Sente, A Liberal Interpretation
Kirk: I'd like to thank everyone who has reviewed this page. Your comments and corrections have been invaluable. Please keep the feedback coming!
This page is aimed at players in the 15-5 kyu range. I am an AGA 2k myself, and often teach and play others in that range. Some of the concepts discussed here are perhaps somewhat "watered down", but it is impossible to absorb the subtle meanings of go terms the first time around. I hope that the way I have organized my thoughts here provide a useful framework for your continued development.
Sente is a pivotal concept in go. The main Sente page says a player has sente if they "do not have to answer their opponent's last move." This is to be interpreted as not having to answer in a local sense. For example:
Does black need to answer white 1 at 'a'? If not, then black "has sente" and can play in another part of the board with impunity (well, not quite, as we'll see in a moment). If black needs to connect, then we say white 1 was sente. It is common to say both "so-and-so has sente" as well as "move X is sente". But how do you know if black needs to play 'a'? Well, like most things in go, it depends.
When the game is nearly over (when positions on one part of the board don't affect other positions elsewhere on the board) we can be quite precise. In the case of Diagram 1, if black fails to play at 'a', white may play there and kill black's group. That would mean five points for the prisoners plus seven points of territory, for a total of 12 points.
(Aside: if this were to happen, it would cost white two moves, 1 and a, to make those twelve points, so white is getting about six points per move on average. This can sometimes be a useful way of thinking about the value of moves.)
Now, the key point about sente is, "it's relative". If black can make a move somewhere else that threatens to make more than 12 points, then white's apparently-sente move at 1 would, in fact, not be sente. Black would "steal" sente (although the moral obligation is really on white, as you'll see). Let's look at an example:
What has happened here? White thought black would respond to 1, but black actually found a bigger threat in 2. If white follows up his threat with 3, then black takes 4 and black has gained four points more than white. After 4, white has sente (just like before white played 1, presumably). So actually, by playing things out like this white (whom we assume had sente to begin with) has actually fallen behind by four points! This is a good example of how making threats does not necessarily mean you are gaining points!
But would people really play this way? Not quite. White should not have played 1, but let's suppose, since he is human (or devious: such tactics are rather common in handicap games), that he did. Once black plays 2, white should realize that 2 is a bigger threat than 1 and defend at 3. Then, assuming there are no other large threats for black, black would also go back and defend. Like this:
Now where does the score stand? Black will get two points and white will get two points, so things are even. White's move at 1 has not cost as much as before, but is it a good move? It didn't gain any points in the corner, but it is possible that it has other benefits. If white had stones at the 'a' points, for example, it would seal off some territory at the top.
The value of white playing 1 has to be weighed against alternatives for white (such as 2). If the points marked a are black, then 2 may well be a better first move for white.
Technically white DOES get sente back in both diagrams above, perhaps a better example is in order (black does steal sente for a moment, but it comes right back). ~srn347
So at the end of the game, when you can calculate precise values for moves, one can be quite clear about which moves are sente and which are not, who has sente at any given time. (Not that I'm saying it is easy -- see the endgame to see the richness of this area of the game.) But this is only one kind of sente: a purely territorial sente. In my opinion, the concept of sente can be applied very broadly to the entire game right from the beginning. It is not possible to calculate precise numerical values for these cases, but there are, nevertheless, qualitative metrics that can assist making these kinds of judgements. This is where go really becomes interesting...
What are the qualitative metrics? Thickness, Territory, Eyeshape, connectivity, and Efficiency are the main ones. Sente can then be "calculated" by summing together the values of these elements (considering the positive effect on your position minus the negative effect on your opponents position -- a positive). Of course, it's not really so simple, but these pages will attempt to shed some light. At least if you understand these elements you will be playing go instead of just randomly putting stones on the board. In other words, I hope these ideas give you something to think about when you don't know what move to make.
What follows are my definitions for these terms along with examples of how the concepts apply to making value judgements.
Territory: well, it's the goal of the game, right? CRITICAL ADVICE: don't consider anything as territory until the very end of the game. I'm dead serious. Think about it: you never know what dumb move your opponent might make. Suppose he plays a move like 1 in Diagram 4. You know this isn't the biggest move on the board, you have a larger threat at 3. And you must make that threat. Diagram 4 shows what could happen if you dont. Rather than two points each, white ends up with three to your two plus additional reducing moves at 5/6 and 7-10. (If white played 3 instead of 1, then you could play at 1 and it would be a case of MutualDamage. As it is, white gains from the 1/2 exchange in the diagram.)
So what should you do? Follow diagram 3, of course. You group might die, but that's okay because you are gaining points overall. That's why you mustn't think the black group in the upper left as territory or even as alive. Look at Diagram 5 to see how this can trip you up.
