Analysis of a rare die landing/balancing on a checker

[Gazzetta1992]

TL;DR

Rare Die landing

Hi everyone,

I came across a video clip from a Backgammon World Championship match showing a very unusual die roll that I would like to analyze from a classical mechanics perspective.

During the roll, after bouncing and losing kinetic energy, the die comes to a complete rest directly on top of a checker piece, balancing steadily on its face. The checker itself has a slightly concave/dished surface, which is standard for professional backgammon sets.

I would appreciate insights from the community on the following points:

Energy Dissipation & Kinematics: What is the likelihood of a die losing sufficient angular and translational kinetic energy to settle flat on top of a small elevated surface rather than tumbling off?

Static Equilibrium: Given the slight concavity of the checker, how do the contact points and the center of mass align to maintain a stable equilibrium in such an impact?

Coefficients of Restitution: How do the material properties (acrylic/acetate precision die hitting a resin/plastic checker) contribute to dampening the rebound at the final point of contact?

Here is the clip for reference: [ ] at 03.27.44

Looking forward to your thoughts and physical breakdown of this phenomenon. Thanks!

 

[A.T.]

the die comes to a complete rest directly on top of a checker piece, balancing steadily on its face

Isn't it rather still spinning?

 

[berkeman]

Welcome to PF.

TL;DR: Rare Die landing

Here is the clip for reference:

The video is 8 hours long? Do you have something shorter that shows the roll you are asking about?

 

[kuruman]

Welcome to PF.


The video is 8 hours long? Do you have something shorter that shows the roll you are asking about?

OP has provided the time of the event as 3:27:44.

I have been playing backgammon for more than sixty years and I have seen this happen quite a few times but not for that long.

 

[berkeman]

OP has provided the time of the event as 3:27:44.

Oh dang it. I'm not very YT savvy, so thank you.

 

[A.T.]

OP has provided the time of the event as 3:27:44.

Youtube allows links directly to a specific time in the video:

 

[A.T.]

I have been playing backgammon for more than sixty years and I have seen this happen quite a few times but not for that long.

You mean a spinning die? Because the OP seems to be under the impression it's in some unlikely static quilibrium:

Static Equilibrium: Given the slight concavity of the checker, how do the contact points and the center of mass align to maintain a stable equilibrium in such an impact?

When throwing dice into a confined box, this spinning top behavior occurs fairly regularly. That it stayed on one of many concave checkers seems not extraordinary either.

 

[kuruman]

You mean a spinning die? Because the OP seems to be under the impression it's in some unlikely static quilibrium:

Yes, that is what I mean. The die is clearly spinning on top of the piece until the player stops it and rolls again. It is definitely not in static equilibrium. The OP is mistaken.

 

[Jason Hogan]

Good catch by @A.T. and @kuruman!

Looking closely at that timestamp (3:27:44), this isn't a case of static equilibrium, but rather a classic demonstration of gyroscopic stabilization / rotational dynamics.

When analyzing the event through that lens:

1. Gyroscopic Stability & Energy Partitioning

When the precision die is thrown into the restricted perimeter of a backgammon board/baffle box, it loses most of its translational kinetic energy ($E_{trans} = \frac{1}{2}mv^2$) through inelastic impacts with the felt and side walls. However, if a high degree of angular momentum ($L = I\omega$) remains along its vertical axis, the die acts like a spinning top. The gyroscopic torque prevents it from tipping over or tumbling off the checker edge as long as $\omega$ remains sufficiently high.

2. Dynamic Center-Sensing on Concave Checkers

Professional backgammon checkers feature a slight dish/concavity on their face. This surface geometry creates a shallow potential well. As the spinning corner/face of the die contacts the dished surface, centripetal friction pushes the contact point toward the lowest point of the concavity, effectively "trapping" the spinning die in the center until it loses rotational velocity or is interrupted by a player.

3. Low Kinetic Energy Conversion

Because precision acrylic dice hitting resin checkers have a relatively low coefficient of restitution for sliding/spinning friction compared to normal impact bounce, the remaining energy is dissipated almost entirely as micro-friction at the single point of contact on the dished checker, allowing the die to spin smoothly in place rather than bouncing off.