Lol, no XD... not unless against all odds you happen to be intolerant to potatoes and bananas. I've heard of people breaking out from bananas here, but only if they have them every day or more than once a day. Once a week should be fine, but try to have a variety of different vegetables/fruit as much as possible. The paleo diet doesn't have potatoes because they're relatively "new" to the human race, only a few thousand years old I think, so they didn't want those things interfering with anything. A boiled or baked potato should be ok from time to time... just no potato chips or french fries unless you know how to make your own. People have already criticized the potato thing with the paleo diet, so if it doesn't cause an issue for you than eat up! I find baked white potatoes with a few herbs twice a week delicious... and cheap. Even though they are a nigh shade vegetable, my eczema doesn't react to them, with or without the skin. We are all different. Make a list of what you enjoy and go from there .

However watch out for the Glycemic Index/Glycemic Load with these two foods:

Bananas, ripe: GI of 62, GL of 16.

If you're bating at about 100 percent on any kind of diet, you can probably have a treat once a week or so. But for the sake of your issue bing acne, try to stay away from treats that have dairy in them (even though dairy products typically are low on the GI?GL scale), with dark chocolate (more than 75 percent dark) being an exception (unless of course cocoa breaks you out).

Try to go for a Low GI/GL and Dairy free diet (and always read the comment sections on these articles since many acne sufferers don't join acne.org):

http://www.npr.org/blogs/thesalt/2013/02/19/172429086/diet-and-acne-for-a-clearer-complexion-cut-the-empty-carbs

http://www.aad.org/stories-and-news/news-releases/growing-evidence-suggests-possible-link-between-diet-and-acne

http://ajcn.nutrition.org/content/86/1/107.full

http://www.dailymail.co.uk/health/article-2281151/Milk-sugary-foods-DO-increase-risk-acne-say-researchers-looked-50-years-research.html

However, the chart bellow is made by the Paleo dieters:

As well as another to read into (practically the same thing):

http://www.health.arizona.edu/health_topics/nutrition/handouts/FODMAPs%20diet.pdf

As you can see, bananas and potatoes are in the SAFE range, and this has helped a lot of people out with their acne and others with IBS or gut issues. This is what I'm kind of doing right now, with the exception of apples, garlic and onions (for my soups), celery, mushrooms, and sauerkraut. Pick out the low GI foods from the safe side, a few in the middle that you like, and stay away or limit yourself to just one item on the avoiding side.

The most strict Paleo diet I've seen is here, known as the gut healing diet I guess, which allows absolutely NO FRUIT:

http://www.eat-real-food-paleodietitian.com/support-files/sibo-gut-healing-protocol.pdf

Have you gone through few of the clinical studies here? Many say the same thing:

If you don't need to be strict than don't, just do your best and explore as much as you'd like :3.