The math of lots and the Greek Fates

      14 Comments on The math of lots and the Greek Fates

The drawing of lots, used to determine the outcome of the tied Virginia House of Delegates election noted in a previous post, has a long tradition in western culture, including the two dominant strains represented by the Judeo-Christian Bible and Greek mythology.

Mathematically, the drawing of lots is a random number generator modeling a uniform probability distribution.  In this case, like a fair coin flip, there are two outcomes, each with a 50-50 chance. In the simplest board games we played as children we used instead a single six-sided die, also a uniform distribution but with six equal probabilities of 16.67% each.

As the games became more complex, we often used two six-sided dice, and the “fate structure” of the game changed. We now have probabilistic randomness, where a total roll of seven is six times more likely to happen than is a roll of the “snake-eyes” two. This is also called a stochastic process. And try as hard as you will, you cannot roll a one. [1] We accept this probabilistic fate as the way the game works, and when we know the odds, we can sometimes use our limited understanding of probability to help shape our own destiny in the progression of the game.

In the Bible’s Pentateuch, lots were used to select from the flock a “scapegoat,” which was used to “bear the sins” of the nation via a ritual sacrifice. [2] In the New Testament, lots were drawn to select a thirteenth apostle when one was chosen to replace the disgraced Judas Iscariot to help preach the emerging gospel of Jesus after his death. [3]

The use of lots and other games of chance to ascertain the “will of God” likely goes back even earlier and more broadly in human culture, and even has a name – cleromancy. Modern believers of cleromancy are frequently found on the news broadcasts exuberantly crediting God for granting them a Powerball lottery win instead of me.

The Greek tradition of the “three Fates,” also called the Moirai, has a fascinating tie to a biological reality. The Moirai were seen as demigods who control the destiny of human lives. The first Fate, named Clotho, spins “the thread of life” to set an initial deterministic course for each person born. The second Fate is named Lachesis, which literally means the “drawer of lots,” and randomly allots [literally] a specific measure of “thread” to each human. Finally, the third Fate, Atropos, chooses the time and manner of each person’s death, “cutting the thread.” [4]

Three thousand years after its origin, the symbolism of the Greek Fates seems quite prescient. Each of us begins life with a unique and probabilistically random DNA “thread,” part taken from your father and part from your mother. Our DNA has a strong deterministic control over our physical and mental development (the first Fate). But some of our genes don’t express themselves unless certain environmental conditions hit our lives, which is our second Fate. And finally, a two-pack-a-day smoker may somehow live to the age of 100, while a healthy runner may get hit by a bus at age 30. Fate #3 at work.

And here you thought Greek mythology was dead. It was just a different “God language” for simplifying and describing a process for which we also now have scientific and mathematical language, and daily we mix the language of our expressions, usually without thinking about it. And we still talk about (and choose) “scapegoats,” and we still apparently practice cleromancy as well. How far we have come!


  1. To see a complete table of two-dice probabilities, click here.
  2. Leviticus 16:8.
  3. Acts 1:26.
  4. “The Fates.”

For additional posts on probability, volition and ethics, follow the Dice icon back or forward where it appears.

Prior Dice  Next