A rule of thumb with RewriteRule, if your first two characters are "^/" then your third character better be a question mark to make that forward slash optional.
That's probably not your problem though. Looking at your rewritelog, your first line indicates that the URI is being stripped down to "asdf" before the pattern is applied. The way you read those prefix lines is that anything after the "->" is what the pattern is getting matched against.
So in your case, your RewriteRule should probably look like this
RewriteRule ^([a-z0-9_-]+)/?$ index.php?room_id=$1 [NC,L]
If you're on a modern version of Apache, which I'm guessing you are because I don't believe the + (one or more) quantifier is available in earlier versions of mod_rewrite, you can use Perl-compatible regular expression syntax in your pattern, including shorthands such as "\d" to denote "0-9".
RewriteRule ^([a-z\d_-]+)/?$ index.php?room_id=$1 [NC,L]