BQM 213

Table of contents Intial question: how to reduce (instead of invade) Discussion about playing elsewhere versus local moves Continuing local discussion Metadiscussion about the scope of the question Tactical analysis of the invasion Extension cum attack? Sector Lines More analysis of the corner invasion, as an answer to the invasion More strategic analysis of the reduction More tactical analysis of the invasion The fighting after the reduction More strategic analysis of playing elsewhere

See also: summary

Intial question: how to reduce (instead of invade)

How should Black reduce?  

Alex Weldon: This is another question about one of the examples for my book about bad habits. The chapter in question is "Invading Instead of Reducing." This is about as perfect an example as I could ask for: in the position shown here, Black played at . Needless to say, it went badly.

To my mind, this is a perfect example of when invasion is counter-productive and reduction is what is called for. The question of the best reduction move isn't so simple, however.

I'm tempted to suggest a, because it's simple, can't really go wrong, and helps Black's moyo on the right. I'm just wondering if it's deep enough. White doesn't necessarily need to defend, because she can easily dodge into the corner if Black next invades at .

I just thought I'd poll the audience to see if there's anyone who thinks that something like b, c or d is better. Maybe e is also good, since it's the last big point and White can't perfect the lower side in a single move anyway - however, I want to contrast the bad invasion with a good reduction, instead of just recommending tenuki.

Bill: Nice example, Alex. It has sparked some very good discussion. :-)

I am wondering, though, did White miss a chance to play at or around n? The stone on the left looks peculiar.

Alex Weldon: Yes, she did. was a response to . Clearly, the lower side is bigger than the top left, so should have been around n.

Andrew Grant: I don't think a pro, given these four choices, would select anything other than a. The others are too close to White's thickness and don't relate well with Black's moyo on the right. Playing at the intersection of two moyos is a fundamental principle. After Black a, he has a huge follow-up at e if White defends the lower side.

Discussion about playing elsewhere versus local moves

Calvin: Locally, I also think a is best, for the same reasons. It follows the proverbs. As for invasions, it would be interesting compare the invasion at to the invasion at C14 f. (I wouldn't invade at f now. Getting sente to take e or something else on the upper side is big; it's just another invasion to think about and compare.) As a potential reader of your book, you'd also have to convince me that playing a is bigger than playing e directly. How urgent is the reduction? Would white's next move in this area be O5 or something else?

Alex Weldon: Well, I was planning on mentioning e as another possibility and saying something to the effect that the choice between a and e is another issue, outside the scope of that chapter. The suggestion following each example is titled "improvement," because while I'm not qualified to talk about best play, I can say with confidence that a is better than . Why I'd use a as the improvement and e as a side-note is that, while they're both thinkable, a illustrates the point of the chapter - reduction instead of invasion - while e is a move that would place this example in the preceeding chapter - invading too early (where the suggested improvements are usually tenuki, instead of invasion/reduction). Why not put it that chapter then? Because it's clearer that reduction is better than invasion than it is that it's too early to play here at all.

Continuing local discussion

So, next question. Since it looks like I'm going to go with my first idea and recommend a, I think I should probably show a likely continuation. I doubt White should defend, so what should she play after Black a? Grab the last big point around e or make a reducing move of her own around g? Or something else entirely?

Andy: This is a nice teaching board position. a is a fine play, but I worry that it is too small both with respect to reducing white's framework and for enlarging black's framework and that it will induce white to directly jump into the corner with z. seems overconcentrated with white's wall so a gentle reduction would be fine. Personally, I like h in this position; I also like b but worry that it is too vulnerable to being split from the right side of the board.

Bill: Ba is the strategic point (Tennozan). Then I think that Wj is the natural response, followed by Bk, etc.

dnerra: Black d looks already a little dangerous to me, but I wouldn't be confident about convincing anyone (not even my opponent in an actual game...) about that. I agree with a, and the natural continuation would be White j, Black l. But maybe White will ignore a and jump up to b.

Metadiscussion about the scope of the question

ThaddeusOlczyk: I think people are missing two obvious things here.

The first is that if people of the the strength of the commentators need to discuss the quality of the moves, does any one believe that the weaker people such a book is aimed at will understand? Do you think they will care?

