A problem with optimization and probabilities?

[Guest]

Say you are asked to draw m sets of x cards out of a deck of d cards. Everytime you draw a set, there is 10% chance an additional card would be drawn. Assuming d = [tex]\infty[/tex] and the rules:
1. You can only draw up to 20 cards per set.
2. You can have as many sets as you want until you draw n cards.
3. The additional cards do not count for n.
Optimize x so that you can draw the most amount of cards before reaching n.