True Craps!

Dice Control by Dice Setting.

Dice control. On no regulation casino craps table, in any regulation casino craps game, can any shooter control, restrict, or preferentially influence the outcome of the dice to any particular number. No one who professes otherwise has ever stepped up to prove their claim. There are several levels of proof that show it cannot be and has not been done.

Many believers claim that dice control is a skill developed and exercised by only a gifted few. These believers claim that the skill is similar to that of a well-practiced professional athlete. Let alone the fact that Olympic and professional world-caliber athletes train for many thousands of hours before reaching their best level of expertise, compared to a few hundred hours for the self-proclaimed dice control experts, comparisons would only work if:

    * Pitchers threw at 2,000 MPH.
    * Billiards cue balls were shot from canons.
    * Golfers used fire hoses instead of clubs.
    * Horseshoes were shot from catapults and had to land on edge to count, while still attached to the horse.
    * In target shooting, each bullet had to hit the target without puncturing it, and then fall perfectly to the ground beneath the target with no bounce off the target using a .45 cal handgun at 3 feet from the target.
    * Arrows were made of balsa wood and shot using a .50 Cal machine gun.
    * Bowling required the ball to stop within 2 mm of the No 1 pin, and touch no other pin, stopping with the holes pointing directly upwards.
    * Darts were made from cooked spaghetti.

Some Serious Facts:
Let's Examine the Physics of Dice Control

How can a die be tossed so as to roll only about one axis upon landing? Let's keep in mind, that all the throws must be from one side of the table to another, and all will be about the same length, such that
you need to control the landing, not the toss!
All you have to do to screw up a controlled throw is have one die twist about 46 degrees off trajectory. How likely is that?

Assumption: The die being tossed is a regulation casino die made of cellulose acetate plastic, measuring .75" square and is not out of balance or square, i.e. rigged. Casino dice are generally square to within 1/10,000 ". A typical die weighs in at about 7 grams.
Assumption: Clear air, no apparent air motion. Barometric pressure at or near a standard day pressure of 29.92" hg.
Assumption: A landing surface of wood or similar product, covered in casino felt.
Assumption: For this examination, we will assume that hitting a casino craps table back wall of rubber pyramids is not required.

When a thrown die lands, its final resting position is determined by the forces it encounters when thrown and during the landing.
If a die is thrown perfectly perpendicular to its lateral axis, it will continue in that direction until acted upon by other forces.
In this perfect situation, it will be possible to predict with certainty that at least 2 of the possible 6 numbers (those on the side of the die) would not end up as the uppermost face, as they remain perpendicular to the plane of the landing surface. Indeed, in this ideal situation, it would be possible to determine which of four faces would end up on top if the energy imparted in the throw were precisely known, and the drag properties of the landing surfaces taken into account.

However, in real life situations, such as on a casino craps table, several factors conspire to confound the ideal world and cause the die to land exposing a randomly selected face. The most important factor is that the dice must land and stop, thus dissapating all of the energy put into the toss. The question becomes:
Is there enough energy in these bodies in motion to upset their orientation at the time of landing?

Let's see if we can answer that question.

The factors involved in any body in motion are:

Mass

Technically, calculating mass requires you to make a list of each element that makes up the object, and count the number of atoms of each element. You will then go to a periodic table of elements, and determine the atomic mass average for each element. And that's just the beginning. You then will multiply each atomic mass by the number of atoms in the formula. From there you can calculate the molar mass, from which you can determine the mass of the object given its size. However, for our purposes the weight of the object (a product of gravity and mass) will be sufficient. One regulation die weighs in at around 7 grams.

Force

Because of Newton's Second Law, force is pretty easy to deal with if we know mass and acceleration. We can calculate force using the following equation:
F=ma
where F=force, m=mass, and a=acceleration.
Using a little 7th grade algebra it can also be stated
a=F/m.
Force is measured in newtons, and one newton (N) of force is enough to accelerate one kilogram (kg) of mass at a rate of one meter per second, per second (m/s2).

Acceleration

Again, a little 7th grade algebra and the Second Law of Mr. Newton lets us calculate acceleration imparted to an object as stated above:
a=F/m.
For this dissertation, we can measure (or estimate) the acceleration imparted to a die by its thrower. Acceleration is measured in meters per second per second, or m/s2. Gravity alone will accelerate objects at 9.8 m/s2, such as any object dropped from a building. This is a fast acceleration. For example if something falls for 5 seconds, it will reach a speed of about 49 m/s. If a car accelerated this fast, we would be talking about 0-60 times of less than 3 seconds.

Torque

Torque equals force multiplied by distance. Simple, huh? Torque is the key ingredient here. If we can determine the amount of torque imparted by a toss, and we know how much torque it takes to move a die, we can then understand the potential to move the die in the direction of question.

Distance

Get out the old measuring stick.

Obviously mass is going to be slightly difficult to pin down without exact knowledge of the makeup of the die. For now, assume a dies weight is its true mass. The fundamental question here is what will it require to move the thrown die off its straight and narrow path? What amount of torque will move this object? If we calculate the amount of torque required to move a die in certain directions, and we determine how much torque, or force is invested in throwing a die the length in question, we can then make some educated determinations, and move forward.

If the force imparted by the throw is roughly equal to the force required to overturn a die, then we should then refine our measurements to seek a closer determination. If however, we find that the force imparted by a throw is a huge magnitude greater than that required to spin and overturn a die, then it is unlikely that we will be off by great magnitudes, and we have our answer.

So, how much force is imparted in a 1 meter throw of a 7 gram object accelerated to 5 m/s2?

F=ma
F=.007*5
F=.035 newtons.

To calculate the amount of torque it will take to move a die in a chosen direction:

    1. Put the die on a board and slowly slope the board to induce the die to move in the direction required.
    2. Find the angle at which the die starts to move (theta).
    3. Find the number of revolutions the die will roll in one meter (revs) in that direction.
    4. Call the torque required, T, the mass of the die m, and the acceleration due to gravity, g.
    5. Then:
    Torque = [ m x g x sin (theta) ] / (revs x 2 x pi)

It is important to calculate the torque required for three directions of movement.
The first being a simple roll from one face to a perpendicular face.
The second direction will be a twisting movement of 90 degrees while remaining on the lowermost face.
The third direction to induce would be a roll across the face of the die, and up onto a point. A line bisecting a face of the die into two right triangles would describe this direction.

Just a rough estimate for a non-spin movement using a mass of 7 grams, a 45-degree angle, and acceleration of 5 m/s2, and 4 cm per revolution.

T=[m x g x sin(theta)] / (revs x 2 x pi)
T=[.007 x 5 x .707] / (25 x 2 x 3.141)
T=[.024754]/157.05
T= 1.57561 newton/meters

After all that, compare this torque required to move a die with the force imparted by a typical casino throw:

1.57561 n/m vs .035 newtons applied to a 2cm2 face.

That is one of the many reasons why Dice Control cannot work. The force of the throw is over 44 times greater than the force required to move the die off its trajectory. If the two values were close, one could argue for a recount or re-evaluation. So deny the facts if you will, but science makes it clear that the casinos are safe (as if you didn't know).

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