Calvin: a is a pivot point between moyos, a concept that should be known to kyu players, although it's not one of the most heavily covered principles, so maybe not so important to all kyu players. Alex wants to show that reduction is better here, and that's a good thing to try to explain. Let me give you another kyu-level question about this position: first of all, what's the score? You can't tell me whether I should invade or reduce unless you give a score estimate before and after reduction to show that reduction is enough. That's useful to kyu players. What is not as useful is a detailed, high-level, tactical refutation of . The sequence described later is beyond my level. There are variations that are implied but not shown, just like in joseki. Neither I nor my opponent would be likely to continue that way. But the principles of not invading near where white is thick or counting the score before choosing between invasion and reduction are things I try to do.

Bill: (To Calvin): 1) It looks like White is a bit behind to me. Black's bottom left corner is low, but is poorly placed. 2) You don't have to count to avoid . Desperation measures on the bottom are at b and d, for instance.

(To Thad): There is a consensus for a. Will kyu players understand? Well, there are degrees of understanding. They will learn to recognize these plays and positions easily enough. Will they care? If they are reading the book, I expect so. :-)

Thad: I am talking about the difference between a and e here. ( In case I was not clear. ) There is some question here, and so I expect that there will be a lot of question in the minds of kyus. I have asked for advice and often times been given opposite choices by two different people ( such as these two moves ). I write this off to stylistic differences rather than a real statement that one is better than the other. It is probably better to say "if you want to reduce whites area ( call it preterritory ) then a is the move".

Many of the population of KGS would describe 'a' and 'e' as "boring pro moves". And as an interesting move. This includes everyone from the lowest kyu to the highest dans. If that is the way people want to play, even though they know better, then let them.

Bill: Do high level dans make such plays? I am amazed.

(Later). And I did not get that you were comparing a and e. However, there is a good chance that Black can play on the bottom with sente, starting with a, and then play on the top, as well. It is not necessarily either/or.

Hicham:' Boring Pro Moves'? I hope I am not the only one whos is a bit shocked by this. starting complicated fighting is not a must, and I find moves like "a" more easy to understand then the complicated fighting that will follow after . What you are saying is that stategy is boring and tactics are cool. This is not the game try to master, we should have both.(Just wanting to say this, this is not intended as a flame or something, and go head Alex delete it if you want)

Thad: Firstly, read what I say. I do not call these moves' boring pro moves'. Many people on KGS do. You may not be the only one to be shocked, but most certainlly there is no one who frequents KGS who is shocked. I hear the sentiment expressed quite frequently. By people of all ranks, and with general concensus of those present. My point is that this attitude is so prevalent that you will have to learn to deal with such moves over the go board.

(Hicham): Thaddeus, when writing it I understood that you ment many people on KGS, but I wrote you to make it shorter, although I was fearing the misunderstanding we have now. I dont think the majority of KGS players has the attitude you discribe, but I concur that a lot do. I think those who do are more talkitave about it, the majoriy of the people doesnt talk on KGS so it is hard to know what they think. It is easy to say: "kill kill", but hard to make a valid startegic point in a chat discussion.I don't like watching dan players on KGS because they often play like you discribe and I get the feeling that I am not learning proper moves but only how to complicate stuff.

The second point is that playing moves like and having them played against you are necessary for those learning go. I have seen such moves played by high ranked dans on KGS, presumably because they have not yet gotten to the point where they decide it is bad to play .

Bill: No offense, but I am not sure that you are categorizing what you have seen correctly.

Thad: So how often do you view games on KGS? I do quite often and I see it all the time. I see not only dans playing such moves but other dans in kibitz. The kibitzers often encourage such moves by yelling ( or the equivalent of yelling in "chat" ) "Kill", "invade" or "cut". The players generally do not hear this during the game, but they can see it afterwards.They also see what attracts observers, which is the fights that ensue from making such moves. One player has taken to calling KGS "overplayland". He also calls many of the KGS commmunity "hikarutards", because he believes that the show (Hikaru No Go )fosters the attitude.

It may seem irrelevant to the rest of the Go world, but I think it is significant. Some of the next generation of pro players will have spent much time on KGS, but I suspect in two generations almost all of the pros will have spent a lot of time on KGS or something similar.

