MySQL lookup based on round(1 + rand() * x) produces NULL and multiple results

I'm trying to select first names from a lookup table at random in MySQL to build a test dataset. I have a table with 200 first names, genders and a row id going from 1 to 200. Something like this:

id   firstname   gender
1    Aaron       m
2    Adam        m
3    Alan        m
etc...

I'm selecting from this table using a random generator with the following query:

SELECT id, firstname FROM firstname WHERE id = round(1 + (rand() * 199));

I am expecting the random number to tally up with exactly one id from the lookup table, thus producing a single results like

id   firstname
43   Jason

Running the code again and again instead gives me a selection of

• single rows (as above)
• or multiple rows like

id firstname 29 Ethan 147 Jean

• or no results (just NULL in both fields).

If I run the random generator on its own, it will always generate a number between 1 and 200. As you can see below, the id field is INT, and the query behaves the same way if I cast the result as SIGNED. I have also tried to use FLOOR instead of ROUND, just to see if that worked any differently - alas, no.

Can anyone tell my why the anomaly? What am I missing?

Here is some code to create the first 20 rows of the original table for testing purposes:

-- First Name --
drop table if exists firstname;

  CREATE TABLE firstname (
  id INT NOT NULL,
  firstname VARCHAR(20) NOT NULL,
  gender VARCHAR(1) NOT NULL,
  PRIMARY KEY (id),
  UNIQUE (firstname)
  );

  INSERT INTO firstname
  (id,firstname,gender)
  VALUES
  (1,"Aaron","m"),
(2,"Adam","m"),
(3,"Alan","m"),
(4,"Albert","m"),
(5,"Alexander","m"),
(6,"Andrew","m"),
(7,"Anthony","m"),
(8,"Arthur","m"),
(9,"Austin","m"),
(10,"Benjamin","m"),
(11,"Billy","m"),
(12,"Bobby","m"),
(13,"Brandon","m"),
(14,"Brian","m"),
(15,"Bruce","m"),
(16,"Bryan","m"),
(17,"Carl","m"),
(18,"Charles","m"),
(19,"Christian","m"),
(20,"Christopher","m");