by luck

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ThesaurusAntonymsRelated WordsSynonymsLegend: luck - by accident; "betrayed by a word haply overheard"
References in classic literature ?
But that present of bank-notes, once made, was measurable, and being applied to the amount of the debt, showed a deficit which had still to be filled up either by Fred's "judgment" or by luck in some other shape.
When a desired outcome is brought about by luck, you must acknowledge that fact.