I also think that before you question someones judgement about an environment you should take a close look at the environment.

Bill: Well, I grew up (in go terms) playing against people who made enterprising invasions. And I have played against plenty of dan players who are very aggressive. Even among them, a 3-dan who would play here is rare.

Thad:

Frankly I think there is only one way of reasoning that makes a move that shouldn't be played. That is when a player would win 100% of the time if was used against him, and he is hoping that his opponent is not as capable.

I play too many games where people play moves like , and I would prefer to play many more games where my opponents debate moves like 'a' and 'e'. But as long as I am unable to punish such moves 100% of the time, I know I should and will get moves like played against me. It's just a part of GO.

jantiff: I'll grant you that a is certainly good enough to illustrate the issue in direction here - no matter how many proponents of the gangster Go style call it a "boring pro move".

But please do not dismiss Alex's effort. Many people who invade at actually don't know better. Even though mistakes are unavoidable, learning from requires both getting punished and careful review. Alex addresses common mistakes that tend to become habits if left unpunished or unnoticed. I'm sure this approach can help many of those who seek a genuine understanding of the game.

Alex Weldon: I'm sure that even pros who write books get another pro to look over their draft before it's published. Pretty much no book, fiction or non-fiction, on any subject, is written in isolation, without input from others. If you think that someone is only qualified to write a book if they can do so without any outside assistance, you'll have a hard time finding anything worth reading. All I'm doing is getting some of the editing process done while the first draft is underway, in order to save time. Anyway, every time I ask a question to help with my book, someone brings up this issue. It's off-topic, so I've created a page to deal with it. If anyone wants to continue this conversation, please move it to Breaking Bad Habits/Discussion. Otherwise, I'll delete this comment in a couple of days.

As for your belief that a move is "wrong" only if it 100% guarantees a loss, all I can say is that it's absurd.

Thad: I did not say that such a move is wrong in the technical sense, but that from an ethical standpoint, such a move should not be considered unethical or insulting or a bad habit.

Any move which you have any hope for making work is a perfectly fine move. It is only moves that you hope will work because your opponent is not competent enough to handle that are ""bad'' in this sense. Even then it is a very vague thing. What Go player hasn't tried to steer a game into a certain style because he knows that he feels more comfortable in that style than his opponent? Is that considered hamete?

It seems like you are upset because you don't like hearing that people don't want to hear what you have to say, and that you don't want to tell them what they want. But the principle you put forward is emphasised in many books, and in many pro game commentaries. The people don't want to know those principle because they allready know them. What they want to know is how to punish their opponents when they violate those principles. Because often times they will make a play to create a position like this, then have played and watch their position crumble.

Alex Weldon: Ahhh. I believe I see the root of the misunderstanding. You think that I mean "bad habit" in the sense of something rude, like rattling the stones, or invading solid territory just before filling the dame. That's not what I mean. If you read the page I created to discuss the book, you'll see that when I say "bad habit," I mean a move that is wrong from an objective standpoint, but gets ingrained in weak players because it isn't always punished correctly, and they may come to believe that it is correct. My goal is to write a book for rather weak players (10-25 kyu) that both explains (conceptually) and illustrates (using examples from real games) why these moves are wrong, so that they can break the habit before they've been doing it so long that it becomes difficult. The goal is to facilitate long-term improvement by eliminating misconceptions, rather than to write a book on Go etiquette.

And you're right that players want to know how to punish the bad moves, not just how to play the good moves. Of course, I cover that as well. For this position, for example, I'll be showing the real game continuation, which was bad for Black, as well as including a few comments about how White could have punished even more effectively.

Regarding the attitude you describe on KGS, yes, I'm familiar with it and it saddens me. I don't expect players with that attitude to buy my, or any Go book. I also do not expect many of them to reach dan level (though, as you say, there are exceptions). That attitude is far from universal, however, even on KGS. I give a lot of teaching games there, and most of the students who come to me show a positive attitude and a desire to understand theory, not just fight all the time. I'm writing this book for them.

Tactical analysis of the invasion

Anonymous: All of you dans seem unanimously agreed that is a poor choice here - can someone show us poor starving kyus how wrong this move is, exactly? What does Black have to fear? I'm not disagreeing with you, I just want to see what is so obvious to a stronger player...

