I've come across several instances where newbie players end up filling the complete goban, and then look up to see if they did well. Or players that discover the game, buy the equipment, rush into a game and then end up in this situation.
This situation is also likely to arise as a result of not completely/correctly explaining the rules; a good explanation should avoid having players bump into this situation.
The Stone Counting Teaching Method does not require to explain anything like this, as it's idea is to minimize the amount of information presented to the beginning player. Another idea is to let players discover this kind of situation on their own; but imagine teaching the game to an audience, and this kind of situation pops up all over the place?
Maybe it might save time to warn players against this happening. In this page, I propose a dialog that will also introduce some pointers to the living group concept, another topic that should not be tackled in an introduction to Go.
Comments welcome; this is only a proposal.
Phelan: This situation could occur during the final counting phase. After both players have passed, stones could be added to empty spaces to make counting easier. I assume you were talking about getting there through alternating play, but thought I should mention it.
Under Stone Counting the game ends once both players pass - no more stones are added after that.
tapir: Atari go naturally leads to sth similar to stone counting (if no stone is captured before, that is :) I think this is a great feature of atari go.
This is an example of the end of a first 5x5 game between two players that did not fully understand the rules, but kept adding stones until the very end rather than passing in time. It is a situation that should be avoided. Can you see what it is? B and W have both filled up all their liberties, and end up without any. Stones should always have liberties at the end of a move.
Let's assume White's last move - in fact the last move of the game - was . That was an invalid move, as White put herself in atari, so that move should not have been played, right? White should have passed.
But notice that Black is also without any liberties. Now let's go one move further back and look at what Black did wrong.
Let's assume Black played . That was invalid too, as he left his group without any liberty. In fact, Black should have passed. But at that point, there's a far better move for Black, can you see it?
Instead, Black can kill the white group by taking its last liberty. White will not be able to recover from this loss. Because both players will continue to add stones, for each white stone will be followed by a black one and White will never be able to even equalize the stone score.
White could have foreseen the catastrophy in the previous diagram: so let's go back a move. Let's assume White played , a tactical mistake that presents the white group on a plate for Black to kill at the remaining free liberty, as we saw before. Better for White is not playing , e.g. by passing. Then, Black will never be able to kill at , as explained in the previous diagram. But White has a far better move: instead of passing...
White takes the last liberty off Black's group, and now it is Black that would lose the game. So Black should have been more careful. Let's go back one more move.
Let's assume Black played - we saw that this was a tactical mistake of Black, better was to leave that spot open. And notice that Black cannot attack White...
So Black should pass instead. White will also pass, and the game ends normally. Just remember: a group with only one liberty can be killed.
In a later phase, the last diagram could be reused to touch the concept of sacrifice. Again, one must judge if it is appropriate to introduce the concept, depending on the level and progress of the audience.