*science. I myself combine riffle shuffling and overhand shuffling - a couple of riffle shuffles, a couple of overhand shuffles, repeat.
The riffle shuffling has a really, really bad and particular weakness: Cards at the top of the deck tend to stay at the top of the deck, and cards at the bottom of the deck tend to stay at the bottom. So - riffle shuffling alone (even 7 times) isn't good enough. So - if you start with (for example) the ace of hearts at the bottom, it will tend to stay at the bottom even after seven riffle shuffles.
This should have been mentioned - it is simple math.

Adding video to channels (Science) - requested by Zawash.

I'm always so distracted by people who keep their eyes closed for the majority of the time they're talking. I always do two things: 1) wonder if they realize what they're doing and how they feel comfortable doing it, and 2) I think about sneaking away quietly and wonder how long it'll take them to realize I'm gone.

The maths is 7-11 riffle shuffles result in a random deck. Your inability to perform a proper ripple shuffle doesn't change the maths.

I disagree with the insinuation that that is intuitive...

I think to answer @Zawash 's concerns, the seven riffle shuffles is probably close to the "sweet spot" because even a card on the very bottom or very top will likely move at least 1-2 places away from those extreme positions (top or bottom) in a single shuffle. Then, on the second shuffle, it is likely to move even further -- the probable "distance moved" is even higher and goes up rapidly away from the extreme edges. By the time that you've riffle shuffled 7 times, it should easily have shifted far enough away from either extreme end to be sufficiently "random".

Sorta like the old elementary school math question of would you rather have a million dollars NOW, or one penny today and then double that amount each day for the next month. We tend to underestimate the value of option 2 (over $5 million after 30 days, $10m+ for 31) because our brains are much better at grasping/predicting geometric growth than exponential growth.

That doesn't have anything to do with "inability to perform a proper riffle shuffle", just a very human tendency to underestimate exponential changes over a few iterations.

You are quite right @MilkmanDan - after seven random shuffles the chances of the top card staying at the top the whole time would be 1/128, which should be sufficient - it would probably sink down a bit sooner, and thus be distributed evenly throughout the deck when you shuffle it that many times. The top card and bottom cards each have a 1/2 chance of staying where they are after a single riffle shuffle.
And I do have a quite decent riffle shuffle; I just had a silly math brain fart.
But hey - what would the sift be if everyone thought things thoroughly over before posting?