Bill: After White attacks, starting with m. This attack drives Black towards White's wall on the left. Even if Black survives, White builds a wall to the right and center which reduces Black's moyo on the right side and supports an invasion or erasure there.

(Later, after Thad's next response). I think I made it sound like is in worse shape than it is. Most likely, both players' moyos will be reduced, but because of White's thickness, hers will be reduced much less than Black's and Black will make less territory in the process. By comparison, if Black plays at a instead, Black will reduce White's moyo while enlarging his own. And may do so with sente.

Thad: While that is true, Black may decide that his chances to win are very low and that he may live while White builds a wall with many weakness or is ineffectively placed. In this case he feels he has nothing to lose, so why not go for it? Plus if he is a dan he may earn some observers.

I'm not saying I agree with this principle, just that it is prevalent. So you must learn to deal with it. Expect people to play it against you. Play it against other people to see how they deal with it. Is that any different from trying out a new joseki in a game to see how it feels?

Bill: Thad, it sounds like you are talking about a different position. As for the comparison with trying out a new joseki, playing here is more like trying out a hamete for the hell of it.

Dieter: If the purpose of the game is to learn how to deal with invasions of all kind, then, since is an invasion (of the abusive kind) it is a good idea to play it, because the proceedings will teach you something about abusive invasions.

If the purpose of the game is to play as well as possible or to win by playing well, then is a bad idea (see below).

If the purpose is to win and the quality of play is irrelevant, then is as good as any other move (including 1-1) but I wouldn't be tempted to help out players with such an attitude.

Overall, I think people will learn more from playing this invasion than from blindly following advice from a book. People will also learn more from trying out ideas from a book than from blindly invading. It all depends on your attitude.

Why the invasion is not so good  

Black 11 at a. may also be at b (discussion welcome). After Black 11, White has to worry about cutting points at b and c. On the whole, Black is running with a weak group and his corner is wrecked.

Calvin: Most 10-kyu or weaker players I know would cut at c instead of attaching at , and I don't know how many would be confident with the hane of . After that exchange, this sequence has already exceeded the level of play of the intended audience.

The wrong reason why the invasion is not so good?  

tderz: Given the sequence above, what would be a continuation and what its evaluation?

If here, I feel that Black could cut with . This seems to be the result of White pushing Black against the wall which is most often correct.

"White has to worry about cutting points at b and c." This is true and the reason why White could also play differently.

Alex Weldon: Maybe is a mistake? How about d instead? I'm not sure what happens if Black then cuts at c. White may be able to handle the fight because she has z in reserve to live in the corner, but I don't have time right now to look into all the variations.

tderz: Alex, I think , are the indication of a mistake, not the cause (which is the wrong direction of IMO). If the necessary d as you suggest, Black could simply jump to e or cut at c

The cut at c & if white defends in her own moyo...  

tderz: The cut at c.
If is answered by (I guess we agree that ponnuki is out of question), Black could attack the corner with (Zwischenzüge) and (or m) and threaten to build a moyo with .
Who is attacking whom then?

if white defends in her own moyo...  

tderz:Of course, White could try to push around somewhat at n etc. before replying with (thereby pushing Black into White's moyo), but eventually it'll be Black who bends around at p.
With a white weakness around r and s and a cut at t, I would not be afraid of being swallowed by White. I'd rather enjoy walking into White spheres of influence and neutralizing them. White hoshi h is even not yet played!

The wrong reason why the invasion is not so good?  

tderz: is crude (but necessary, an indication that White wants too much) and
Black p and r are miai.

Crude period  

Dieter: is plainly crude and wrong.

The wrong reason why the invasion is not so good?  

tderz: I think or a are also possible.
After (or a) Black has miai of defending with and losing the corner by White z or vice versa.
This way the moyo with the white wall is bigger than in Dieter's diagram above.
(Yes, I know the proverb "You shall not make territory with a wall")

Why the invasion is not so good  

Dieter is probably better, but Black has . Anyway, seems that the dans have a hard time showing convincingly that the invasion is abusive. Many of us are relying on proverbs which we intuitively apply to situations which we probably are not all that capable of dealing with convincingly.

