[luca3v]

If one player picks 50 of boxes, the probability of finding a particular number will be 50% independently of the strategy.

(Note that sum([1.0/(100-n) for n in range(70)]) is more than one: the probability is 1/100 + 99/100 * 1/99 + ... which adds 1/100 in each try)

The point of the cycle strategy is that there is at least a 30% probability that all 100 people will succeed, while this should intuitively happen only with probability (1/2)^100 which is inconceivably small.