[BruceZ]

1) The problem is asking for 'the number of hands that you must be dealt for the probability to be at least 50% that all 1326 hands on your list have been marked'. This seems to be the same as asking: 'On average, how many hands will it take for you to mark off all of the hands?'.

This is absolutely not the same thing. The average value does not in general coincide with 50% probability. The issue is the difference between the mean and the median, the median being the value at which half will lie above and half will lie below. We want the median in this problem, and you have attempted (perhaps successfully) to calculate the mean.

There are some problems where the 50% probability is finite, and the expected value is infinite. An example is the time it takes to go broke playing an even money game against an infinitely wealthy opponent. The average time is infinite, but the time it takes to have a 50% probability of busting out is finite.