I am somewhat new to the community. I played prior to 1977 in high school and only stumbled on to it again fairly recently. I have been a mathematics educator for about 35 years and now wonder if my students could benefit from involvement in some form of mathematical recreation. I have made available to them some interesting information about Twixt. I am wondering if anyone has any suggestions on how to encourage new players to give it a try?

Here are some resources.

Alan Hensel's page here on LG has a link to an interactive puzzle page and other cool stuff.

Anyone can play the Twixtbot here but it is very strong. Newcomers might prefer to download and play against T1j instead. It offers row handicapping, so you could take a handicap or give one.

The BoardGameGeek Twixt page is a hub link. Check out the Strategy and Sessions Forums, and the external links section.

There are two places to play online in real time, Game Center and Boardspace. Game Center has handicapping options implemented. I offer handiap play to anyone who wishes. Maybe we could meet on Game Center some time and I could play handicap games simultaneously. You could email me to discuss details. On Boardspace we are starting a new tradition of a monthly “quad” tournament. See this post.

So, play, look at puzzles, read. I also have a book of chants, but I got into legal trouble about that so never mind.

Hi again, Bailey. Again, you have addressed two different topics here, so I want to remark to both. As far as playing and learning Twixt, the links that David gave you above should prove useful.

You are 5 years ahead of me, since I (only) spent 30 years as a Mathematics educator, before quitting the business! One of my positions, in a G&T program, was to teach an enrichment class for middle school called 'The Math of Sports and Games'. Teachers had much flexibility, and I designed most of the course myself. In fact, contact me privately if you want more information on my curriculum.

This was some years back - I recall units on baseball statistics, odds and payouts on casino games, poker probability, a bit on Chess, an outdoor experiment involving throwing objects and using physics to predict their path of flight, and more stuff.

I did not think of Twixt as a game to really inspire MATHEMATICAL thinking and analysis. Of course NOW, with the success of Deep Mind, Alpha Go, Alpha Zero, and Twixtbot, one can see how game strategies might be developed statistically. (As I have remarked before, this is not the way humans think and may have limited use in human play.)

Now 2 games come to mind immediately that I would consider more in the line of Mathematical. One of them is available commercially as 'Qubic', or 3D Tic-tac-toe on a 64 square board. Even though I let the kids play on the two sets that I brought to class, I showed them that the 3D board can be represented on graph paper (2D) by drawing four levels, and the game can be played this way. I believe that this activity promoted geometric visualization, and the strategies of planning were also useful for learning.

I rather enjoy Qubic, only the game has been SOLVED - it is a forced win for the first player, WITH PERFECT PLAY. However, I can still beat people going second, since not everybody plays perfectly. I still wonder if the game would be feasible here if the first move advantage is taken away by the pie rule - however, I have a feeling that if the first player does NOT make a winning first more, then the SECOND player has a forced win with perfect play! Here again, though, is that 'perfect play' proviso.

Pefect play also arises in 'NIM' games, and I did teach some elementary NIM games to the kids. In this game, the player who CHOOSES WHETHER TO GO FIRST has a forced win with perfect play. But when NIM is set up with more numbers, rows, etc. the so-called 'perfect play' can become rather obscure - it requires much MATHEMATICS to solve; I believe one generally uses binary arithmetic, though I never became personally proficient at this game.

But our 'DOT AND BOXES' games, played here, are in fact based on the concepts of NIM. This game can become extremely complicated, and requires much Mathematics to be analyzed correctly. I think this would be a great game for Math classes, and I would say, if you want more expertise and discussion, then our current champion syLph would be the one to talk to.

Another activity I did with the classes was The Game of Life, created by John Conway (passed away last year from CoVid, alas). This is not exactly a 'game' - it is a solitaire. I had so much fun creating Life 'organisms' on graph paper during my days in high school and college, that I thought that kids might enjoy it. They did. This would be an example of a mathematical simulation. I can see that one might devise competitions using Life, and it's fun just watching the organisms change through generations (there are Life simulators available on the web). The guy to talk to about this, in the absence of Conway, would be our very own Alan Hensel - former Twixt champion, curator of Twixt Commentator, and a Life enthusiast. Alan has published papers on Life and done way more research on it than I ever have!

I hope I gave you some ideas of use, and if some of your students pop up at Little Golem as new Twixt competitors, so much the better!
(meow)

Regarding 4x4x4 Qubic, I wrote a program to play the game, which is accessible online.

http://www.haplessgenius.com/mocha/

There are three lists below the green screen. Look for “Load Bin” and scroll that list down to Fourcube.
Select Fourcube and click Load Bin.

• Press the 6 key for the strongest version.
• The up and down arrows scroll the cursor through the cells.
• The left and right arrows rotate the board.
• Press Enter to make a move where the cursor is.
• If you find the blinking cursor, distracting, rotate the board.
• There are really only two different initial cells to make the first move in, as far as game play is concerned. The 8 corner cells and the 8 central cells are all isomorphic to each other. These could be called the strong cells. Similarly, all the other 48 cells are essentially the same first move as far as game play is concerned. These could be called the weak cells. So, one move equalization can be simplified. Just say you must play in a weak cell on the first move. If you want the computer to make such a first move at the start of the game, press the F key. I call that the “Faircube” option.
• The D, or “Demo” key tells the computer to take over both sides. You could press F at the start and then D to watch a “Fair” game. I believe the first player has a win even when starting in a weak cell. Strength 6 is not perfect but it is close.

Regarding Dots & Boxes, I recommend the book “Dots and Boxes: Sophisticated Child's Play” by Elwyn Berlekamp.