, currently no program for TwixT exists which cannot be easily beaten by an experienced human Twixt-player.

Known Twixt-programs are:

http://www.buus.us/Peri_Damon/Video%20Game%20AMOK/Index.htm (Windows only). The playing strenth is similar to www.twixt.de (Visual Basic).
The Twixt-playing program, which was formerly hosted at www.twixt.de, can now be found here. It looks nice, but plays not too strong. (2001, Java, German language.)
pvs-bot, which was hosted on the k2z Twixt server, only smaller sizes 12x12 were supported (mid-2004)
one program by "ab" (littlegolem): a modified version of T1 (C++), with own ai (and slightly changed Gui) [it was called T2]; played good opening, but later lots of bad moves ...
See this page for some information about the program "T1" (2004, C++).
See this page for some information about the program "T1j" (2006, Java). The 2nd version is the best program, currently.
MaraTwixtPP: see "Do it yourself" page:This is a try to animate people to write their own TwixtBot. It's some kind of template where the GUI is implemented and you just can fill in your code to calculate the next move based on the given information.

Any other?

More information is also at:
http://senseis.xmp.net/?Twixt

Basic algorithms

maraca — Thu, 17 Jul 2008 14:12:47 CDT

Here I try to describe three algorithms, so that everyone can understand it. Maybe it's not the most efficient way to implement something, but it's easy and of course, it's only one possibility you can make it in many other ways too.

How to check if a peg connects to another?
First look at the picture on the right side. The yellow peg (say placed at row, col) is the peg you want to test if there is any connection to another one. The red pegs show all positions where the distance (not diagonal) to the yellow peg is 3 (line with comment 1 at the code). The green area is the rectangle with top left (row-2, col-2) and bottom right corner (row+2, col+2). The points who match both criterias and where's a peg with same color as the test peg (//2) are the points we're looking for. In java this could look like this:
Warning: this is not the complete method, just the main parts, of course you got to make sure that you don't have an index out of bounds and if the connection you get is not crossed by one of the opponent. For this problem see next chapter.

public void connect(

int[] point, // point[0] = row of peg to test, point[1] = column (both 0 to 23)
int[][] board) // board[row][col] = 0 --> no peg, 1 --> peg up-down, 2--> peg left-right

{

for (int i = -2; i < 3; ++i)
for (int j = -2; j < 3; ++j)
if (Math.abs(i) + Math.abs(j) == 3 && //1
board[point[0]][point[1]] == board[point[0] + i][point[1] + j]) //2
{
// We can connect from (point[0], point[1]) to (point[0] + i, point[1] + j)
// ATTENTION: not tested if a link is crossing
}

}

How to check if a link crosses another one?
There are two ways to do that. You can calculate the connections who would cross your connection and then look if this connection exists or you can check for every connection if it is crossing your one. Second way is explained here because it can be done with simple mathematics, but the other way would probably be faster.
In words: A connection is crossing another one if the start and end point of both connections are on different sides of the line going through the other connection.
In mathematics:

Legend:
(x1, y1) = startpoint of connection 1
(x2, y2) = endpoint of connection 1
(x1', y1') = startpoint of connection 2
(x2', y2') = endpoint of connection 2
g = straight line through connection 1
h = straight line through connection 2
y(x) = the formula for g
red = the test we need to test if the points of connection 2 are on different sides of g.

So the drawing only shows one test, youve got to do the same for h. You get this test if you replace every 1 by a 2 and every 2 by a 1 in the formulas. This works for all connection, doesnt matter if they stored from left to right, up-down or whatever...

This can be implemented by some for loops. With the given information above, I think a code example wouldn't be necessary and just ballast for this site...

How to check if your move is a winning move?
Lets say you played your last peg at (row, col). You can calculate all reachable positions from there and see if there is one reachable position at each side of the board. This can be done recursive, here a java code example:

// more about Connections in 'Do it yourself'
private boolean[][] reachable;

public boolean isWinningMove(int row, int col, Connections myConnections) {

reachable = new boolean[24][24];

calcReachablePos(row, col, myConnections);
// now you can test with a for loop if you have
// on both of your sides a reachable position,
// for example if you playing left right
// At least one of reachable[1 to 22][0] and
// at least one of reachable[1 to 22][23] has to be true.

