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Let's say that there's a 80% odd of something happening and it happened. Is there an idiom that expresses the general idea of convenience of such thing happening in your favor?

I don't think "by a stroke of luck" is appropriate or any term related to luck, because it was highly probable in the first place.

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Informally,

Good thing (x happened)!

Lucky for me, (x happened)!

Fortunately, (x happened)!

All three work no matter how likely x was. There are plenty of other ways for this to be expressed also.

We tend to use the phrase "luck" as long as there was any chance of the thing not happening due to circumstances out of our control.

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I've no clues about any such idiom, but I serendipitously know of a single word that should work fine.

Definition of serendipity

: the faculty or phenomenon of finding valuable or agreeable things not sought for

also : an instance of this

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    Hmm... But OP seems to be seeking for the 80%-likely event.
    – user45266
    Mar 4, 2019 at 5:16
  • If it happened, you couldn't have made it happen, and it helped you, saying it was serendipitous doesn't imply luck necessarily. I'm not familiar with any words off-hand that even make a distinction between the event being more than 50% likely versus less than 50% likely, let alone specifically 80%. If such a word comes up, I'll vote for it and remove my answer from the running.
    – Ed Grimm
    Mar 4, 2019 at 5:59
  • I just mean that the question doesn't seem to specifically ask for an unsought discovery, although I think you're right; I doubt there's a good word that distinguishes between percentages.
    – user45266
    Mar 4, 2019 at 6:01
  • Every other word I've thought of has the idea of either luck or fate associated with it... such "good luck" or "fortunately". "Good thing" doesn't itself, but it feels to me like it's heavily associated with assertions that something had been lucky. Words associated with fate seem to imply things were truly either 0% or 100% likely, with neither luck nor effort involved.
    – Ed Grimm
    Mar 4, 2019 at 6:12
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As it was expected...

or

As it was highly expected...

they should both work. There is no hard rule to determine words for numbers in this case. The example above suggest not only possibility, but (high) probability.

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