I think the black has a slight advantage doesn't have anything to do with what color you were playing, it's giving an overall view of the position.
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No, after the mate it said black has a slight advantage
I'd have to take a look at the analysis, but seems to me if it's giving you a line to play then it's saying from that position black has a slight advantage not after the line being played and if played exactly at that line then you'd win, but humans aren't as even keeled and predictable as all that.
On one of my game analysises, the computer showed a forced mate that I missed, and then said black has a slight advantage ((I was white)), Anything wrong?