}

private void calcReachablePos(int row, int col, Connections myConnections) {

if (!reachable[row][col]) {
reachable[row][col] = true;
for (int i = 0; i < myConnections.getSize(); ++i) {
int[] c = myConnections.get(i);
if (c[0] == row && c[1] == col)
calcReachablePos(c[2], c[3], myConnections);
else if (c[2] == row && c[3] == col)
calcReachablePos(c[0], c[1], myConnections);
}
}

}

Conclusion
I hope this text gives a small insight in the computer thinking of Twixt. Comments and contributions welcome ;-)

--- Update Jul 18 2008 ---

I developed a new way to store a twixt board. For the advantages see below. Maybe someone has any use for it. That's how it works:

You store all in a 48x48 integer array instead of a 24x24 array (in the whole text it is assumed that the first index is 0). This means one "cell" contains of a 2x2 array which I use like this:

numbers:	even	odd
even	peg	connection
odd	connection	free for use

Pegs: The pegs are stored on their normal position multiplied by two. 0 means no peg. -1 is the player from left to right and 1 the player from top to bottom.

Connections: The middle point of every connection is stored. 0 means no connection. The sign gives the color. For the two possible directions you can use 2 constant values.

Free for use: Here you can attach some information to a peg coded as an integer or use it as index for another data structure where peg-relevant information is stored.

The advantages of using this way instead of the common way:

All information is on the board, you don't have to search in a list of connections, means better performance.

There are 9 connections that can cross another one. On this board there are stored on only 7 spots and they can be found very easy:
* \ * X P
\ . \ . \
P X * \ *
Explanation: 'P' means peg, so the connection goes from bottom left to top right. Stars '*' are Positions where pegs could stand. The 'X' are the spots where connections in both directions cross the other one and the '\' are positions where only a connection from top left to bottom right intersects. So you see all the 7 possibilities to cross a connection are stored within the rectangle given by the connection itself.

All possible connections to or from a peg are stored in the square surrounding the peg (the characters mean the same as above):
* \ * / *
\ . . . /
* . P . *
/ . . . \
* / * \ *

Because the color of a player is represented by the sign and the direction by a constant value. You can work good with absolute values if you just want a direction or with signs if you just want the color. The -1 and +1 values of the pegs are practical for multiplication too (if you want to paint something a specific color ;-), because they don't change the absolute value.

The advantages in short words: The board is more "human" (easier to get a picture what's really going on with a scan of the board) and the performance is better.

I would like to hear your opinion, does this make any sence to you or is it just useless?

The Opening moves

alhensel — Thu, 17 Jul 2008 12:27:38 CDT

The first peg

It is usual to place the first peg within the upper left area (marked yellow in the picture below).

The reason for this is that it is easier to compare different matches.

Strength of the first move

The effect of the pie rule is to force the first player to look for a neutral first move. But what's a good neutral first move?

Alan Hensel's Twixt First Move Statistics of over 25,000 games played on Little Golem tries to answer this question. You can get some good ideas from it, but unfortunately, there is still a lot of noise in the picture, because players tend to have favorite spots.

What really constitutes a good first play is still largely a matter of opinion, but the following table is probably pretty close to current expert player opinion of the strength of first moves:

In this table, the numbers are approximately the percentage of games you can expect to win against an evenly matched player with your first peg on that spot. Color is directly related to the number. The graph shows only one quadrant (or, all four folded over) because the board is symmetrical. The a-x column is not shown because it's not a legal first move.

The subsequent opening moves

Some general, very helpful hints by Alan Hensel you find here.

From a personal (still growing) database of Twixt matches you can check the most popular opening sequences.

Do it yourself

JohannesSchwagereit — Tue, 16 Oct 2007 06:14:05 CDT

Introduction
First I want to apologies for my bad english, but hope you understand what I'm trying to say.

The history
I wanted to write a Twixt AI, but how to write one if you can't display your moves? So I started to write a java programm called "MaraTwixt P&P" with a GUI. Then i thought, why don't make it public, so that everyone can try to write a strong Twixt AI? The code is unfortunately uncommented but all you got to know is explained in the next chapter. If you find any bugs just send me a message or feel free to correct them ;-).

MaraTwixt P&P
Download: MaraTwixtPP.zip (zipped source files) or MaraTwixtPP.jar (runnable, including source files)

First steps

To run the program, either doubleclick the jar or use:
java -jar MaraTwixtPP.jar
MaraTwixt requires Java 5. Currently there is no AI implemented.

Download the zipped sourcefiles (MaraTwixtPP.zip). Extract all files and save them at the place you want. Now you can begin to work. If you haven't programmed java yet it would be very helpful if you make a java tutorial first. Here you can find more than you need ;-) http://java.sun.com/

Don't like the colors?
You can change the colors in the class Constants in the gui package. This is the only documented code, so you shouldn't have any problems. The name of your Twixt AI you can change there too.

