create or replace function mcPi(n) as (
  with recursive cte as (
    select -1 as i, 0 as count, NULL::DOUBLE as x, NULL::DOUBLE as y
    union all
    select i+1 as i,
           count + if( x*x + y*y <= 1, 1, 0) as count,
           random() as x,
           random() as y
      from cte
      where i < n
   )
   select last( 4 * count / n order by i)
   from cte
);

# Examples:

select n, mcPi, format('{:.5f}', (mcPi - pi()) / pi()) as "relative error"
from (select n, mcPi(n) as mcPi
      from (select unnest([100, 1000, 10000, 100000, 200000]) as n));