Help with query_posts()

you might need to use get_posts() to grap the latest 10 posts, and use that together with the current $post->ID to exclude them from your query;

also do not use query_posts() for secondary loops – use WP_Query() instead ( http://wordpress.stackexchange.com/questions/1753/when-should-you-use-wp-query-vs-query-posts-vs-get-posts?rq=1 ).

example:

global $post;
$latest = get_posts('posts_per_page=10');
$latest_ids = array();
if( $latest ) foreach( $latest as $late ) { $latest_ids[] = $late->ID; }
$exclude = array_merge( $latest_ids, array( $post->ID ) );

$args = array(
		'posts_per_page' => $show_count,
		'post_type' => 'post',
		'post_status' => 'publish',
		'orderby' => 'rand',
		'post__not_in' => $exclude
	);
$random = new WP_Query($args);
if( $random->have_posts() ) while( $random->have_posts() ) : $random->the_post();
/* here we go loopy-loo */
endwhile; wp_reset_postdata();

(untested)

http://codex.ww.wp.xz.cn/Class_Reference/WP_Query