You said: mysql_query("UPDATE ships SET credits='".($credits+$taxtopay)."' WHERE character_name='$playerrace[leader]'");
Actually, I think he is trying to do something a little different than what you showed. The "credits" is the value from in the database, and I don't think he has a variable named $credits. Try this:
mysql_query("UPDATE ships SET credits=credits+".$taxtopay." WHERE character_name=$playerrace[leader]");
Another way to do it would be to create a variable like $query that will hold your query as you build it. ie,
$query="UPDATE ships SET credits=credits+";
$query.=$taxtopay;
$query.=" WHERE character_name='";
$query.=$playerrace['leader'];
$query.="'";
$result=mysql_query($query);
This should work, and you can do it in less lines than that too...
dave