# It's not Chinese

June 3, 2007 8:24 PM Subscribe

For starters, it's not Chinese. It was probably inspired by a British fave called Hoppity, and its immediate forbearer, Halma was invented by a Bostonian professor/surgeon. There are a number of variants, but you're probably most familiar with the ubiquitous star-shaped version. Inevitably, some people take it too seriously. Wanna play?
See also, DIY and stop motion Fergiliciousness.
(Personally, I prefer Hex.)

No-name mystery posts make the baby Jesus cry.

posted by gottabefunky at 10:59 PM on June 3, 2007

posted by gottabefunky at 10:59 PM on June 3, 2007

Just tried hex. 12 times. Didn't win once - I can't quite get my head around what a winning strategy might be, but playing a real person instead of a computer might be a helpful start.

posted by Jimbob at 11:06 PM on June 3, 2007

posted by Jimbob at 11:06 PM on June 3, 2007

Hex is fun. During and after my Computing Science BSc, I worked as a research assistant on a team that made a strong Hex playing program. Along the way, we solved every opening of the game of 7x7 Hex.

Jing Yang was the first person to solve 7x7, by showing that if the first player moves to the center, they can win with perfect play. He has an applet demonstrating that here. He also proved that 17 more easy opening moves were wins or losses.

However, most people play Hex with the swap rule, meaning that the second player has the option of switching colors after the first player moves. There is a proof that, without the swap rule, the first player can win with perfect play. The proof doesn't tell us how the first player wins, just that they *can*. With the swap rule, then, the game has a second player winning strategy. So, it's useful to know whether a win is possible or not for every opening move - if the first player plays a win, the second player should swap; if the first player plays a losing move, the second player should not swap.

We wrote a paper (link) explaining some of the cool optimizations we made for our program (it turns out you can add pieces to the board to simplify it without changing the outcome of the game), and showed whether every opening move for the first player was a win or a loss. I made a copy of the important diagram of the openings, too. This shouldn't ruin the 7x7 game for you - it shows whether it's possible to win or lose with each opening move, but actually doing it still takes a lot of skill!

The game can be played on boards as big as you like, and Hex on boards like 14x14 will be safe from computers for a long time. The search space just grows too fast.

Happy hexing!

posted by Fully Completely at 12:47 AM on June 4, 2007 [2 favorites]

Jing Yang was the first person to solve 7x7, by showing that if the first player moves to the center, they can win with perfect play. He has an applet demonstrating that here. He also proved that 17 more easy opening moves were wins or losses.

However, most people play Hex with the swap rule, meaning that the second player has the option of switching colors after the first player moves. There is a proof that, without the swap rule, the first player can win with perfect play. The proof doesn't tell us how the first player wins, just that they *can*. With the swap rule, then, the game has a second player winning strategy. So, it's useful to know whether a win is possible or not for every opening move - if the first player plays a win, the second player should swap; if the first player plays a losing move, the second player should not swap.

We wrote a paper (link) explaining some of the cool optimizations we made for our program (it turns out you can add pieces to the board to simplify it without changing the outcome of the game), and showed whether every opening move for the first player was a win or a loss. I made a copy of the important diagram of the openings, too. This shouldn't ruin the 7x7 game for you - it shows whether it's possible to win or lose with each opening move, but actually doing it still takes a lot of skill!

The game can be played on boards as big as you like, and Hex on boards like 14x14 will be safe from computers for a long time. The search space just grows too fast.

Happy hexing!

posted by Fully Completely at 12:47 AM on June 4, 2007 [2 favorites]

Fully Completely, you've got me utterly frustrated. The rules of Hex don't seem consistent.

Jing Yang's applet lets the first player take the centre square, therefore they always win.

In the applet linked in the original post,

Wins so far...

Me: 0

Computer: 61

posted by Jimbob at 4:59 AM on June 4, 2007

Jing Yang's applet lets the first player take the centre square, therefore they always win.

In the applet linked in the original post,

*only*black can play the centre square on the first turn, but white gets to go first. Therefore the first player*cannot*take the centre square, so I can't play the strategy I derive from Jing Yang's game.Wins so far...

Me: 0

Computer: 61

posted by Jimbob at 4:59 AM on June 4, 2007

*only black can play the centre square on the first turn, but white gets to go first.*

That's done precisely so that you can't do what you're trying to do. Since there's a known winning strategy for the first player playing in the center square, that's no fun, and it forces you to take a different option.

An interesting thing about Hex is that the "Games never end in a tie" fact is equivalent to the Brouwer fixed point theorem. The 1-d version of Brouwer's theorem is a standard easy exercise seen in just about any Calc I class, but then even in 2-dimensions the techniques required to prove it are entirely different.

It's also interesting with Hex, as with Dots-and-Boxes and other combinatorial games, how wide the gap between "theoretical understanding" and "practical game-winning skill" is.

Six is probably the strongest computer hex-playing engine, but if you rather play against people, there's Kurnik.

posted by Wolfdog at 5:55 AM on June 4, 2007

I liked chinese checkers for the marbles.

My first game like hex was Bridg-It. There is a java game of it here. (Enter n= how big the board is). There are some studies on how to win Bridg-It, although it seems like Bridg-It is a solved game while Hex (>6) is not.

Then there was Twixt and Mudcrack Y.

posted by MtDewd at 6:05 AM on June 4, 2007

My first game like hex was Bridg-It. There is a java game of it here. (Enter n= how big the board is). There are some studies on how to win Bridg-It, although it seems like Bridg-It is a solved game while Hex (>6) is not.

Then there was Twixt and Mudcrack Y.

posted by MtDewd at 6:05 AM on June 4, 2007

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posted by Popular Ethics at 9:06 PM on June 3, 2007