PostgreSQL sub-query LIMIT behaviour

explain analyze.txt

 Nested Loop  (cost=2.10..14.80 rows=1 width=21) (actual time=0.082..0.780 rows=5 loops=1)
   Join Filter: (t3.t2_id = t2.t2_id)
   Rows Removed by Join Filter: 30
   ->  Seq Scan on t2  (cost=0.00..1.01 rows=1 width=10) (actual time=0.006..0.019 rows=11 loops=1)
         Filter: ((t2_val)::text ~~ 'he%'::text)
   ->  Nested Loop  (cost=2.10..13.73 rows=5 width=15) (actual time=0.017..0.063 rows=3 loops=11)
         ->  Limit  (cost=1.33..2.25 rows=5 width=7) (actual time=0.010..0.023 rows=4 loops=11)
               InitPlan 1 (returns $0)
                 ->  Aggregate  (cost=1.32..1.33 rows=1 width=8) (actual time=0.050..0.051 rows=1 loops=1)
                       ->  Seq Scan on t1 t1_1  (cost=0.00..1.26 rows=26 width=0) (actual time=0.002..0.024 rows=26 loops=1)
               ->  Seq Scan on t1  (cost=0.00..1.65 rows=9 width=7) (actual time=0.008..0.015 rows=4 loops=11)
                     Filter: ((t1_id IS NOT NULL) AND (t1_id < 100) AND ((t1_val)::text ~~ 'h%'::text) AND (random() <= ('5'::double precision / ($0)::double precision)))
                     Rows Removed by Filter: 17
         ->  Bitmap Heap Scan on t3  (cost=0.76..2.28 rows=1 width=8) (actual time=0.004..0.004 rows=1 loops=49)
               Recheck Cond: (t1_id = t1.t1_id)
               Heap Blocks: exact=35
               ->  Bitmap Index Scan on t3_pkey  (cost=0.00..0.76 rows=1 width=0) (actual time=0.001..0.001 rows=1 loops=49)
                     Index Cond: (t1_id = t1.t1_id)

test-case.sql

BEGIN;

DROP TABLE IF EXISTS t1;
DROP TABLE IF EXISTS t2;
DROP TABLE IF EXISTS t3;

create table t1 (
    t1_id int,
    t1_val varchar,
    PRIMARY KEY (t1_id)
);

create table t2 (
    t2_id int,
    t2_val varchar
);

create table t3 (
    t1_id int,
    t2_id int,
    PRIMARY KEY (t1_id)
);

INSERT INTO t1 VALUES(0,  'hi');
INSERT INTO t1 VALUES(1,  'hi');
INSERT INTO t1 VALUES(2,  'hi');
INSERT INTO t1 VALUES(3,  'hi');
INSERT INTO t1 VALUES(4,  'hi');
INSERT INTO t1 VALUES(5,  'hi');
INSERT INTO t1 VALUES(6,  'hi');
INSERT INTO t1 VALUES(7,  'hi');
INSERT INTO t1 VALUES(8,  'hi');
INSERT INTO t1 VALUES(9,  'hi');
INSERT INTO t1 VALUES(10, 'hi');
INSERT INTO t1 VALUES(11, 'hi');
INSERT INTO t1 VALUES(12, 'hi');
INSERT INTO t1 VALUES(13, 'hi');
INSERT INTO t1 VALUES(14, 'hi');
INSERT INTO t1 VALUES(15, 'hi');
INSERT INTO t1 VALUES(16, 'hi');
INSERT INTO t1 VALUES(17, 'hi');
INSERT INTO t1 VALUES(18, 'hi');
INSERT INTO t1 VALUES(19, 'hi');
INSERT INTO t1 VALUES(20, 'hi');
INSERT INTO t1 VALUES(21, 'hi');
INSERT INTO t1 VALUES(22, 'hi');
INSERT INTO t1 VALUES(23, 'hi');
INSERT INTO t1 VALUES(24, 'hi');
INSERT INTO t1 VALUES(25, 'hi');

ANALYZE t1;

INSERT INTO t2 VALUES(0,  'hello');
ANALYZE t2;
INSERT INTO t2 VALUES(1,  'hello');
INSERT INTO t2 VALUES(2,  'hello');
INSERT INTO t2 VALUES(3,  'hello');
INSERT INTO t2 VALUES(4,  'hello');
INSERT INTO t2 VALUES(5,  'hello');
INSERT INTO t2 VALUES(6,  'hello');
INSERT INTO t2 VALUES(7,  'hello');
INSERT INTO t2 VALUES(8,  'hello');
INSERT INTO t2 VALUES(9,  'hello');
INSERT INTO t2 VALUES(10, 'hello');

INSERT INTO t3 (t1_id, t2_id) VALUES(0,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(1,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(2,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(3,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(4,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(5,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(6,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(7,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(8,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(9,  0);
INSERT INTO t3 (t1_id, t2_id) VALUES(10, 0);
INSERT INTO t3 (t1_id, t2_id) VALUES(11, 0);
INSERT INTO t3 (t1_id, t2_id) VALUES(12, 0);
INSERT INTO t3 (t1_id, t2_id) VALUES(13, 0);
INSERT INTO t3 (t1_id, t2_id) VALUES(14, 0);
INSERT INTO t3 (t1_id, t2_id) VALUES(15, 1);

EXPLAIN ANALYZE
SELECT * FROM
(SELECT * FROM t1
 WHERE t1_id IS NOT NULL AND
 t1_id < 100 AND
 t1_val LIKE 'h%' AND
 random() <= (5::double precision)/(SELECT COUNT(*) FROM t1)
 LIMIT 5
) AS t1
JOIN t3 ON t3.t1_id = t1.t1_id
JOIN t2 USING (t2_id)
WHERE t2.t2_val LIKE 'he%';
COMMIT;

test-dbi.pl

use strict;
use warnings;

use DBI ();

sub main {
    if (@ARGV != 4) {
        print { \*STDERR } "Usage: $0 <host> <database> <username> <password>\n";
        return 0;
    }
    my ($host, $database, $user, $pass) = @ARGV;

    my $dsn = "dbi:Pg:database=$database;host=$host";
    my $dbh = DBI->connect($dsn, $user, $pass);
    die "error connecting to database" unless $dbh;

    my $sql = q{
SELECT * FROM
(SELECT * FROM t1
 WHERE t1_id IS NOT NULL AND
 t1_id < 100 AND
 t1_val LIKE 'h%' AND
 random() <= (5::double precision)/(SELECT COUNT(*) FROM t1)
 LIMIT 5
) AS t1
JOIN t3 ON t3.t1_id = t1.t1_id
JOIN t2 USING (t2_id)
WHERE t2.t2_val LIKE 'he%'
};

    while (1) {
        my $rows = $dbh->selectall_arrayref($sql);

        my $n = scalar @{ $rows };
        if ($n <= 5) {
            next;
        }
        print "received $n rows\n";
        last;
    }

    return 1;
}

main() ? 0 : 1;