When packing pieces away, most gamers have given the box a shake to get the bits to pack better.  For most people this is instinct, but there is science behind it as reported by Asencio et al., in Physical Review Letters in 2017.^1,2  Tapping a box of marbles or sand will encourage the pieces to pack themselves progressively more tightly, however, the effect quickly reaches the point of diminishing returns; the maximum density is only approached after a very long time and the right tapping sequence. Asencio et al.,¹ report experiments with a cylinder full of dice, showing that with vigorous twisting back and forth, the pieces rapidly achieved their maximum density.

– Image from physics.aps.org

These studies show that the degree of ordering depends strongly on the rotational acceleration applied on each twist.  Only ten thousand twists are needed where the acceleration is around half that due to gravity (0.5 g), but below that, packing proceeds so slowly that it is unclear if the dice would ever reach their maximum density.

¹ Asencio, K., Acevedo, M., Zuriguel, I. & Maza, D., Phys. Rev. Lett. (2017), 119, 228002; doi:10.1103/PhysRevLett.119.228002.
² Buchanan, M., Phys. (2017), 10, 130; doi:10.1103/Physics.10.130.