A Rich Man Should Not Pick Quarrels
This is a proverb indicating that it is not a wise strategy for the player who is ahead on the board to engage in complicated and risky fights or exchanges on the board. He should strive to settle the shapes and decrease the complexity of the game. The player who is behind on the other hand will want to complicate matters, in order to create opportunities for himself to win points back.
There is a third kind of player though: the one who doesn't have a clue about whether he's ahead or behind. That's why it is so important to estimate the score as often as you can during the game.
Although a rich man shouldn't pick quarrels, he should also look out not to become lazy or overconfident. There is a fine line between settling shapes by playing solid moves, and squandering points by playing slack moves. A couple of these in a row is sometimes already enough for the opponent to overcome the gap again.
I take the freedom to quote Barry Phease, who answered a thread on RGG about mindset and Go. The words between double brackets refer to other posts which are not repeated here.
What is perhaps not realised is that this ((element of chance due to fighting)) exists even if you choose not to fight. In any situation you can work out your likelihood of winning if everything proceeds smoothly without fighting. You might say that if you are ahead then you should avoid fighting. However your opponent could choose to fight and the only way to avoid fighting is to play moves that don't give them the opportunity. In that case you might have to play moves that reduce your likelihood of winning.
To win a game of Go requires you to play on the knife-edge. If you push too far then you instigate fighting that may be unfavourable (but probably unknowable exactly), however if you don't push far enough and avoid allowing your opponent to start a fight which may be unfavourable to you then you give up a little with each move and guarantee a loss.
If you have a favourable position then your opponent will have to instigate fighting. The only way to avoid fighting is to allow your opponent to feel that they have good chances of winning without fighting.
The ((skill)) is to make moves that shift the balance in your favour. If that means starting a fight that you are slightly more likely to win then that is still skill.
And the best method to beat ((the type concerned with balance and harmony within themselves)) is to upset the harmony and force them to fight when they don't want to. If they are really strong then they will show their reading ability and that their desire for balance comes from hidden fighting ability. However most people (amateurs) who seek balance above fighting do so because they can't fight well.
Bill Spight: I think Barry makes a very important point. :-)
I do disagree, however, that "the only way to avoid fighting is to allow your opponent to feel that they have good chances of winning without fighting." As one who cannot fight well, I do occasionally win a game because my opponent assumes that because he has won the battles he has won the war. ;-) There is technique to avoiding fights, however.
The natural, aggressive, and typically correct play for White is to hane. The nobi of White 1 is solid, passive, and sometimes too passive. But it is the kind of play you make when you are ahead. It reduces the options available for Black. If it costs anything, it is usually around 1 point. Cheap insurance. :-)
Imagist: All this is fine and good, but I think this proverb tends to give the impression that one should play only or mostly defensively when ahead, which I don't really think is the case. Too often I have been significantly ahead and played a defensive move that lost two points but avoided a complicated variation, only to have missed a tesuji on another part of the board that puts my opponent one point ahead. I would say that when there is a choice between to equal moves, the player who is ahead should choose the less complicated, but I don't think that he/she should choose a move that loses points just because it is safe.
Additionally, for those of us who are playing to learn and not so much to win, there's a lot more to be gained from playing the variations that challenge one's reading abilities.
OneWeirdDude: Is this logical, or is it psychological? Is it always a good strategy, or only in applicable handicap and similar games?
Slarty: It's a different kind of logic than the normal stuff you use inside the game. Related: playing aggressive fighting moves can be a good way to improve your strength, even though choosing those moves defies in-game logic to some extent.