In reply to Bill Hull.

Most humans do not have a good intuition about randomness and probability. The situation you describe is known as the "coupon collector's problem." An easy to visualize situation is rolling a six-sided die and asking how many rolls should you expect to need before you have seen all six faces?

For the digits 0-9, imagine rolling a ten-sided die. How many times do you expect to roll it before all 10 faces have appeared? The answer is 10/10 + 10/9 + 10/8 + ... + 10/1 = 29.3 rolls. So it is not odd at all that you have to look at 32 decimal places in pi until all digits appear!