`random()` in subquery is only executed once

I discovered this morning that random() when used in a subquery doesn't really do what you think it does.

Random generally looks like this:

> select random() from generate_series(1, 3)
      random
-------------------
 0.856217631604522
 0.427044434007257
 0.237484132871032
(3 rows)

But when you use random() in a subquery the function is only evaluated one time.

> select (select random()), random() from generate_series(1, 3);
      random       |      random
-------------------+-------------------
 0.611774671822786 | 0.212534857913852
 0.611774671822786 | 0.834582580719143
 0.611774671822786 | 0.415058249142021
(3 rows)

So do something like this:

insert into things (widget_id) 
select 
  (select id from widgets order by random() limit 1)
from generate_series(1, 1000);

Results in 1000 entries into things all with the same widget_id.