The tighter wind is usually the wrong wind. You can easily simulate the double kink problem thusly:

1. grab two adjacent loops of a cord and rotate your hands in opposite directions so as to expand the loop until you have a new loop that doubles back on itself
2. repeat that on the next loop and keep doing it

You'll now have a cord that has the correct spiral on either end with a length of incorrect spiral in the middle.

I think how this occurs in the real world is that people twist the cord open without unfurling it until it twists on itself. Then it keeps going and keeps going until the single kink separates itself and moves outward. You might be able to simulate this by simply untwisting a cord for a while.