Alex Weldon: Well, as I keep saying, "better" is much easier to prove than "best." The position is complicated enough that it's hard to pick out White's best punishment. The important thing is that almost any of these diagrams (except maybe the one where White crawls for life on the second line) is better for White than if Black had played the horse's head reduction (a in the very first diagram).

Heck, White could even avoid complications by attaching underneath and get a good result. If the invasion of in the original diagram allows White to play this passively and still get a better result than if Black played the move we want to recommend, I think that's proof enough.

Not the strongest play, but still good for White  

Dieter: I do not agree that this is good for White:

 

Black easily lives at the bottom and White has cutting points. Yes, she can fix one by exchanging a for b but that will give points to Black. Her thickness has been converted merely into central influence while Black's stones seem unaffected. I would not call this a big success for Black but certainly not better for White either.

Alex Weldon: I think my point got confused because there are several slightly different conversations going on at once. I certainly wouldn't recommend this line of play to anyone; clearly some of the other diagrams are better. I was trying to find a simple proof in order to quell the misgivings of those who were saying that it might be hard to convince a typical kyu player that the invasion is wrong.

When I said it was good for White, I meant that it was good relative to the result if Black had played the good reduction instead of the bad invasion to begin with.

Let me rephrase all of this in a more logical format, because I still feel that I'm not explaining myself very well.

1) The attachment underneath lacks variations and is a middlegame joseki, so we cannot blame the result on mistakes later in the sequence.

2) The end result is better for White than if Black had reduced instead of invading.

Therefore, the Black invasion is provably a mistake. You could also prove this with better lines of play for White, but they have more variations, so you'd have to go into endless "but what if..." scenarios in order to convince an inquisitive kyu. Add to this:

3) The attachment underneath is a substantial mistake for White (harder to prove this, but intuitively obvious to most of us).

And you can strengthen the above claim by saying that the Black invasion must not only be a mistake, but it must be a larger mistake than White's attachment, so a big one.

Andy: This also seems easy for white. The black invasion doesn't have to be "wrong" or "punishable"; being "small" is bad enough. White could also simply take one of the (previously discussed) big open points on the board, ignoring black's provokation and then white gets the nice double-wing extension instead of black.

Take the corner  

Dieter: Indeed. White's circled stone is still a fine extension from the White wall. The squared stone provides aji so that Black probably can't take sente here. I like this explanation best.

dnerra: To me, entering the corner is a little counter-intuitive (when I was young, I would have claimed "wrong direction" :P) while you are trying to build a moyo outside. I would imagine Black a, White ''b', Black at the marked point, after this, and the White wall has lost quite some power.

negative value exchange  

zinger: I look at it this way: the exchange , loses points for black - that is, (or at a) clearly has greater value than . So black has taken a loss versus doing nothing here. Furthermore, black b has lost much of its value.

Dieter: If moves would have clear values then there would not be so much discussion. You may have a deeper insight that I lack (I am not being ironical or disrespective), but I need either tactical analysis or an indication of where the points are, before I can judge that clearly has greater value than .

zinger: Perhaps I should explicitly state "in my opinion" :) Anyway, my own perception is that has very little value, because as tderz pointed out above, c and d are miai for white. Whereas greatly enhances white's moyo. This is why I think is worth more than , and therefore that the exchange - has negative value for black.

In addition, I do not mean to claim that is the best move - only that it is enough to show that is a mistake. If white can do better - probably by a method shown here by our more skilled deshis - I certainly won't be surprised.

dnerra: I actually like this idea. Black has to play at c immediately, I think, and then White takes the hoshi at the top. The advantage of compared to the keima is that White can tenuki, having played more solid shape.

Mutual erasure  

Bill: When I made my earlier remarks, I overestimated the power of . :-( When I made my later comment, this is the kind of thing I had in mind. :-)

[edit]

Extension cum attack?

Extension cum attack  

Bill: With a possible continuation like this. makes an extension while attacking Black's center group.

