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Message: <blockquote data-quote="Borlon" data-source="post: 2619050" data-attributes="member: 27589">If the dice are fair, the average number of rolls before you get a 1 on an N-sided die is N.  So the average lifespan of a wand with those ruls is 50 charges.  While you are unlikely to roll all the numbers between 2-20 before you roll a 1, you will probably roll some other number two or three times.  To see this, imagine that you roll a 20 sided dice 2000 times.  How many 1s do you expect?  Around 100.  2000/200 is 20; the average wait between 1s is 20 rolls.  How many 2s do you expect.  Around 100; the average wait between 2s is 20 rolls.  And so on for all the numbers.  Sometimes the wait is more, sometimes less; you could roll three 1s in a roll, for example.  But the average wait between repeats of a particular number on an N-sided die is N rolls.</blockquote>