Game Design Perspective: Go

In this Game Design Perspective, we're gonna turn the clock back. Waaaaay back. No, further than that. We're talking ancient China. According to legend, the First Emperor of China had a problem - his son and heir was a snot. He entrusted his councilor Shun to create a game that would ennoble his son. (Cue the "I’ll Make a Man Out of You" song from Mulan.) Thus was born the game of Go.

While the origins of the game might be lost to legend, the first recorded reference to Go dates to the 5th Century BC. This makes it older than chess, although not so old as checkers, circle and cross games, or senet. In my opinion, Go blows all these ancient games out of the water. Nearly a decade ago, I first discovered the game and it quickly became an obsession. Go is a masterpiece of design, perhaps the most perfect example of complex strategy emerging from simple rules. A study in its game design is richly rewarded.

The game of Go is played on a 19 x 19 grid. White and Black take turns placing a single stone from their pile onto the grid spaces on the board. If a white stone (or cluster of white stones) is orthogonally surrounded by black stones, the white stones are removed. The same rule applies if white stones surround black stones. A player cannot place a stone that would be immediately captured, unless placing that stone would capture the other player's stones first. A stone cannot be placed that recreates an earlier board state. The game ends when both players pass, and whoever has the most occupied territory at the end is declared the winner.

Pictured: Basic capture rules for single stones and groups of stones.

That's it. Those are all of the rules. The beauty of Go lies in how complex strategy emerges from these simple rules. How complex does the strategy get? In 1997, IBM's Deep Blue defeated Gary Kasparov at chess. It took nineteen years of advancements in hardware and AI techniques before Google's Alpha Go was able to defeat Lee Sedol, an equivalent player, in 2016. In 1997, Deep Blue was running an ostentatious 32 CPUs and 512 specialized chess chips, clocking in at 11.38 gigaFLOPS (FLoating point Operations Per Second). For comparison, the iPhone SE released in 2016 ran at about 300 gigaFLOPS. AlphaGo ran on 1920 CPUs and 280 specialized GPUs, topping one petaFLOPS (or one million gigaFLOPS). Safe to say it's much more floppy.

After Deep Blue, it took over a decade to create a Go program that could defeat a reasonably-proficient child. If the rules are so simple, why did it take so long? The answer lies in the profound implications of the simple rules stated above.

Let's talk about life and death - it's a huge topic in Go. Groups of stones in Go are thought of as alive, dead, or (often) somewhere in the nebulous between. As the rules above state, a group of stones surrounded by enemy pieces is captured and removed from the board. Now, picture a square-shaped donut arrangement of Go pieces, or a 3x3 square that's missing the middle piece. This is known as an eye. If Black has an eye, White cannot place a piece in the middle of the eye (because it would be captured instantly) - with one important exception. If White has the eye otherwise surrounded, then the white stone played in the middle will capture all the black stones before it gets captured itself. The eye can still be taken.

Pictured: Capturing an eye.

Now, what would happen if Black's group has two eyes? In that case, White can never place a stone that would capture the group, since "poking" out one eye would leave the other open. The move fails to capture Black's pieces and White's "eye poke" is forfeit. Thus, a group with two eyes is said to be alive - nothing the opponent can do can ever capture the piece.

Pictured: It’s aalliiiiiiivvveeee!

Nearly as important is the concept of dead groups. Dead groups are groups of stones that cannot possibly survive. If White has a dead group, and escape or rescue attempt is doomed to fail with proper play by Black. Any play by White on a dead group becomes Black's advantage.

Because of life and death, the edges and corners of the board are extremely important. On the edges, you can form an eye with only 5 pieces. The corners are even cheaper, requiring only 3 pieces in the very corner. Almost every Go game starts off with players claiming and contesting the corners of the board. In fact, a player's initial stone placement will oftentimes reveal the broad strokes of their strategy. Placing a stone on a 3-4 point (that is, in a corner area on a point three lines away from one edge and four lines away from another) signals that the player will be more focused on claiming territory immediately. Playing a stone one line over on the 4-4 point signals that they are playing for "influence". That 4-4 stone is harder to defend from invasions, but it is more likely to provide support elsewhere on the board.

Pictured: Completely different games.

Remember, nothing about life and death and edges and corners is found in the rules of Go. These are just the emergent consequences of the rules.

In Go, the idea of influence is key. The 19x19 board is large enough that a move in one corner does not affect moves on other parts of the board. Or, at least, it doesn't affect those areas right away. A given stone played early in the match on one side of the board may unlock new options on the other side of the board a half game later. Go only has a single type of piece, unlike chess with its pawns and knights and rooks. All the stones are equal to each other. The strength of a shape or position on the board is solely in the arrangement of its stones. Distant pieces exert influence on each other because they can be linked up by other friendly stones, forming a new cluster.

The mere threat of linking up can be a powerful move. Remember the dead groups discussed earlier? Even if a group is dead, it can still be valuable. If you approach the dead group from a short distance away, you can threaten to link up with the dead group and give it new life. Your opponent will be forced to respond and spend moves preventing the dead group's resurrection. You can use these turns to get an extra move or two in, solidifying a position or a new invasion into enemy territory.

Using a dead group relates to another interesting idea in Go - the idea of "aji". Aji is unfinished business, loose ends, and potential future trouble. Or, more poetically, aji is the stone in your shoe while you're running late. If you had time to stop and take it out, it wouldn't be a problem. It's a problem because you don't have the time. A game of Go can be thought of as a conversation between two players. With each move, the players are saying "This is the best move I can make right now," or more generally "This is the most important part of the board right now." Sometimes players disagree on the most important part of the board. Let's say White plays in one area of the board, perhaps the lower left corner. Black may choose to play in another area instead of responding locally, and White may follow Black's lead in playing there. Even so, the "conversation" about the lower left corner might not be done yet. It can still influence the later game in ways difficult to foresee. Dead groups, lone stones, weaknesses in the opponent's shape - all of these can be exploited for profit later.

I am by no means a great Go player, and this article isn't even trying to touch on all the strategy and tactics involved in the game. There are whole books written about topics I didn't even mention, like the proper timing of invasions and the direction of play. I'm hoping more that this article serves as an introduction to some of the basic ideas of Go. I don't really use the term "beauty" to describe game mechanics, but I will make an exception for Go. Like the best mathematical theorems, it has an elegance in its simplicity. The way this huge strategic complexity arises from such basic rules is nothing short of astounding. In my opinion, the design of Go ranks up there with anything else from humanity’s collective creative achievements.

Being a game that's been played by so many for so long, Go has accumulated a collection of proverbs. Many are inscrutable to the uninitiated - "Never ignore a shoulder hit." Some have a particular zen-like quality, like the pair "If you have lost all four corners, then you have lost the game" and "If you have won all four corners, then you have lost the game." (This pair of proverbs tells beginners that if you have not paid any attention to the corners and lost them all, you will probably lose. Likewise, if you focus so much on winning all four corners that you give up the rest of the board, you will also probably lose.) My personal favorite is "Never go fishing when your house is on fire," which implores the player to take care of urgent defensive needs before they dither around elsewhere on the board. That's good life advice in general, especially if you ever find your house on fire.

Pictured game from Yuan Zhou’s excellent book Single Digit Kyu Game Commentarys.