# A problem with optimization and probabilities?

Probability theory and statistics

### A problem with optimization and probabilities?

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 = $\infty$ 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.
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