If I have a 20 sided die and I want to roll a 20, and I have failed 100 times, can the probability increase because of the failed attempts? I am pretty sure this is a no, but had to ask!
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No, the probability could only decrease, as failing $100$ times in a row increases the chances that the die is loaded against $20$. – A.S. Nov 26 '15 at 20:15
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It's not so bad with a $20$-sided die, but if I threw a six-sided die $100$ times, and I never got a $6$, I would start to suspect it was loaded, which will affect the probability. – Arthur Nov 26 '15 at 20:20
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Each subsequent roll would be the exact same 1/20 chance of getting any value, on its own. When quantified and taken as a group however you should expect a 20 approximately 5 times in a 100 rolls, and to that extent, a batch of rolls would have a higher chance of rolling a value that hasn't been rolled yet.
The final chart should, given a large enough sample of attempted rolls, provide an even spread of all values.
Luponius
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You should NOT expect to see $20$ $5$ times out of $100$. It will be $Bin(100,1/20)\approx Pois(5)$ and hence probability to see exactly five $20$'s is $\approx 18%$ only – A.S. Nov 26 '15 at 20:48