^
Also, there's the simple fact that they were wrong with their projection that the Dominion war could not be won in the first place. And it was won without (as far as we know) direct intervention by the Prophets since that projection, since Statistical Probabilities occurs after Sacrifice of Angels. If they were wrong about that, how can we be sure they would have been right in their projection that "no one dies"?
It's an interesting question - why were they wrong?
That the Jack Pack got surprised and betrayed when trying to do their thing isn't an answer, or even the beginning of one, despite our heroes offering it as such: they hadn't committed their exceptional smarts to predicting the outcome and pitfalls of their own efforts. But they failed to predict key twists and turns in the thing they
did try and tackle in full, that is, the war, because we know the outcome was different from what they presented. Why? Or perhaps, what twists and turns?
Might be they simply were stupid and both their prediction technique
and their self-diagnostic technique (the one telling them they weren't wrong and stupid) fundamentally flawed.
Or might be they erred on their key assumptions. None exhibited knowledge of S31 and its unorthodox methods that ultimately resulted in the Alpha Axis victory; S31 would be news several episodes down the line in Season 6. The other variable would be the surprisingly interventionist nature of the Prophets, but on that the Jack Pack already
had data, from the preceding "Sacrifice of Angels". What other factors could stand out as so totally surprising that they would differ from the general vagueness of necessary assumptions about, say, Dominion policymaking or industrial capacity or Klingon homefront stamina or whatnot? What else could have taken the Jack Pack utterly by surprise?
Timo Saloniemi