How often is "more often than not"?

Solution 1:

It happens more often that it does not happen.

50.000001% and over

There is no official percentage. It just happens more often than it does not happen. So at least 50.000001%.

As pointed out in the comments, often can be any percentage that implies somewhat frequently - and depends on the circumstances.

Solution 2:

The literal meaning of more often than not is in more than 50% of cases. As this is so obvious and no other precise meaning is well known, you can expect that at least some people will use it in precisely this sense. I guess the need for more often than not arose because almost all other expressions that describe a frequency or probability are relative to some normal or expected frequency or probability and are not related to any fixed percentage.

On the other hand, I am sure a lot of people use the expression figuratively as a longer, more impressive alternative to often, meaning a somewhat higher probability than often.

I won't try to interpret this, but in the Google corpus, much more often than not - which I think most people will understand literally - accounts for (not much) less than 1% of uses of more often than not.