Rationality Lessons in the Game of Go
There are many reasons I enjoy playing go: complex gameplay arises out of simple rules, single mistakes rarely decide games, games between between people of different skill can be handicapped without changing the dynamics of the game too much, there are no draws, and I just like the way it looks. The purpose of this article is to illustrate something else I like about playing go: the ways that it provides practice in basic habits of rationality, that is, the ways in which playing go helps me be less wrong.
I’ve tried to write this so that you don’t need to know the game to follow it, but reading a quick introduction would probably help. (ETA: A commenter below has helpfully pointed to more go info online.) The main aspect to understand for this article is that go is a game of territory. The two sides vie to occupy space and surround one another. If a group of stones is surrounded without sufficient internal space to support itself, it is killed and removed from the board.
Lesson 1: Having accurate beliefs matters.
Here are three examples of a group of white stones being surrounded by black stones. The important distinction between them is whether the white stones will eventually be captured, i.e. whether they are “dead” or “alive”.
Fig 1: The white stones are dead.
Fig 2: The white stones are alive
Fig 3: The white stones have ambiguous status.
In Figure 1, the white stones are being smothered by the black stones. They are overwhelmed and cannot escape eventual capture. They are “dead”.
In Figure 2, the white stones are surrounded but have sufficient structure to protect their internal space and thus will not eventually be capture by the black stones. They are “alive”.
In Figure 3, the issue is unsettled. Depending on how play proceeds, the white stones may eventually live or may eventually die.
Accurately determining whether the white stones in situations like Figure 3 are doomed or not is essential to winning go. There are go training books that consist of nothing but hundreds of exercises in correctly assessing the status of stones and learning the subtleties of how their arrangement affects that status. Correct assessment of life and death is one of things besides a large branching factor that makes computer go so hard.
I once read something on LessWrong which was later labeled The Fundamental Question of rationality: “What do you believe, and why do you believe it?” I have found this useful to adapt to go: when playing, I constantly ask myself, “Are these stones alive or dead, and how do I know that?”, and this practice in turn has encouraged me to ask the original fundamental question more in the rest of my life.
Lesson 2: Don’t be too confident or too humble.
Overconfidence leads to bad play. If white were to mistakenly play further in the scenario of Figure 1 in an attempt to salvage the position, she would be throwing good stones after bad, giving black the chance to make gains elsewhere. But underconfidence also leads to bad play: if white were to play further in Figure 2, she would also be wasting her time and giving up the initiative to black. As is true in general when trying to achieve your goals, too much humility is a bad thing. Go punishes both false hope and false despair.
Lesson 3: Update on new evidence
The status of a group of stones can change over time as play in different areas of the board grows and interacts. Stones that once were safe could become threatened if nearby battles have a side effect of increasing your opponent’s strength in the area. It is thus essential to constantly update your assessment of stones’ status when presented with new evidence (new moves), and act accordingly. This used to be a big weakness of mine. I often would take a strong lead during the opening and middle of the game, only to lose when a large group I thought was safe gets captured late in the game because I forgot to pay attention to all the implications of further moves elsewhere.
Lesson 4: Be willing to change your mind
Even when you pay attention diligently, it can be difficult to act in response to new information because of emotional attachment to your previous beliefs. When I launch an invasion of my opponent’s territory, sometimes the battle that follows reveals that my invasion was too aggressive. My invading stones are doomed. But I don’t want to give up. I throw good stones after bad and in the end only end up strengthening my opponent’s position. Better play would be to 1) realize as soon as possible that the invasion was overplayed and then 2) shift from using the invading stones as part of the attack to using them to aid your efforts at containing rather than invading (this idea is called Aji). Go rewards those who are willing to change their minds as soon as is warranted.
Lesson 5: New evidence is the arbiter of conflicting beliefs
Games usually end in a curious way: by mutual agreement. When both players believe there are no more moves they can play that will either expand their own territory or reduce their opponent’s, both pass. The players then reveal their beliefs about the “alive” or “dead” status of each group of stones. This is done to avoid the tedium of playing out all the moves required to actually capture doomed stones. If the players agree, then dead stones are removed and the score is counted. But if the two players disagree, the solution is simply to resume play. Further moves inevitably reveal who had the more accurate belief about whether a group of stones was doomed or not.
Lesson 6: The road is long
One interesting feature of go is the broad range of skill levels at which it is played. If you want to make a line of players such that each of them could defeat the player on their right 90% of the time, you can make a longer such line of go players than players of any other game I know. This game is deep. And as with rationality, it takes practice to internalize productive habits of thought and banish self-delusion.
Moreover, as with rationality, it is usually possible to appreciate the skill of those one or two levels more advanced than oneself (kind of like the way listening comprehension leads speaking ability when learning a language). Thus, there is a constant pull, an encouragement to reach over one’s own horizon and achieve a deeper understanding.
Lesson 7: Shut up and count
Go games are decided by a balance of points (roughly speaking, one spot on the board or one stone is worth one point). Out of a few hundred points available, games between closely matched opponents are often decided by a margin of fewer than 10 points. (Different counting systems vary the absolute numbers here but not the spirit.) This means that accurate quantitative evaluation of the board is essential to good play. It’s not probability theory, but it definitely shows how numbers can serve your goals better than feelings and hunches. No matter how skillfully you manage to read ahead the moves of a complicated tactical fight, if you pursue that fight instead of playing a simple move elsewhere that has a bigger impact on the score, you’re making a mistake.
As much as I enjoy go, I feel I should finish by noting that in the end it is still just a game. Time spent playing will probably not do as much to advance your goals as actual direct work. Sometimes, the more you play, the less you win.