Update table with SUM from another table

I am trying to what I thought was going to be a simple update of a table with the sum from another table, but for some reason, it is only updating one row. Here is what the relevant info from the tables look like:

games

gameplayer|points
 ----------------
 John      |5
 Jim       |3
 John      |3
 Jim       |4
 

playercareer

playercareername|playercareerpoints
 -----------------------------------
 John            |0
 Jim             |0
 

Now ultimately, I would like the last table to look like this after running the update:

playercareer

playercareername|playercareerpoints
 -----------------------------------
 John            |8
 Jim             |7
 

This is the query I attempted that only updates the first row:

UPDATE playercareer
 SET playercareer.playercareerpoints = 
     (
 SELECT 
     SUM(games.points) 
 FROM games
     WHERE
      playercareer.playercareername=games.gameplayer
     )
 

I can't seem to find the answer to this. Thanks in advance for your time and advice!

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