function.php

<?php

session_start();

add_filter( 'posts_orderby', 'randomise_with_pagination' );
function randomise_with_pagination( $orderby ) {

	if( is_front_page() ) {

	  	// Reset seed on load of initial archive page
		if( ! get_query_var( 'paged' ) || get_query_var( 'paged' ) == 0 || get_query_var( 'paged' ) == 1 ) {
			if( isset( $_SESSION['seed'] ) ) {
				unset( $_SESSION['seed'] );
			}
		}
	
		// Get seed from session variable if it exists
		$seed = false;
		if( isset( $_SESSION['seed'] ) ) {
			$seed = $_SESSION['seed'];
		}
	
	    	// Set new seed if none exists
	    	if ( ! $seed ) {
	      		$seed = rand();
	      		$_SESSION['seed'] = $seed;
	    	}
	
	    	// Update ORDER BY clause to use seed
	    	$orderby = 'RAND(' . $seed . ')';
	}

	return $orderby;
}
?>