What does more than chance mean? I'm interested in what exactly sentences like this mean: 

In the former case, participants correctly chose the larger city in
  55% of the pairs, in the latter in 54% of the pairs, both rates
  significantly different from chance.

Is it basically just that its significantly different from 50%?
UPDATE:
Here's another one:  
But now here's another one I've found: In a pretest, one brand had been rated as higher quality, and participants could identify the higher-quality product 59 percent of the time in a blind test (substantially higher than chance, which was 33 percent). I still don't get how is 33 determined?

How do they get 33?
 A: Yes, that is probably what was intended, given the phrases "of the pairs".
Of course statistically significant, especially with a large enough sample, does not need to mean substantial. 
Added as a response to comments:
The context seems to be described here, including

Imagine you are confronted with the names of two German cities, and
  you recognize neither of them. There is no more information available
  to infer which city is larger. What can you do?
...
Drösemeyer (2000) and Hell used the names of smaller German cities,
  between 45.000 and 60.000 and between 20.000 and 25.000 inhabitants.
  This resulted in their German participants sometimes having heard of
  neither of the two, and sometimes just recognizing the two by name,
  but with no further information available from memory. In the former
  case, participants correctly chose the larger city in 55% of the
  pairs, in the latter in 54% of the pairs, both rates significantly
  different from chance. Although these effects are tiny, they point to
  an interesting exploitation of information from the mere names, even
  if both cities are unrecognized.

That makes it clear that guessing one out of two is what was involved and suggests that there is on average a tiny positive amount of information about cities' sizes in their names.  But obviously it is not a particularly reliable way of estimating city size.
