There is a pile of $5\leq N\leq15$ cards.
$x=3$ or $6\leq N$ cards need to be randomly chosen from this pile (uniform distribution).
To do this any number of $6$-sided dice can be rolled any number of times.
What are efficient methods of doing this? Or if it's not possible to do better than the method I've listed as an answer, why?
Efficiency $E_1$ is the expected number of individual dice rolls needed.
Efficiency $E_2$ is the expected number of rolls needed (simultaneous rolls count as 1 roll).
As this puzzle arises from a practical situation where one may or may not have multiple dice, both of these measures of efficiency are useful to take into account.
Also note in practice, a maximum of $\approx3$ dice can be rolled at the same time.
$x=6$ most of the time, especially when $N\geq10$.
- $N\approx 15$ most of the time, so being able to find more efficient methods for any of the cases when $N\geq10$ is desirable.
If you're wondering, this problem arises from a common occurrence when using the card Pot of Indulgence in the card game Yu-Gi-Oh, hence the specific numbers, etc.