How fair is an almost perfect riffle shuffle?
An almost perfect riffle shuffle of a 52 card deck is not perfectly random, but should be sufficiently fair for any casual purpose.

I decided to test this experimentally.  I coded up a quick python function* to perform riffles and almost perfect riffles.  

When performing a perfect riffle, the code takes a "deck" of integers and rearranges them so that the first half and second half are interlaced, so the deck  


  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51]  


becomes


  [26, 0, 27, 1, 28, 2, 29, 3, 30, 4, 31, 5, 32, 6, 33, 7, 34, 8, 35, 9, 36, 10, 37, 11, 38, 12, 39, 13, 40, 14, 41, 15, 42, 16, 43, 17, 44, 18, 45, 19, 46, 20, 47, 21, 48, 22, 49, 23, 50, 24, 51, 25]


For an imperfect riffle, the function adds a defect where two numbers are kept together without an intervening one from the other half.  For example, the 0-51 range might instead become


  [26, 0, 27, 1, 28, 2, 29, 3, 30, 4, 31, 5, 32, 6, 33, 7, 34, 8, 35, 9, 36, 10, 37, 11, 38, 12, 39, 13, 40, 14, 41, 15, 42, 16, 43, 17, 44, 18, 45, 19, 46, 20, 47, 21, 22, 48, 23, 49, 24, 50, 25, 51]


The defect is added at a random point during the interlacing.



Repeating the perfect riffle shuffle on a 52 card deck 7 times generates a very regular pattern:


  [40, 28, 16, 4, 45, 33, 21, 9, 50, 38, 26, 14, 2, 43, 31, 19, 7, 48, 36, 24, 12, 0, 41, 29, 17, 5, 46, 34, 22, 10, 51, 39, 27, 15, 3, 44, 32, 20, 8, 49, 37, 25, 13, 1, 42, 30, 18, 6, 47, 35, 23, 11]




The imperfect shuffle on the other hand, generates a unique pattern every time.  One example was


  [31, 0, 38, 51, 26, 8, 44, 29, 14, 36, 2, 20, 3, 5, 27, 46, 24, 33, 32, 17, 40, 25, 10, 22, 48, 30, 35, 1, 50, 42, 7, 12, 45, 13, 39, 37, 19, 43, 4, 18, 28, 34, 15, 23, 16, 41, 6, 11, 21, 49, 9, 47]




That looks pretty random. Is it, though?  I decided to Monte Carlo it, and "shuffled" the deck 100,000 times to look at how the numbers distributed.  

It turns out that this is not nearly as random as it appears.  In a perfectly random shuffle each number should have a 1/52 chance (1.92%) of appearing in any position.  But my results were instead that the probabilities ranged from 0.02% to 18.5%.  That's a great deal more likely than 1.92%.

But while it's not good that card 10 is ending up in slot 26** 18% of the time, it's not something that is easy to abuse either.  Did you know what card #10 was?  Do you care what card #26 is?  Your goal is not a random deck, but instead a fair one.  That means that a bit of unrandomness is fine, as long as no players are taking advantage of it.  7 almost perfect shuffles leaves patterns that could be taken advantage of, but they are sufficiently complex enough that you would have to dedicate significant time and energy to do so.

And it's easy to add extra randomness by cutting the deck or throwing in a few extra shuffles.  Furthermore, I've almost certainly underestimated the amount of randomness, since the "almost perfect riffle" pictured in the OP has 3 defects instead of 1, and shufflers will not always perfectly divide the deck in half like I assumed.

All told, I do not think that you need to worry about your excellent riffling skills disrupting your card games.  But perhaps be careful if you play with professional card counters.



*I can share the code if anyone's interested, but it isn't really relevant. 

**Or possibly the other way around.  I get my axes confused sometimes.