MySQL update one table from another joined many-to-many

Question

I have two tables, events and plays joined many-to-many by a third table plays_in_events.

Where the events.Name field is blank, I want to set it equal to the name of the play that was performed in that linked event.

I have tried

UPDATE `events` 
  INNER JOIN `events` ON (`plays_in_events`.`EventID` = `events`.`EventID`)
  INNER JOIN `plays` ON (`plays_in_events`.`PlayID` = `plays`.`PlayID`)
  SET events.Name = plays.Play
WHERE 
  events.Name IS NULL and plays_in_events.PlayID = 1

but get a syntax error

SQL Error: Not unique table/alias: 'events'

(I'm trying to limit any damage from accidental multiple updates by only testing it in the first instance for PlayID = 1, but have hundreds of records to update, so I don't want to do it manually).

There is only one table events in the database.

What's going wrong here please? I can't see it, unfortunately.

LATER

Maybe I've got the JOIN wrong altogether.

This SELECT query works to join the two main tables, and was produced by a visual query editor:

SELECT 
  `events`.`EventID`, `events`.`Name`, `plays`.`Play`, `plays`.`PlayID`
FROM
  `plays_in_events`
  INNER JOIN `events` ON (`plays_in_events`.`EventID` = `events`.`EventID`)
  INNER JOIN `plays` ON (`plays_in_events`.`PlayID` = `plays`.`PlayID`)
WHERE
  `events`.`Name` IS NULL AND 
  `plays`.`PlayID` < 10

How could I make the JOINS in the UPDATE based on this working?

Answer 1

This works - I had the JOIN wrong

UPDATE `events` 
  INNER JOIN `plays_in_events` ON (`plays_in_events`.`EventID` = `events`.`EventID`)
  INNER JOIN `plays` ON (`plays_in_events`.`PlayID` = `plays`.`PlayID`)
  SET events.Name = plays.Play
WHERE 
  events.Name IS NULL and plays_in_events.PlayID = 1

and the earlier comments were quite right, but it took me a while to 'get it' - thanks for your help. I had just copied the JOIN lines from the working SELECT query, but when I looked again, I could finally see what the commentators meant about events appearing twice, and plays_in_events not appearing properly in the JOINs.