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mysql - Order SQL by strongest LIKE?

I have the following query:

SELECT * FROM table_name
WHERE (col_1 LIKE '%$keyword%'
    OR col_2 LIKE '%$keyword%'
    OR col_3 LIKE '%$keyword%')
  AND .... <some optional filters> ... 

is there a strategy to sort based on the most relevant results?

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If you mean that col_1 is more relevant than col_2 and so on, then :

select *
      ,case when col_1 like '%$keyword%' then 1
            when col_2 like '%$keyword%' then 2
            when col_3 like '%$keyword%' then 3
       end as [priority]
  from table_name
 where col_1 like '%$keyword%'
    or col_2 like '%$keyword%'
    or col_3 like '%$keyword%'
 order by [priority]

If you meant with the most column match then :

select *
      ,(case when col_1 like '%$keyword%' then 1 else 0 end) +
      ,(case when col_2 like '%$keyword%' then 1 else 0 end) +
      ,(case when col_3 like '%$keyword%' then 1 else 0 end) as [priority]
  from table_name
 where col_1 like '%$keyword%'
    or col_2 like '%$keyword%'
    or col_3 like '%$keyword%'
 order by [priority] desc

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