Ko question (game 8k against 6k)

Teaching
1

In the following game, from move 139 to about 190, there was an invasion leading to a game-deciding ko that I lost by misreading a move as a ko threat that wasn’t which is sad but not particularly mysterious.

However, I have a few question regarding this ko:

  1. My impression is that during the last moves leading up to 187, White should have been able to get a two-step ko instead of a one-step ko, is that right?

  2. I had big trouble counting, so I worked under the assumption that without the invasion, White would win with less than 10 points and that the won ko would give me 30 points. Under the assumption that the margins are actually 10 and 30, is it true that Black needs ko threats worth at least 10 points and White needs ko threats worth at least 20 points?

  3. If the ko were a two-step ko, how would the numbers change? It seems to me that Black still needs ko threats worth at least 10 points while White can be content with ko threats worth half the 20 points. Is that right?

2

I have put up a few variations that should answer your questions

  1. yes this should be a 2 step ko
  2. any ko threat that wins you the game is big enough
  3. it’s not that white needs ko threats worth half as much rather she can make a move that is not a ko threat, but threatens to make more e.g. the bottom right corner. however, in this case black can live by filling the ko, so that strategy doesn’t work as the ko is then over, making that invasion a regular ko threat
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