So I'm going to the casino this weekend and it got me thinking about probability. If I have an n-sided die and roll it n times, what are the chances of me hitting a specific number, x? For example, if I flip a coin (n=2) twice, what are the chances of me hitting heads at least once? Answer (obvious for n=2): 1-.5^2 = .75 It's obvious for most n's until they get large. I've simplified it to this equation: 1-((n-1)^n)/(n^n) If I go back to n=2, we see that we arrive at the same answer of .75. My TI-89 can calculate up to an n of 100, which gives a value of .6340. I'm very interested in this value as n increases, though. Unfortunately I don't have access to math software that could solve the problem as a limit. How can I solve this, or more importantly... WHAT'S THE ANSWER? It's driving me crazy! My best guess is that it tends towards 1/2. Thanks for any help!