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[go]$$B What is the best move ?
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X b O |
$$ . . . O O X a |
$$ . . . . O O X |
$$ . . . . . O . |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

Very often apparently simple position are not that easy.
AGA rule : for a theoritical point of view what is the best move for black? a or b ?

I forget if the AGA rules allow for suicide, but 'a' should be superior to 'b' in any ruleset that does. For black to play 'b' leaves 'a' as a ko threat.

For me AGA rules do not allow suicide. BTW, if you prefer you can also consider you use chinese rules (I mean area counting).
I do not understand your point with ko threat : after black "a" white has also a ko threat availbale hasn't she?

If both players play alternatively then a and b are equivalent:

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X 1 O |
$$ . . . O O X 3 |
$$ . . . . O O X |
$$ . . . . . O 2 |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X 3 O |
$$ . . . O O X 1 |
$$ . . . . O O X |
$$ . . . . . O 2 |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

But suppose Black plays a. Later if there is a ko fight, White ataris to make a ko threat, Black doesn't respond and White kills.

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X 4 O |
$$ . . . O O . . |
$$ . . . . O O . |
$$ . . . . . O 2 |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

If another ko appears later then Black still has chances to survive by playing twice in a row. Then Black lives with 2 points and there is one dame left.

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X . . |
$$ . . . O O 7 5 |
$$ . . . . O O . |
$$ . . . . . O O |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

On the other hand if Black plays b, after one ignored ko threat by Black and one ignored ko threat by White, Black lives with 3 points.

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X 1 O |
$$ . . . O O X 4 |
$$ . . . . O O X |
$$ . . . . . O 2 |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

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[go]$$B
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X X . |
$$ . . . O O X 7 |
$$ . . . . O O 5 |
$$ . . . . . O O |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

The end result depends on the parity of the number of dame at the end of the game, but with the assumption that the sequence of plays is Black-White-White-Black-Black, then b is superior by 1 point on average.

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[go]$$B What is the best move ?
$$ ---------------------------------------
$$ . . . O O X . |
$$ . . . O X X X |
$$ . . . O X b O |
$$ . . . O O X a |
$$ . . . . O O X |
$$ . . . . . O . |
$$ . . . . . O O |
$$ . . . . . . . |[/go]

Very nice jlt I agree entirely.
Here is an example where it remains only three small areas for the yose.
Black "b" is the best move in order to avoid the following (wrong) sequence :

You're right. I was just thinking of the suicidal ko threat, but the external atari is there with the other move. My mistake.

Here is another problem:

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[go]$$B
$$ -------------------
$$ . . . X . . . . . |
$$ . . . X X X O . . |
$$ . . . . X O . . . |
$$ . . . . O . O . . |
$$ . . . . O O . . . |
$$ . . . . . O O O . |
$$ . . . . . . . X . |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

What is the best choice :

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[go]$$B
$$ -------------------
$$ . . . X . . . . . |
$$ . . . X X X O . . |
$$ . . . . X O . 3 . |
$$ . . . . O . O . . |
$$ . . . . O O . . 2 |
$$ . . . . . O O O 1 |
$$ . . . . . . . X . |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

or immediatly

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[go]$$B
$$ -------------------
$$ . . . X . . . . . |
$$ . . . X X X O . . |
$$ . . . . X O . 1 . |
$$ . . . . O . O . . |
$$ . . . . O O . . . |
$$ . . . . . O O O . |
$$ . . . . . . . X . |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

I guess it's the same philosophy as the first example: if white is going to respond to the peep, then the outcome is the same regardless of move order, so the real question is what happens if white ignores the peep?

If white responds: you're going to end up with this position in either case --

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[go]$$B
$$ -------------------
$$ . . . X . X X O . |
$$ . . . X X X O O . |
$$ . . . . X O O X . |
$$ . . . . O . O . . |
$$ . . . . O O . O O |
$$ . . . . . O O O X |
$$ . . . . . . . X X |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

and the point is to stop white gaining a tempo with this way --

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[go]$$B
$$ -------------------
$$ . . . X . X X O . |
$$ . . . X X X O . . |
$$ . . . . X O . W . |
$$ . . . . O . O . . |
$$ . . . . O O . . O |
$$ . . . . . O O O X |
$$ . . . . . . . X X |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

If white is going to ignore, then the - exchange below looks like an example of a reverse in CGT terms: black doesn't gain anything, and possibly loses something (one point from becoming a prisoner)?

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[go]$$B
$$ -------------------
$$ . . . X . . . . . |
$$ . . . X X X O . . |
$$ . . . . X O . 3 . |
$$ . . . . O . O . . |
$$ . . . . O O . . 2 |
$$ . . . . . O O O 1 |
$$ . . . . . . . X . |
$$ . . . . . . . X . |
$$ . . . . . . . X X |
$$ . . . . . . . . . |
$$ . . . . . . . . . |[/go]

So I'd say just play at directly, an example of the 123 principle.

What have I missed?

I understand your point. If white doesn't answer the peep then peeping immediately is better and I agree with you.
However what happens if you suppose all remaining yose points of the board are quite small ? In other word suppose black timing is good and white has to answer the peep in the two considered sequences ? Witch one is the best?

Here is a hint:

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[go]$$B
$$ -----------------------------------------
$$ | . X . O . . . . . . . . . X . . . . . |
$$ | X X X O . . . . . . . . . X X X O . . |
$$ | . . X O . . . . . . . . . . X O . b . |
$$ | X X O O . . . . . . . . . . O . O . . |
$$ | O O O . . . . . . . . . . . O O . . . |
$$ | . . . . . . . . . . . . . . . O O O a |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

AGA rules. By just adding a ko threat and a dame in the upper right corner do you see which of the two moves "a" and "b" is the best?

I agree entirely with you xela, the exchange followed by the peep at is generally inferior to the immediat peep. I like very much the 123 principle and its application is good sense.
A proof of the 123 principle efficiency is that is is quite difficult to change a little the position in order to make the better.
Maybe here is an exemple after a lot of tries:

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[go]$$B
$$ -----------------------------------------
$$ | . X O O . . . . . . . . . X . . . 3 . |
$$ | X X X O . . . . . . . . . X X X O O . |
$$ | . . X O . . . . . . . . . . X O X X . |
$$ | X X O O . . . . . . . . . . O O O . . |
$$ | O O O . . . . . . . . . . . O O . . 2 |
$$ | . . . . . . . . . . . . . . . O O O 1 |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . X X |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

If I am not wrong, due to the white ko threat existing in the top right corner, the exchnage followed by the standart move is better than the immediat move.
Here again it is only an exception. The 123 principle is a very good principle isn't it?