Sounds like you need to close the app completely and restart it from scratch. That is the general fix for any app that is not behaving as expected. I have not run into that issue on the Facebook app, personally, although I've never played those slot games.
There are two ways to do this, depending on the situation
One way that works while you're in the app you want to kill: hold the power button until you see the screen that shows up asking you to slide to power off. Let go of the power button, and don't slide to power off. Just hold in the home button until you're kicked back to the home screen. The app you were in will be forced to close, and it will start up fresh next time.
The other: if you're on iOS 4 or later with an iPhone 3GS or newer, you can also close it from the multitasking dock, which may be faster with practice.
From the home screen, or any other app besides the one you want to close, double-click the home button to bring up the multitasking dock. The app you want to close will appear somewhere in that dock (might take some scrolling).
Press and hold on any icon until they start to jiggle, then tap on the small circle with the minus symbol in the upper left corner of the icon to force that app to close. It's the same gesture you use to delete an app from the phone, except instead of a black & white X, it's a red & white minus symbol, and it only closes the app, it doesn't delete anything.
Tap back to the home screen and open Facebook again.