Board Thread:Tips, Tricks, and Questions/@comment-173.228.31.82-20130922184450/@comment-207.76.138.72-20130926174747

It was discovered that while you can buy a maxiumum of 40 slots, it's possible to go beyond that with leveling up. So to get the absolute maximum # of slots, purchase 40 at the start of your game before you're rewarding any slots from leveling.

Tapjoy offers are the "free" way to get gold and max the slots.

Reference: http://forums.toucharcade.com/showpost.php?p=2980652&postcount=40