How about a .htaccess redirect?
Add a line like
Redirect /links/Some-Casino xhttp://adserver.somecasino/?member=MySillyUsername
to your .htaccess and then use the link xhttp://mysite.com/links/some-casino to send your traffic to that casino. If you are nervous about google, just add /links as restricted directory into your robots.txt and you’re good to go.
This has three advantages I like:
1) Sometimes the affiliate programs’ links don’t even have the casino’s names in them, which makes the links seem kinda suspicious to some.
2) Super simple solution to the problem, yet it works perfectly with every browser.
and most importantly
3) Links are quick & easy to update. All the links are in a single text file, so if for any reason you need to change the url for Some-Casino’s traffic you only need to update that one line in .htaccess.