[jason_t]

answer: 26c13/(26c13 + 25c13)

Now,

26c13 = 25c13 + 25c12 = 25c13 + 25c13 = 2 * 25c13

since

n choose k = (n-1) choose k + (n-1) choose (k-1)

and

n choose k = n choose (n-k).

Thus

26c13/(26c13 + 25c13) = (2 * 25c13)/(3 * 25c13) = 2/3.

Therefore the answer is 2/3.

This calculation also shows why the answer isn't surprising. There are twice as many ways to choose 13 cards from 26 as there are to choose 13 from 25.