Write your own AI
Open the class AI in the ai package. There is only one function, that's where you can fill in your code:

public int[] getMove(int mycolor,

int[][] board,
Connections myConnections,
Connections opConnections,
boolean swap,
JProgressBar prog)

The arguments

mycolor: 1 = you playing from top to bottom, 2 = you playing from left to right.
board: Represents the board. With the following command you can get the information if there is a peg at (row, column), where 0 = no peg, 1 = peg, from player playing up-down, 2 = peg from player playing left-right:
board[row ][column] //ATTENTION: values from 0 to 23, this means highest row = 0th row.
myConnections: Represents your connections.
opConnections: Represents your opponents connections.
swap: true if you can swap, otherwise false
prog: You can set a value from 0 to 100 to show the user how far your move calculation is. Only command needed:
prog.setValue(yourValue);

More about Connections
A connection is represented by 4 integer values, where the first 2 give the startpoint, and the 2nd pair is the endpoint. With hasConnection(row1, col1, row2, col2) you can check if theres a specific connection from point1 to point2 (or point2 to point1). If you want to read all connections do it like this:
for (int i = 0; i < myConnections.getSize(); ++i) {

int[] c = myConnections.getConnection(i);
// c[0] = row1, c[1] = col1, c[2] = row2, c[3] = col2

}

How to make a move
This is the easiest part. Just save the row you want to place your peg in point[0] and the column in point[1] after you finished your calculations. Return (0, 0) to swap.

Start the programm
Compile all files and start the Main class in the gui package. No idea what I mean? Click on the link in the first steps chapter.

Click here for more information about Basic algorithms.

6.m18

Kd_Hoffmann — Tue, 19 Jun 2007 14:10:56 CDT

Possible moves after 6.m18:

11 matches ( 3 wins by White and 8 wins by Black)

7.o17

5 matches ( 2 wins by White and 3 wins by Black)

7.m19

3 matches ( 1 wins by White and 2 wins by Black)

7.m17

2 matches ( 0 wins by White and 2 wins by Black)

7.j15

1 match ( 0 wins by White and 1 wins by Black)

5.l16

Kd_Hoffmann — Tue, 19 Jun 2007 14:07:25 CDT

Possible moves after 5.l16:

16 matches ( 4 wins by White and 12 wins by Black)

6.m18

11 matches ( 3 wins by White and 8 wins by Black)

6.l12

4 matches ( 1 wins by White and 3 wins by Black)

6.l14

1 match ( 0 wins by White and 1 wins by Black)

5.n13

Kd_Hoffmann — Tue, 19 Jun 2007 14:03:22 CDT

Possible moves after 5.n13:

11 matches ( 9 wins by White and 2 wins by Black)

6.n15

6 matches ( 5 wins by White and 1 wins by Black)

6.m15

4 matches ( 3 wins by White and 1 wins by Black)

6.o8

1 match ( 1 wins by White and 0 wins by Black)

5.o13

Kd_Hoffmann — Tue, 19 Jun 2007 14:01:56 CDT

Possible moves after 5.o13:

13 matches ( 4 wins by White and 9 wins by Black)

6.o16

9 matches ( 3 wins by White and 6 wins by Black)

6.o17

2 matches ( 1 wins by White and 1 wins by Black)

6.n17

1 match ( 0 wins by White and 1 wins by Black)

6.o8

1 match ( 0 wins by White and 1 wins by Black)

4.j10

Kd_Hoffmann — Tue, 19 Jun 2007 13:59:25 CDT

Possible moves after 4.j10:

10 matches ( 3 wins by White and 7 wins by Black)

5.p12

7 matches ( 3 wins by White and 4 wins by Black)

5.h13

2 matches ( 0 wins by White and 2 wins by Black)

5.i13

1 match ( 0 wins by White and 1 wins by Black)

4.j17

Kd_Hoffmann — Tue, 19 Jun 2007 13:54:39 CDT

Possible moves after 4.j17:

18 matches ( 4 wins by White and 14 wins by Black)

5.l16

16 matches ( 4 wins by White and 12 wins by Black)

5.f17

2 matches ( 0 wins by White and 2 wins by Black)

5.m14

1 match ( 0 wins by White and 1 wins by Black)

5.m15

1 match ( 0 wins by White and 1 wins by Black)

4.p14

Kd_Hoffmann — Tue, 19 Jun 2007 13:44:40 CDT

Possible moves after 4.p14:

24 matches ( 16 wins by White and 8 wins by Black)

5.n13

11 matches ( 9 wins by White and 2 wins by Black)

5.h14

5 matches ( 5 wins by White and 0 wins by Black)

5.l14

4 matches ( 1 wins by White and 3 wins by Black)

5.k14

2 matches ( 0 wins by White and 2 wins by Black)

5.g16

1 match ( 1 wins by White and 0 wins by Black)

5.r13

1 match ( 0 wins by White and 1 wins by Black)