I think the problem may stem from the presence of the FULLTEXT index itself.

Every time there is a query involving a FULLTEXT index, the MySQL Query Optimizer tends to whack the query into a full table scan. I have seen this over the years. I also wrote an earlier post about this most trifling behavior in FULLTEXT indexes.

You may need to do two things:

1. refactor the query so that the FULLTEXT index does not throw the MySQL Query Optimizer into a state of confusion
2. Add an additional index that will properly support the refactored query

REFACTOR THE QUERY

Here is your original query

SELECT post_id  
FROM phpbb_posts  
WHERE topic_id = 144017  
AND post_id != 155352  
AND MATCH(post_text) AGAINST('http://rapidshare.com/files/5494794/photo.rar') 

You will need to refactor the query like this:

SELECT subqueryA.post_id
FROM
(
    SELECT post_id FROM phpbb_posts
    WHERE topic_id = 144017
    AND post_id != 155352
) subqueryA
INNER JOIN
(
    SELECT post_id FROM phpbb_posts
    WHERE MATCH(post_text) AGAINST('http://rapidshare.com/files/5494794/photo.rar')
) subqueryB
USING (post_id);

CREATE A NEW INDEX

You will need an index to support subqueryA. You already have an index on topic_id. You need to replace it as follows:

ALTER TABLE phpbb_posts ADD INDEX topic_post_ndx (topic_id,post_id);
ALTER TABLE phpbb_posts DROP INDEX topic_id;

Give it a Try !!!

UPDATE 2012-03-19 13:08 EDT

Try this one first

SELECT post_id FROM
(
    SELECT * FROM phpbb_posts
    WHERE topic_id = 144017
    AND post_id != 155352
) A;

If this runs fast and return a small number of rows, then try this nested subquery:

SELECT post_id FROM
(
    SELECT * FROM phpbb_posts
    WHERE topic_id = 144017
    AND post_id != 155352
) A
WHERE MATCH(post_text) AGAINST('http://rapidshare.com/files/5494794/photo.rar');

UPDATE 2012-03-19 13:11 EDT

Compare the running time of this:

SELECT count(*) FROM phpbb_posts  WHERE MATCH(post_text) AGAINST ('rapidshare.com') LIMIT 0, 30;

with this

SELECT count(*) FROM phpbb_posts WHERE 1 = 1;

If there running time is the same, then the MATCH clause is being executed on every row. As I mentioend earlier, using FULLTEXT indexes tends to nullify any benefits attempted and contributed by the MySQL Query Optimizer.

I can provide with a general explanation, but it may not apply specifically to your particular case:

The way decision making works is by evaluation cost of execution plan, then picking up what is hopefully the cheapest plan. This you already know.

When it comes to indexing, though, stuff are getting interesting. The way to evaluate the usefulness or viability of an index is to estimate the selectivity given some value.

For the moment, forget about your FULLTEXT index, and let's assume a simple index on some column col1, and another index on some column col2. Given the following two queries:

SELECT * FROM t WHERE col1 < 10 and col2 = 4;
SELECT * FROM t WHERE col1 BETWEEN 100 AND 110 and col2 = 4;

It may happen that the query is evaluated differently in these two cases. Why? Because it may happen that col2 = 4 returns more rows than col1 < 10, in which case we prefer to use index on col1. But then, it may return less rows than col1 BETWEEN 100 AND 110, in which case we prefer the index on col2.

Your case is not very much different. MySQL estimates the number of rows returned by some index query. When you use more columns, MySQL gets the impression your index is likely to result with few rows. So it chooses to start with TableA, then joins what should be very few rows with TableB.

But if MySQL believes the index to return many rows, it may prefer starting with TableB. Why is that? Because you are sorting on indexed columns of TableB. Sorting is a lot of work, too. So MySQL may choose to first sort the rows, then join to TableA and filter by fulltext index. It may not be a bad idea if the fulltext search yields with many rows anyhow.