Number of stones

[RobertJasiek]

You mention the number of stones for overconcentration and efficiency, but it is not the number of stones that is relevant. It is also not the difference of Black's and White's numbers of local stones, but it is the difference of numbers of local plays (althogether or added recently, depending on what one wants to study)!

Both player's plays must be taken into account, because a player may spend more plays if the opponent wastes more plays on creating his own useless stones, dead stones or removed stones. Plays instead of stones must be counted, because then removed stones are taken into account at all.

[SmoothOper]

I still think there should be a way to quantify aspects of players play be analyzing liberties, though I'm not sure what a formula or formulas would look like, since the liberty counts are dynamic during a game, though I wouldn't be surprised if raw liberty counts at the end of the game weren't strongly correlated with winning, since a liberty is also a point, except for dame which would be shared between players, unless of course there were large dead groups, but even then dead groups usually don't die because they have liberties.

[daal]

the only time I consider stone difference numerically is in the opening, and primarily restricted to the idea that if I am outnumbered 2-1 in a corner, I had better have a good reason to play elsewhere.

Not that evening the stone count is bad, but please let me disabuse you of that notion.

At the beginnings of modern opening theory, a few centuries ago, play often began with the sequence, 3-4 point, 5-3 approach, pincer, play in a new corner. Top level players had already learned that they did not have to defend against a pincer, that play in a new corner was usually better.

I guess we can say that those old professionals had a good reason. Nowadays though, it's not so common to have an empty corner as an alternative to evening up the stone count in a corner. When the chance does arise, there is still the matter of knowing how to cope if a third stone gets played.

BTW, the advice not to tenuki in the opening when one is behind 1 stone to 2 comes from Yilun Yang (The Workshop Lectures, Volume 1). However, he also says that if one is behind 1 stone to 3, that one may tenuki, and if one is behind 1 stone to 4 that one must tenuki. Then again if either of these are the case, one has already ignored his advice once.

[Bill Spight]

the only time I consider stone difference numerically is in the opening, and primarily restricted to the idea that if I am outnumbered 2-1 in a corner, I had better have a good reason to play elsewhere.

Not that evening the stone count is bad, but please let me disabuse you of that notion.

At the beginnings of modern opening theory, a few centuries ago, play often began with the sequence, 3-4 point, 5-3 approach, pincer, play in a new corner. Top level players had already learned that they did not have to defend against a pincer, that play in a new corner was usually better.

I guess we can say that those old professionals had a good reason.

Well, if you tenuki and your opponent plays a third stone in the corner to make it three to one, you are better off than if he had made an enclosure (two to zero), because you have some aji.

Nowadays though, it's not so common to have an empty corner as an alternative to evening up the stone count in a corner.

Good point.

When the chance does arise, there is still the matter of knowing how to cope if a third stone gets played.

It can be good training to let your opponent make that third play, to get practice in using your aji.

BTW, the advice not to tenuki in the opening when one is behind 1 stone to 2 comes from Yilun Yang (The Workshop Lectures, Volume 1). However, he also says that if one is behind 1 stone to 3, that one may tenuki, and if one is behind 1 stone to 4 that one must tenuki. Then again if either of these are the case, one has already ignored his advice once.

Good point.