I think this is plainly better for White than if Black had started at a.

tderz: I rather like this development for Black and
notice here that Black is Getting ahead with a one-point jump vs. and the White invasion option z is diminuished because it would weaken the white ---group. Black got his territory on the right solidified (e.g. by the - exchange). If White wants to compensate for this, then it had to come from the area around y by attacking, but san-san x is still open. I experience this task as complicated and troublesome. If the attack for making territory comes from the y-direction, then Black would get stronger, perhaps by a bamboo v-connection (which loses White's sente, because the ---group is attacked). Furthermore the white w-invasion options are less possible (because Black could set up a splitting attack after driving them to -- or a leaning attack - in short White is weaker than Black -; Black t are sensible points). The funny looking Black s seems to aim at the cut a (thereby destroying eye shape in sente) and protect against the slide r by the attachment p.

Who attacks whom? The roles are changed.  

tderz: After , White (or a for also clearly demonstrating the bad white shape) to defend against the black cut b,
Black attacks gladly with .
Has White really the tempo to play ?

dnerra: I agree with your analysis. I think W has to continue the running battle:

Continue running.  

Letting black get the key point in a running battle isn't my cup of tea, so is the only move IMHO. I am not sure how to evaluate the result, I think I like it a a little better with White.

The proper move?  

The proper move(?) is slow. Trying with white a or b for some complications is difficult too.
Perhaps these problems indicate that pushing Black to the left is not the best strategy.
White remains 1 step behind in the running fight.

Sector Lines

Turn the tables  

Bill: Normally I think of breaking sector lines, but this follow-up to TDerz's suggestion looks good. :-) Now White is the one who has extended her moyo while erasing Black's. (OC, could be at a.)

crux: I agree that White at or at b looks better than a stronger attack - after all, that ends up driving Black straight through White's moyo. Isn't / aji-keshi though? Instead of , how about a 3-3 invasion?

Bill: prevents Bc, which is another frontier play that also prevents from running. OC, - reduces White's aji in the bottom right, but it's a trade-off. And aren't and Wa bigger than the 3-3 invasion after ?

dnerra: I like this, too. However, I might prefer around d, as the two keimas look weak to me (s.th. like Black e looks liek an immediate possilibity to me), and it is easy for Black to ignore .

Alex Weldon: I think the epiphany that we're all reaching here is that we started off thinking of the invasion as an overplay (because bad invasions usually are), but that the correct attitude in punishing it is to think of it as an underplay and take a relaxed attitude towards it.

dnerra: I still think that White has a lot of weaknesses here.

Testing White's formation.  

dnerra: is asking for a move around , and I wouldn't know how to deal with it.
tderz: now is not so coordinated with present .
Perhaps around . Black at (=) and a are then perhaps miai. This is less weak. dnerra: Hey, great idea, could almost be mine! ;-))) (see above) I still find it difficult to evaluate the two keimas. E.g. should one really play the / exchange before playing at ? tderz: I would like to know too, the answer is beyond my playing level. In such cases it remains for us a question of style of confidence (how to deal - before or after black preparations around p - with a cut at c, or bad-style-cuts at e.g. d the corner aji at x (and y if white does not play ) etc. ) This is the point, where reading and confidence in once's own reading makes a difference.
How many "secure" points will black have, how many points will white have to generate from the two moyos? I did not look at this at all, but it is necessary for decision making. My former idea for came in a flash and I wrote about it. It is by no means a guaranteed right track, so how do I know about the follow-up moves?

Attacking??  

dnerra: Attacking the marked black stone with a cap is, IMHO, a dangerous plan. White is accumulating more weaknesses. On the other hand, if White replies around or , then the marked white stone must have been wrong.

[edit]

More analysis of the corner invasion, as an answer to the invasion

Take the corner  

Dieter: I was thinking about handling the corner invasion this way, but I can't find any good move for .

Black continuation  

Bill: Isn't it here? Dieter: Yes, nice example of a Good Empty Triangle

Black continuation  

Take the corner: white resists being pressed down  

What if white plays as in 4464Enclosure33Invasion with this type of sequence? White gets the corner and still gets sente to pick either a big move at the top or expansion at the bottom.

Corner aji (1)  

tderz: - is a threat against White's life.

Corner aji (2)  

tderz: is positioned right here (usually such a stone is around hoshi and the immediate attemt to kill will not work).

