I would expect that players might opt for a strategy with a higher chance of winning despite having a greater chance of losing by a greater point difference. But after they see that they will lose, do they continue to play their best to score as well as they can?
Go appears to be different from e.g. chess, where by contrast the game is typically not played out to checkmate and often ends in forfeit when a player realizes that he cannot win.
In general, if you realize that you can't win, you should resign. It's considered rude to make plays that will only allow you to catch up if your opponent makes a stupid mistake.
I don't think Go is different from chess in this way. I would say around half of my games end in resignation.
Sadly I do not have a reliable source for this answer, but as far as I know, continuing when clearly behind is not generally considered rude, at least at professional level.
One reasoning was that it is good manners to try your best until the end. Of course one would still try to play good moves to minimize the loss, not just play on for the sake of it. This may be somewhat country-specific, too.
I also remember a professional game that was lost during counting, i.e. a mistake when filling dame (the order mattered). The comments commended the attention to detail of the eventual winner.
Some amateurs, on the other hand, have strong opinions on when a game should be resigned. They may be scarred from bad experiences with players who continued even though the game was over, i.e. dame was filled, but they kept playing all remaining ko threats or even non-threats, dead stones inside the opponents territory, just to avoid passing. This varies a lot for different players, so if you want to be on the safe side, it seems sensible to resign rather sooner than later.
In games that are not rated (not tournament), I would resign a lot quicker just to be able to play another game instead, and certainly many people do so.
The general answer to this question is no.
Go players play for win or loose, not for the difference of score. When a player lying behind does not see a chance to turn the outcome of the game into Eir favour, E resigns.
The caveat here is the word general:
There are some tournament formats (used, e.g., in the Go-to-innovation tournament in Berlin, Germany) using a scoring system based on point differences. The Hahn system assign a full point only with a score difference of 40 points or more, each 10 points missing on board make the score 0.1 smaller.
Also, in the Korean gambling Go bangneki score differences (in terms of 10 points on the board) were used to measure the amount of money won or lost.
There are different player characters out there, some of whom may quickly resign a game of Go, while others will continue playing even after suffering a severe loss. The later is not without reason: Even if some of your stones die, it does not mean they are worthless.
The point is, that many dead stones leave tons of good aji to be exploited. Once you realize that, you realize that you still have decent chances of winning games that you would otherwise have wanted to give up.
Also, estimating final score is actually quite hard in the early stages of a game of Go. I cannot count the number of times I've been surprised by the final score of a game. Like, I was thinking I would loose, but then a win would be counted, and vice versa. I just had such a game with an opponent who resigned after less than a hundred moves, because he lost a big fight. Nevertheless, when I counted the game by playing it out, it was still him who should have won the game.
Thus, if you make a habit of resigning games early, you are not playing to your full strength, you are loosing games that you would have won.
Many Go players know this, either explicitly or intuitively, and are slow to resign consequently. The ones who don't know this unfortunately have a hard time realizing their mistake, as they never see how their resigned games would have played out.
I would rephrase the question as, "Do Go players play to minimize score difference after realizing they WILL not win?" And the answer to that question is yes.
A "cannot" win game is one where a professional player is down by 5-10 points or more with only "endgame" left. In that case, the losing pro will resign because there is no possibility another pro will blow a lead that large in a non-dynamic position.
On the other hand, a "will not win" game is when the pro is one or two points behind in an endgame situation. Against another pro, one usually "will not" win such a game. But if each move is worth two points, and the leading pro makes a two point mistake, the gap could be closed. These instances are rare, but not unheard of, especially under time pressure.
In those cases, a pro may elect to play the game to the end and try to narrow the gap, knowing he has no legitimate chance to win, but hoping to "get lucky."
Source: Appreciating Famous Games
