Today's Free App of the Day is Combat Mission : Touch
This seems to be a game that lets you reenact a WW2 battle; the negative reviews are mainly due to in-app purchases, though a few complain about the contols on the Fire.
17 of 33 reviews are four stars and above.
These apps are compatible with the original Fire and with my Fire HD 8.9" 4G. To tell if an app works for your Fire HD or other Android device registered to your Amazon account, click on the above link and look on the right side of the web page. Amazon will tell you if it will work with your registered device.
Also check out the other digital deals from Amazon, including great deals on MP3s and videos: