Actually, if there's a needle somewhere in the hay field, you will have zero chance of finding it unless you search the entire field. (Come to think of it, that's not true, as you might find the needle in your first five minutes of search. But I wouldn't place a large bet on it if I were you.)
Unless you have some way of narrowing the location down to some extent. But we can't do that, because it would be "profiling."
Actually the term is ‘needle in a haystack’ not ‘hayfield’. Searching the hayfield would be pretty discouraging if the the hay has any growth. Right after cutting, then you just get out the metal detector. With the haystack, just burn it (if you don’t like the hay!); the needle might be worthless, but you’ll find it in the ashes.