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"At most once" has the implication of "you may never get it" (if the one and only attempt failed anywhere along the way)

"Effectively once" implies "you got the same thing 1000 times but ignored 999 of them because you already got it."

With an "exactly once" guarantee, I could send you a stream of integers (1,2,3,4,5) and you could blindly/naively/simplistically add them with no special concern and be confident that your answer of 15 was correct.

With "effectively once," you'd have to keep track of what you've seen before so you know not to add 4 an extra 6 times and come up with the wrong sum of 39.

With "at most once" you may be sitting around with a sum of 0 and think that's correct.

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