Obtendo registros aleatórios de uma base sem utilizar ORDER BY RAND()

1lr-query.php

<?php
$pdo = new PDO('mysql:host=127.0.0.1;dbname=base', 'user', 'pswd');

$stm = $pdo->query('
    SET @count = (SELECT COUNT(*) FROM tabela);
    SET @query = CONCAT("SELECT * FROM `tabela` LIMIT 4 OFFSET ", 1 + FLOOR(RAND() * @count));
    PREPARE stmt FROM @query;
    EXECUTE stmt;
');

$stm->nextRowset(); //SET @count...
$stm->nextRowset(); //SET @query...
$stm->nextRowset(); //PREPARE...

foreach ($stm->fetchAll(PDO::FETCH_OBJ) as $row) { //EXECUTE...
    var_dump($row->name);
}

1lr-query.sql

#obtendo o total de registros da tabela
SET @count = (SELECT COUNT(*) FROM `tabela`);

#criando a consulta para obter 4 registros sequenciais, iniciando de um ponto aleatório
SET @query = CONCAT("SELECT * FROM `tabela` LIMIT 4 OFFSET ", 1 + FLOOR(RAND() * @count));

#preparado a consulta
PREPARE stmt FROM @query;

#executando
EXECUTE stmt;

4r-query.php

<?php
$pdo = new PDO('mysql:host=127.0.0.1;dbname=base', 'user', 'pswd');

$stm = $pdo->query('
    SET @count = (SELECT COUNT(*) FROM tabela);
    SET @query = CONCAT("
    SELECT *
    FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t1`
    UNION SELECT *
    FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t2`
    UNION SELECT *
    FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t3`
    UNION SELECT *
    FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t4`");
    PREPARE stmt FROM @query;
    EXECUTE stmt;
');

$stm->nextRowset(); //SET @count...
$stm->nextRowset(); //SET @query...
$stm->nextRowset(); //PREPARE...

foreach ($stm->fetchAll(PDO::FETCH_OBJ) as $row) { //EXECUTE...
    var_dump($row->name);
}

4r-query.sql

#obtendo o total de registros da tabela
SET @count = (SELECT COUNT(*) FROM `tabela`);

#criando a consulta para obter 4 registros aleatórios
SET @query = CONCAT("
SELECT *
FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t1`
UNION SELECT *
FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t2`
UNION SELECT *
FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t3`
UNION SELECT *
FROM (SELECT * FROM `tabela` LIMIT 1 OFFSET ", 1 + FLOOR(RAND() * @count), ") AS `t4`");


#preparado a consulta
PREPARE stmt FROM @query;

#executando
EXECUTE stmt;