What is the rationale behind the sizes of Go boards?

[Alcadeias]

Hello.

I don't know much about Go, but I heard that the standard Go board has a 19x19 grid.
I first thought that the fact that it was an odd number was pretty strange. But then I immediately noticed that 19x19=361, one more than 360 which is a superior highly composite number (a number which has more divisors than any other number scaled relative to the number itself).

I've also read that other sizes of Go boards also exist: 9x9, 11x11, 13x13 and 17x17.
Of these only 11x11 seems a logical choice: 11x11=121, one more than 120 which is also a superior highly composite number (120 is my favorite of all the superior highly composite numbers because of the facts that 11x11=121 and 7x17=119 and 13x132923=120^3-1 which gives us intuitive divisibility test by all primes up to 17 in base 120).

But I have no idea about the rationale behind the other sizes of Go boards. The most obvious thing is that they are all odds, and it looks pretty improbable that this is just a coincidence. Wouldn't it be more logical to take even numbers? Like a 16x16 board.

So my two questions are:
- Why do all the sizes of Go boards feature odd numbers but no even numbers?
- Why is the most common size of Go board 19x19? Does it really have something to do with the superior highly composite number 360, or is there another explanation?

Thanks in advance for your answers.

[DrStraw]

You can find some information here:

http://senseis.xmp.net/?DifferentSizedBoards

[Jujube]

Here http://senseis.xmp.net/?UnusualGobans is a fun page describing different variations of boards.

I think the size must have been settled over many years. I feel that it probably has something to do with what makes a good balance of fighting and strategy. Also think about the balance of territory and influence, and how that would change the dynamics of the game on different board sizes. As to the even/odd number of squares, all I can think of is that it 'looks' nicer, to have an even division of 4 sections, splitting the board down the centre and across the middle. It would 'feel' weird to play on a board that was even.

Edit: Also info here http://boardgames.stackexchange.com/questions/5516/why-is-the-19x19-board-so-much-more-common-than-other-sizes

[TheBigH]

I actually quite like playing on some of these "unusual" sized boards.

11x11 is not as cramped as 9x9, but still small enough for beginners.
15x15 is a good compromise when you don't feel up to a full 19x19 but you don't think 13x13 is quite enough. That's a common feeling for me.

[Bonobo]

[..]

11x11 is not as cramped as 9x9, but still small enough for beginners.

[..]

I wonder … where do you have the corner star points here? 3-3 or 4-4?

TIA, Tom

[Joaz Banbeck]

Don't believe all the fancy speculation. It all depended on the size of available trees.
Because of global warming, we'll soon be playing on 25x25 boards.

[Bantari]

19x19 is the largest possible odd-number-of-lines board on which the edge territory is larger than the center territory - i.e. it is the largest size which emphasizes edge over center, which has a huge influence on strategy.

Visualize black stones along the 3rd line all around the board, and white on the 4th line, so black has edge and white has center - and black wins. In the same situation on 21x21 board, white wins. Since anything less than 19x19 is less complex by definition, 19x19 is a logical choice.

[jug]

So my .. questions are:
- Why do all the sizes of Go boards feature odd numbers but no even numbers?

On DGS you can play all quadratic board-size from 5x5 up to 25x25, though the odd-size boards are preferred (perhaps some like the symmetry of having a tengen more than on even-sized boards):

Here some stats of finished games on the different board-sizes from DGS:

Code: Select all

| Size | CNT    |
+------+--------+
|    5 |   2464 | 
|    6 |    466 | 
|    7 |  11015 | 
|    8 |    434 | 
|    9 | 101230 | 
|   10 |   1256 | 
|   11 |   3166 | 
|   12 |    716 | 
|   13 |  65205 | 
|   14 |    455 | 
|   15 |   4656 | 
|   16 |    315 | 
|   17 |   1145 | 
|   18 |     91 | 
|   19 | 639319 | 
|   20 |    293 | 
|   21 |    371 | 
|   22 |    104 | 
|   23 |    265 | 
|   24 |     79 | 
|   25 |   3657 | 

[moboy78]

19x19 is the largest possible odd-number-of-lines board on which the edge territory is larger than the center territory - i.e. it is the largest size which emphasizes edge over center, which has a huge influence on strategy.

Visualize black stones along the 3rd line all around the board, and white on the 4th line, so black has edge and white has center - and black wins. In the same situation on 21x21 board, white wins. Since anything less than 19x19 is less complex by definition, 19x19 is a logical choice.

Basically what this guy said

[Shawn Ligocki]

One interesting thing about 13x13 and 9x9:
19*19 = 361 spaces
13*13 = 169 (close to 361/2 = 180.5)
9*9 = 81 (close to 169/2 = 84.5)

In fact these sizes are the closest possible squares numbers to each halfs. I wonder if that was part of the aesthetic reason for choosing those sizes? In general, it gibes with my impression that 13x13 take half as long as 19x19 to play and 9x9 take half again the time.

Why 19x19? I have no idea. Balancing edge and center territory sounds like a good reason, although for true balance I'd expect you'd want more center territory than side, since center is harder to defend.

[Cassandra]

Boards of size 17 x 17 lines (= 16 x 16 fields), can be generated in the most easiest manner:

Just halve distances repeatedly.

This implies that the change to boards of size 19 x 19 lines (= 18 x 18 fields) in Ancient China must have been well-founded, either by reasons

-- resulting from some inner characteristics of the game itself (e.g. edge vs. centre), or
-- resulting from some religious based tradition (e.g. the flow of the days of the year), or
-- both.

[Uberdude]

A traditionally-sized 19x19 board has 42 squares on it, which is the answer to life, the universe, and everything.

[Bill Spight]

A traditionally-sized 19x19 board has 42 squares on it, which is the answer to life, the universe, and everything.

A traditionally sized 19x19 board is longer than it is wide. What squares?

[Uberdude]

A traditionally-sized 19x19 board has 42 squares on it, which is the answer to life, the universe, and everything.

A traditionally sized 19x19 board is longer than it is wide. What squares?

Exactly, and that ratio is why there are 42 and not 18x18 + 17x17 + 16x16 + ... 2x2 + 1x1 = 2109.

[DrStraw]

A traditionally-sized 19x19 board has 42 squares on it, which is the answer to life, the universe, and everything.

A traditionally sized 19x19 board is longer than it is wide. What squares?

http://senseis.xmp.net/?HowManySquaresOnAGoBoard