No, no, no, no, no.
The answeers to Jordan Drachman’s first question is NOT 2 in 3. I’ll explain:
50% odds the first card is an ace. 100% odds that the second card is an ace. 50% odds that we will pick each card. Therefore we have a 50% of 50% plus 100% of 50% odds of picking an ace. That gives 75% (.5 * .5 + 1.0 * .5 if you prefer) odds of getting an ace out of the hat. This equates to 3 out of 4 times. Not 1/2, not 2/3 but 3/4.
I wonder if Cecil will read this…