I figured that they traded the top right corner for black bottom left group but in the end black group lives and white refuses to play on top to at least make it a ko.

Why on earth does black play a move like 181? Why not just kill the top right corner right away and prevent any ko fights?

If black killed the corner instead of playing E18 I think black wins by ~10 points or so.

I simply don't understand the complexity of these moves, and I call myself a SDK player :/

The white group at the top right isn't dead. It has too many liberties. If black tries to create bent 4 in the corner, white just throws in and makes two eyes with oshitsubushi.

And if black throws in at T19, white plays P18 and either gets a second eye or connects underneath.

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T19 , P18 , P19 , N19 no?

Now I think I see it...

darn :/ I didn't think of that.

It's worth noting that even if the connection at N19 didn't exist, White would not need to create a ko, but could live outright. The shape is essentially this common tsumego problem:

Click Here To Show Diagram Code

[go]$$B White to live unconditionally
$$ ------------------
$$ | . . . . . . . . .
$$ | . O O O X . . . .
$$ | O O X X X . . . .
$$ | X X X , . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Indeed, 1-1 is the key.

We don't even know how bad we are at understanding simple things until we are placed in front of them

Only if we allow white to play two moves in a row.

That common shape exists after white plays P18. And it is alive only if white plays next.

The connection underneath to M18 is an essential part of white's ability to live.

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Not really. The common shape in my diagram already exists on the board after move 156. Krama's question was why White didn't spend another move (from 158 on) to make the group a ko. My point was that, if the M19 connection didn't exist, White would spend one move to make himself alive (t19), not a ko.

Of course you're right to the extent that, if the M19 connection didn't exist, Black-157 would be a killing move, but I understood Krama's question to be assuming the Black tenukis were played.