Matt W. Barrow writes:

You have a million people within 500 feet (the range of a fob/garage door
opened) of you at any one time?

They're LONG odds, not impossibility.

If there are 200 cars within range in a parking lot, with a million codes, the
odds of two cars having the same code are about 1 in 5000. However, if you
commute twice a day in different parking lots with 200 cars in range for work,
there's about a 10% chance that you'll find another car with the same code at
least once a year.

This is still better than keys, which often have only a very small number of
"codes." In some cases there are only a dozen or so different keys for all
the cars of a specific model or even a specific group of models. On one
occasion, after locking myself out of a rental car, I was able to open the
door with a key for our own car, and the only thing the two cars had in common
was the manufacturer. On another occasion, I got into a car in the parking
lot that matched my key, paint job, etc., only to discover that it wasn't
mine.

Anyway, you need a lot more than one million different codes to be secure.