Hence White had to lose sente , if she wanted to save the corner, perhaps by moving positively to white (and not in the corner itself). This could threaten to move out (with here ) and the situation would be again complicated:

Black really wants to make the double wing formation on the top, yet could lose the initial invasion stone we are talking here on this page.
But then, if White were moving out with (or similar) and saves ,

then Black could enlarge his double wing formation even more by a or b below:

completed double wing formation  

Corner aji (3): are white a or b reasonable?  

tderz: Of course, both players have to investigate: are white a or b reasonable?

Corner aji (4): if white a  

tderz: ... if white a - the outcome is not fully clear to me:

Corner aji (5): if white a  

tderz: Only an idea: ... White wants too much on the left and would lose there after black =a+b, yet White yould attack at c.

This idea seems flawed, White does not need to defend at against the ladder (broken by hoshi) and would like to defend around =.

On the other hand, if White does not take away a liberty from +, then Black can capture in geta:

Corner aji (6): geta  

Corner aji (7): White wants to avoid geta  

tderz: I think White is doomed,
ladder or geta threatens
because she wants too much (but remember, all started with an allegedly unreasonable Black invasion; hence, who erred where?)

I leave out the analysis for Bb now, I think it is easier for White.

Conclusion: I still like my original proposal somewhere above.

More strategic analysis of the reduction

Dieter: Suppose Black plays the reduction move as advised and White jumps into the corner. I guess Black will then grab sente to play at the upper side first.

Black continuation  

If White plays here, the same thing happens. So, ...

Black continuation  

... perhaps White has to play here, keeping a and b as miai. And thus, probably too is better at ?

More tactical analysis of the invasion

Black continuation  

Dieter : has anyone suggested here ? and the marked stone both are not strong, so attacking may be less called for than simply defending .

Bill: I thought about it, but did not like the development after Ba.

Yet another idea.  

dnerra: I have yet another suggestion. How about this one? The idea is to abandon the white stone at the highest price possible, while still keeping 3-3 in the lower right corner as an option.

Alex Weldon: I changed to in the diagram, under the assumption that that's what you meant.

[edit]

The fighting after the reduction

Miai?  

Q: since the ladder is good for her, can go at x instead?

Bill: After - , play may continue as in this diagram.

Miai? (ii)  

Bill: Now threatens a.

(Later): Hmmm. Maybe it's better to play Ba instead of , anyway.

(to introduce an edit marker)

Fight  

Bill: Something like this?

LukeNine45: I'm getting off topic maybe (I've enjoyed this page a lot), but this looks like a disaster for white to me. I'm assuming I'm wrong, but why? White lives small in the corner, and it looks like she'll have a hard time using the wall on the left to attack the four black stones (which can either get an eye at a, connect at b, or run at c-- so there's very little chance of them dying). looks pretty lonely to me...

tderz: Now capture Wh, followed by Bb for Black's safety is one possibility,
but White had no reasons to feel happy.

Fight  

tderz: Bill or LukeNine45, given your variant as a fact,
if White feels too much behind like this (the wall is then completely useless), then she could try

• -> b (idea is to separate Black and make use of White's wall, while entering Black's sphere of influence)
  • i) if Ba capture, Wk can perhaps start to neutralize some B moyo on the right. (Perhaps B adds a stone at n in gote for safety).
  • ii) if Bi-Wh capture and the black ladder Bm is broken by hoshi.

Fight  

tderz: (I do not like this variant above at all, but comment on an individual move of it:)
like this seems better for White than above diagram:
after :

• i) if Bd-Wh capture, Bk? => life
• ii) if Ba capture:
  • ii-a) if then We-Bd-Wg-Bf-Wi (I do not look into Bk now) horrible for the White moyo, but still better than above diagram
  • ii-b) if We-Bg-Wd-Bi does not work for B

More prudent  

Bill: Maybe White should play more prudently, as with here.

Another fight  

Bill: could lead to a different fight. Difficult position.

[edit]

More strategic analysis of playing elsewhere

Top first  

Bill: is big, but isn't bigger?

kokiri: fascinating discussion. The way I see it, black has the choice between the invasion, which clearly complicates things significantly, as the discussion has shown, and the play on the seam of the two moyos, which is simple, and obviously good. Thus it is not necessary for white to refute the invasion absolutely; rather the very fact that it's hard to see who benefits from the invasion is enough.

Maybe a corollary to the point that Alex is after is that there's no need to complicate things uneccesarily unless you're noticably behind.