A Friction Problem (Experimentation) A Square dice $( 0.8$ cm $\times$ $0.8$ cm$)$ face is noted and it is released exactly $1$ cm from a ground with Friction coefficient  $(\mu = 0.25 )$ (say).

*

*What is the chance that the dice rolls?

*Why does it exactly roll even from a height of $1$ cm?

These questions randomly popped as I was fiddling around with the board dice. So, I decided to do perform several experiments :-
I released the same dice 10 times on my plywood study desk and recorded the results




No. of times released
Rolls?




1
Yes


2
Yes


3
No


4
Yes


5
Yes


6
Yes


7
Yes


8
Yes


9
Yes


10
Yes




Still I wasn't so satisfied with my experiments so I decided to roll a few time more till 20 but later scrapped that idea because the Question would become too long.
So, the final answer to the 1st Question was $9/10$ time it rolls.
For the 2nd Question though, I have a contradiction to my very own question. When the dice is released from $1$ cm, it should not budge because of the friction of the ground. Heck the dice should even roll. But the experiments shows a different thing all together. What am I exactly missing in here?
 A: Friction between the die and the ground is almost entirely irrelevant to this phenomenon. If the die has enough energy after the collision with the ground to lift its center of mass high enough to roll over, and the collision involves sufficient torque (because of falling not quite straight down, so that one edge or vertex impacts the table slightly before the rest of the face) that it actually does tip over, it will roll. If it has enough energy to do that several times in any direction, it will roll fairly. You're dropping your die's center of mass from a height of $1.4cm$ to a height of $0.4cm$, you're probably imparting a little bit of rotational kinetic energy as you drop it since your hands are not perfect frictionless leveling machines, and it needs to rebound with a little bit more energy than needed to reach to a height of half its longest diagonal ($0.4\sqrt{3} \approx 0.7cm$) in order to tip over in any direction, or a little bit more energy than needed to reach a height of half its shortest diagonal ($0.4\sqrt{2} \approx 0.6cm$) in order to tip over at all.
With a 1cm falling distance and a 0.2 to 0.3cm minimum rebound distance, your experiment indicates that your die bounces from the plywood surface with at least 20-30% of the kinetic energy with which it struck.
Since your die does not roll fairly (or even roll at all every time), it indicates that it does not rebound with significantly more than 30% of the kinetic energy with which it struck.
This matches my expectations based on my everyday experience for objects made of wood and plastic. If you retried the experiment with a hardened steel die on a heavy hardened steel anvil, such that about 90% of the kinetic energy of the collision was retained in the rebound, I predict that you would find that you could roll the die at a height of about $0.4cm$ above the table.
