The values don't change between tests because a special random sequence is used that is always the same. Otherwise there would be indeed small changes between tests.

The median AR is the AR at 50% confidence level, i.e. 50% of results are worse and 50% are better. It _is_ the most likely outcome, and also useful for comparison with the 'real' AR. A real AR that is always better or worse than the median AR reveals some information about the system, f.i. a negative or positive self-correlation of the results.

The AR at 95% is not the most realistic AR, it only means that 95% of results get this _or_ a better AR.