Consider this:

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[go]$$Bc Asymmetrical Seki
$$ ----------------------
$$ . O X . X O O O O X .
$$ . O X O X . O . O X .
$$ . O X . X . O O O X .
$$ . O X X X X O X O X .
$$ O . O O O O X X X . X[/go]

Both black and white are called "alive" but in seki but black has both a prisoner and a bigger eye than white.

After all other end-game moves have been played, does black have to exploit this with:

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[go]$$Bc 4 at 2, 5 captures
$$ ----------------------
$$ . O X 2 X O O O O X .
$$ . O X O X . O . O X .
$$ . O X 3 X 1 O O O X .
$$ . O X X X X O X O X .
$$ O . O O O O X X X . X[/go]

for three prisoners? (existing stone, white 2 and white 4)

Or, during the scoring, do you simply count black's eye as 3 + 1 and white's as 1, yielding 3 points for black?

All such questions depend strictly on exactly which ruleset you are using.

Someone tell me if I'm wrong, but under Japanese rules, I believe Black will benefit from the additional capture, but will not get points for the eye in the seki.

I'm less sure about this, but under (some?) area rules, filling the dame gives Black an extra point, but playing inside his eye and capturing changes nothing.

I think that in some rulesets, Black must capture the white stone in order to count the eye in his territory.

As Robert says, it depends heavily on your ruleset.

_________________
Occupy Babel!

It is different under
- Japanese 1989 Rules
- World Amateur Go Championship Rules (which are also Japanese style)
- Verbal-Japanese Rules
- various go server Japanese-style rulesets.

Click Here To Show Diagram Code

[go]$$Bc Asymmetrical Seki
$$ ----------------------
$$ . O X . X O O O O X .
$$ . O X O X . O . O X .
$$ . O X . X . O O O X .
$$ . O X X X X O X O X .
$$ O . O O O O X X X . X[/go]

Black can force a protective play.

Click Here To Show Diagram Code

[go]$$Bc Protective play
$$ ----------------------
$$ . O X 2 X O O O O X .
$$ . O X O X . O . O X .
$$ . O X . X 1 O O O X .
$$ . O X X X X O X O X .
$$ O . O O O O X X X . X[/go]

By area scoring, Black has 14 points in the seki, White has 12, for a net difference of 2 points.

In this position Black has 11 stones and White has 13 stones, so the 2 point difference can be attributed to territory 4 points of territory. (You can also just count the territory: 5 points for Black to 1 point for White. )

Territory scoring rules that count territory in seki, such as Lasker-Maas and Spight rules, yield the same territory scores. Japanese rules do not count territory, but do count the stones that are captured. In this case, that is 3 White stones that Black captures, for a local score of 3.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

For sure if they have already become prisoners. Before it depends.