Say I have a D sided dice and I toss it N times. Given a value K where K >=1 and <= N, what are the odds that K of the rolls have the same number? What are the odds that >= K of the rolls have the same number?
As a bonus follow-up, how does the above change if there is a consistent probability p that a number becomes unrollable in the future every time it is hit? That is to say, numbers become progressively less likely every time they are rolled by some consistent probability.
