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How to avoid full table scan when using OR operator on an Index

Essentially, I want to get intersection between 2 tables based on matching IDs with the option of wildcard '*' to return all IDs:

Select * from A a inner join B b on b.id = a.id or b.id = '*'

Table A is fairly large (10 M rows), and I have setup the id to be index already.

Because of OR, index id is not used, and it does a full scan (Takes 20 secs).

If I don't allow the wildcard:

Select * from A a inner join B b on b.id = a.id

It uses id index and takes only 300 ms

Edit:

By separating into 2 select with Union helped. Detail here: https://stackoverflow.com/questions/5901791/is-having-an-or-in-an-inner-join-condition-a-bad-idea