53/27 =~ 1.962962963
According to Wizard of Vegas member ThatDonGuy, if the total number of cards is c and the number of blockers is b, then the expected cards drawn is (c+1)/(b+1).
For example, in the question at hand c=52 and b=26, so the answer is 53/27.
If cars were drawn until an ace appeared, there would be four blockers, so the answer would be 53/5 = 10.6
This question is asked and discussed in my forum at Wizard of Vegas.