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database - MySQL Rank with ties

I am new to sql and I have never used variables or conditions in mysql, but know that from other programming languages. Since a few days I try to find a way to rank a user score. I read a lot of articles, and also questions that asked on stackoverflow and finally I found a solution that nearly does it like I want it.

SELECT
  score_users.uid,
  score_users.score,
  @prev := @curr,
  @curr := score,
  @rank := IF(@prev = @curr, @rank, @rank +1) AS rank
FROM
  score_users,
  (SELECT @curr := null, @prev := null, @rank := 0) tmp_tbl
WHERE
  score_users.matchday = 1
ORDER BY
  score_users.score DESC

But my Problems are tie scores. I don't want to get consecutive ranks, like this:

+------------+------+--------+
| uid | name  | rank | score |
+------------+------+--------+
| 4   | Jon   |   1  |  20   |
| 1   | Jane  |   2  |  19   |
| 2   | Fred  |   2  |  19   |
| 9   | July  |   3  |  18   |
| 7   | Mary  |   4  |  17   |
| 3   | Toni  |   5  |  12   |
| 5   | Steve |   5  |  12   |
| 6   | Peter |   6  |  11   |
| 8   | Nina  |   7  |  10   |
+------------+------+--------+

I would like to get a result like this:

+------------+------+--------+
| uid | name  | rank | score |
+------------+------+--------+
| 4   | Jon   |   1  |  20   |
| 1   | Jane  |   2  |  19   |
| 2   | Fred  |   2  |  19   |
| 9   | July  |   4  |  18   |
| 7   | Mary  |   5  |  17   |
| 3   | Toni  |   6  |  12   |
| 5   | Steve |   6  |  12   |
| 6   | Peter |   8  |  11   |
| 8   | Nina  |   9  |  10   |
+------------+------+--------+

I guess I have to create a new temporary table, and some if conditions, but I couldn't find a solution and become desperate! Also, I have to keep an eye on performance, maybe there are better ways to get the rank on score as I did it? I would be very grateful for hints or some code snippet.

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You can use another variable to count the same ranks so instead of incrementing @rank by 1, you increment @rank by the counter value, like this:

SELECT
  score_users.uid,
  score_users.score,
  @prev := @curr,
  @curr := score,
  @rank := IF(@prev = @curr, @rank, @rank + @i) AS rank,
  IF(@prev <> score, @i:=1, @i:=@i+1) AS counter
FROM
  score_users,
  (SELECT @curr := null, @prev := null, @rank := 0, @i := 0) tmp_tbl
WHERE
  score_users.matchday = 1
ORDER BY
  score_users.score DESC

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