It may come to pass that your large, one-eyed group is desperately seeking a way to live and you are faced with the choice in diagram 5. White just played 1 and you need to choose bewteen 'a' and 'b'.
If black saves the corner with 'b' he gains three points but loses the large one-eyed group, 43 points. Net 40 points to white. Conversely, if he plays 'a' to save the large one-eyed group, he will gain 2 points for the group but lose about 24 points to white. 24 points? Is the corner really that big? Yes, because all the points marked 'x' are no longer black's sente endgame moves, so they also count as part of white's gain.
How does this relate to sente and not taking life for granted? Well, earlier in the game, you might have thought it okay to give white the marked wall knowing you could jump to 'c' to reduce the territory there (see MonkeyJump). The liability of saving your corner group is larger because you are counting on it to reduce white's territory there.
My point is this: you don't know what the future course of the game will be -- in fact, your opponent will try to thwart you at every turn, so don't take anything for granted. Easier said than done, I know.
Making moves based on territorial concerns can often turn out to be wasted. I'm sure you've had it happen to you: you make a move to define some territory and your opponent immediately sets about nullifying that very territory. These nullifying moves need to be accounted for when estimating the territorial value of a given move. A lot of the time it is much smaller than you might like to think. Here's an example where a move is played for territorial reasons, but then that reason is later invalidated:
White just played the marked stone and black has replied with 1. Perhaps black thinks the upper left side is going to be his territory and 1 is a good, solid move to define the boundary (he might choose 'a', 'b', or 'c' as well, but the point ends up being the same). Note that I'm not saying 1 is a bad move, I'm more interested in clarifying the misconceptions some people may have about it.
But the upper left may not become black territory. What if white does this?...
Now black 1 is not defining territory at all. That doesn't mean it is completely useless -- it is preventing white from making life in the upper left -- but the territorial motives for it no longer apply. This is the point I'm trying to make: when considering what move to play in the opening and middle game, territorial concerns take a back seat to the other issues we will be discussing here.
A taste of things to come... It is fairly common for that black 1 to be a good move. Notice that black has a position down the left side. Black 1 works with this to help expand blacks area of influence over the center. Black is open at the top (white could take many points by jumping to a, but the potential for black in the center is better. Helping you to learn how to make these kinds of judgements is a goal of this page.
One more example of why you should never consider territory definitely yours: ko. Suppose there is a fairly large ko fight going on. You stand to gain, say, 50 points if you win the fight. Elsewhere you have a small group of eight stones on the second line: technically alive. But your opponent threatens this "live" group as his ko threat. If he kills your group he only stands to gain, say 30 points, so you should definitely ignore the threat, win the ko fight and lose your eight stone group. The point is this: sometimes it is better for you in the overall scheme of things to let your groups die. Somewhat unintuitive, but definitely true.
Territory: Closing Thoughts
The main Sente page also says this: "A move is sente if the value of the follow-up move (when the move is not answered) is larger than the value of the move itself (when the move is answered)." These situations are called priviledged and it is good to recognize them because it can help you estimate where territorial borders will finally stand. Remember to consider that when sacrificing a group, you give up not only the stones and territory they surround, but also their potential for reducing your opponents territory.
In fact, the value of living groups is not only territory reduction -- a living group is a strategic asset which can pay dividends all over the board. When your group is alive your opponent has less options against it and you have less liabilities to constrain your actions. Stones are never played with the intention of giving them away. It is only in response to the board situation (created also by the opponent) that a sacrifice may become appropriate.
Thickness: A wall of stones that face out into an open area, generally not yet technically alive but unlikely to die. Their strength comes from the fact that they have many liberties and are well-connected. Enemy groups don't want to get too close because cuts tend to be more likely to succeed in the presence of thickness. Thickness can be very valuable if it isn't nullified by corresponding strong opponent positions. It is also not very useful if it is too close to strong groups of the same color.
This is the kind of thickness I'm talking about. White has taken territory on the left edge and in return black has enormous thickness. Black may often find himself in this predicament after white invades what black thought was his territory on the left! The question now is, what do you do with it? The end goal is of course to gain territory somehow, but how do you do that?
In order to gain sente from your thickness, you need to create a threat your opponent can't afford to ignore. The more you can create those threats, the more you dictate the direction of the game, and (assuming your perceptions are accurate) the more you can guide it towards the desired outcome.
Generally, thickness is used indirectly which can make it hard to see how it works. Unlike territory where you can count up the points quite accurately, thickness is a qualitative element. Let's look at a cross-cut for inspiration:
In isolation, there are a number of things black could do here. It is hard to say much without further context. However, when we place the thickness in the diagram:
Now black's answer to the cross-cut is clear as a bell. Black 1 uses black's thickness. White's stone nearest the edge will always fear that thickness. It is not a direction that white wants to move. White has no forcing moves (local sente) there and is unlikely to live after white a through black d.
