On the off chance
Meaning: unlikely to happen, but still, hoping that something may be possible, although it is not likely
Example: I went to the station on the off-chance that she'd be there. On the off chance that you don’t find him at work, here’s his home address.
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Example: I went to the station on the off-chance that she'd be there. On the off chance that you don’t find him at work, here’s his home address.