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I've read a minimal amount about this in some of the questions which have been posted already here and the posts which were linked. However, I'm still unsure if the Duckworth-Lewis method is applied in the following scenarios:

  1. When the rain interrupts in the middle of the first innings of a 50 over match?
  2. When the rain interrupts once the first innings is complete?
  3. When the rain interrupts once the second team has batted a certain number of overs?
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Yes, the Duckworth-Lewis method would be applied in all three scenarios. The only scenario in which a rain-shortened match does not have the Duckworth-Lewis method applied is if the match is shortened before the start of the first team's innings, as in that case both teams are equally aware of the number of overs they will face before starting their innings.

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