Dice Probability

"There are domains in which expertise is not possible. Stock picking is a good example. And in long-term political strategic forecasting, it's been shown that experts are just not better than a dice-throwing monkey."
~ Daniel Kahneman

Cock & Bull... The Perfect Dice Game?

Cock & Bull is based on the number 6, and in a twist of irony, numbers don't lie or even exaggerate.
Six is the only number that is both the sum and the product of three consecutive positive numbers.
Since six is equal to the sum of its proper divisors (1+2+3 = 6) six is the smallest perfect number.

There are 6 faces on each of the Cock & Bull dice cubes.
There are 3 cocks, 2 Bulls, and 1 Monkey on the faces of the dice, the proper divisors of 6.
There are only 6 possible dice rolls with a pair of Cock & Bull dice.

Peg movement on the mantle is by 1, 2, 3 or 6 points, all divisors of 6.
After you capture all 3 cocks with your chips, additional pairs of cocks are worth 2 points, 3 x 2 = 6.
After you capture the 2 bulls with your chips, additional pairs of bulls are worth 3 points, 2 x 3 = 6.
After you capture the crown with your chip, additional pairs of monkeys are worth 6 points, 1 x 6 = 6.
The number of points it takes for a player to peg out and win the game is equal to 6 squared, or 36.
The number of chips it takes for a player to chip-in and win is 6.

The Six Faces of the Cock & Bull Dice:

I have always been fascinated with dice, I love the sound they make and the way they feel in your hand. To me dice are a contradiction, I would even go so far as to say, a paradox. In the long run, say over the course of hundreds of games played, the cumulative roll outcomes are a mathematical certainty. However, in the span of a single game, each roll of the dice would appear to be totally random and unpredictable. This makes dice games very appealing to me.

To make Cock & Bull interesting, I reduced the faces of the dice down to just three unique images. Compared to 21 different rolls with a standard pair of dice, there are only 6 different rolls with Cock & Bull dice, two of which will cause you to lose your turn. So essentially, there are only 5 different dice plays in the official Cock & Bull rules.

A win is never guaranteed in this game, but I profess that you can gain an edge and win more frequently by basing your strategy on the odds of what your next dice roll might be. ~F.M.S.

Pair of Monkeys

Probability:
1 of 36 possibilities
1 in 36 rolls

Pair of Bulls

Probability:
4 of 36 possibilities
1 in 9 rolls

Pair of Cocks

Probability:
9 of 36 possibilities
1 in 4 rolls

Cock and Bull

Probability:
12 of 36 possibilities
1 in 3 rolls

Bull and Monkey

Probability:
4 of 36 possibilities
1 in 9 rolls

Cock and Monkey

Probability:
6 of 36 possibilities
1 in 6 rolls

TAKE HEED:
The combined probability of losing your turn by rolling a single monkey:
10 of 36 possibilities
1 in 3.6

Space Curve Ball

Albert Einstein

"This is what we mean when we talk of the 'curvature of space'. The fundamental concepts of the 'straight line', the 'plane', etc., thereby lose their precise significance in physics. In the general theory of relativity the doctrine of space and time, or kinematics, no longer figures as a fundamental independent of the rest of physics. The geometrical behavior of bodies and the motion of clocks rather depend on gravitational fields which in their turn are produced by matter."

Nikola Tesla

"I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view."

Stephen Hawking

Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in curved space, which is called a geodesic. Light rays too must follow geodesics in space-time... this means that light from a distant star that happened to pass near the sun would be deflected through a small angel, causing the star to appear in a different position to an observer on the earth.

Steven Wright

“I heard that in relativity theory, space and time are the same thing. Einstein discovered this when he kept showing up three miles late for his meetings.”

“Light travels faster than sound. Isn't that why people appear bright before you hear them speak? ”

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