When you can cut your opponent in the presence of your thickness, it is often wise to do so. The cut is more likely to be effective because you can push your opponents weak stones towards your thickness where they have no forcing moves and you have more power. Conversely, if it is your opponent who is thick, it may not be prudent to cut.
If your opponent has no stones to cut or attack, then it can be sente to develop a large framework from your thickness. In this case, black plays 1. If black gets to follow up with 'a', it will be hard for white to make a base on the side, so white will probably...
...invade right away with 1. If white continues to 3, he has formed something of a base on the side. Black has already gotten a significant gain from his thickness. It's true: black got to play at 2, a valuable extension from his corner stone, in sente. Black's thickness can always back up threats against white's two-space formation at the top edge later in the game as well. The value of thickness is not always realized all at once, but it can pay dividends over the course of the whole game. The key thing is to understand its strengths and ensure they are not wasted.
For example, if black played the star-point and subsequenty joseki shown here, his thickness would be largely wasted. Granted black can follow up at 1, but with the sequence shown, white leans into the potential territory and makes black overconcentrated. In general, you don't want to use your thickness to make territory -- unless it's a nice big territory. Black gave up about 15 points of territory to white on the left edge for that thickness and he is getting about 15 points for it now, so isn't that a fair exchange? NO! Black also had to play 1, 3, and 5 to secure that territory whereas white got to play 2, 4, and 6: useful moves that face the center and will affect the rest of the game. The exchange of 1,3,5 for 2,4,6 is a pure loss for black, which is why this diagram is a failure for black.
As discussed here, the word thickness has meant a wall with few defects facing an open area, but thickness can mean other things as well. Often it simply means "strength" as opposed to "territory". It is something with future potential that must be understood and respected if it is to retain its value.
The relationship between sente and thickness is subtle, but important. You opponent will rarely have many sente moves in areas near your thickness. Furthermore, you will often have more sente moves against your opponent in areas near your thickness. This is because aggressive cutting maneuvers that might not work otherwise, do, in fact, work in the presence of supporting thickness.
It would be great to be able to measure the relative values of thickness and territory, but in practice it is quite difficult. Joseki books provide some examples of what amount of thickness is a fair exchange for what amount of territory, but these need to be evaluated carefully. Joseki are never played in isolation, and the value of thickness is always relative to the rest of the positions on the board.
When you keep your opponent separated, you keep his stones weak. One of the hardest judgements in my opinion is knowing when other concerns outweigh keeping your opponent separated. I'd like to look at a few examples of why you might want to let you opponent connect (own weakness too great, larger move elsewhere). I'd also like to look at cases where you should not connect your own stones (larger move elsewhere, indirect defense of peep). A key to this is, of course, understanding the values of moves that are not simply territorial in nature.
When I teach games to middle-kyu players, the advice I give most often is "keep white separated" and "keep your stones connected". The full value of a connecting or separating move isn't always obvious right away, but they are moves that pay dividends.
If white is allowed to play at 1, then black needs to jump back to the 3-3 point to make life in the corner and white can connect all his stones together.
But so what? White isn't making any territory with these moves, so what't he big deal? White's group is too big to die. Groups of a certain size just don't die (well, white groups, anyway!) -- they have too many ways to squirm and make eyes. If white's group lives, then, where is black's territory? It is also rather lacking. But the larger point is this: black has three separated groups (the corner, the right side and the left side), whereas white has one group. Say white attacks the corner:
Black must defend the corner. Now white's group (his only group) has gotten stronger. Now white can attack the top black group, with, say 3. Black naturally moves out into the center. Now white plays 7 and 9 which threatens the left group.
The point of this diagram is not so much to demonstrate a good sequence for white, but rather the fact that white can dictate the course of events becuase he has one strong group whereas black has several (and therefore) weaker groups. Therein lies the strength of connectivity.
When your stones are connected, they are stronger tactically because they form a larger group. However, they are also stronger strategically because there are less groups to manage.
This is the ability for a group to make eyes, and thereby live. Oftentimes it will be possible to make life against the side, but in the process be sealed off from the center. In general, this is a bad idea because a group that is sealed off has almost no effect on the rest of the game. But, of course, that is not always the case. In this section we will look at examples of the relative values of eyeshape and connectivity. I'd also like an example of when it is okay to allow a weak group to develop, and under what conditions that can happen.
Sometimes a single stone stands out because it does so many things simultaneously. If we can find moves that have multiple meanings, we are doing well. To truly excel, our moves should have meaning into the future as well. Like the "wasted move" example under the Territory section, we should strive to keep our stones flexible in the sense that they can be developed in different ways depending on how circumstances progress.