Playing Yahtzee® with God

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Yesterday I had the opportunity to see the award-winning documentary Three Identical Strangers, about identical triplets who had been raised separately, only to meet for the first time when they were teenagers. The film first explores the question of why these three men were so similar but ends on asking why their lives turned out so differently. The classic “nature versus nurture” argument occupies much of the film’s focus, yet missing is much discussion of two recurring themes of this blog, probabilistic randomness and volition (“choice” or “free will”).

We tend to get hung up in trying to figure out the “destiny” apparently imposed on us by our genes and our upbringing, but in this post I want to add these two additional concepts into the “nature versus nurture” equation using a long-lived popular dice game as a model.

What is a model?

In math and science, a model is a simplification of a more complex reality. Think of a “model airplane,” for instance, a simple version of a real airplane. It is not a real airplane, but using the model, you could probably pick out the real one if you saw it. Sometimes models help us to better grasp the larger reality, and sometimes they get too confining in their simplicity. Our model airplane may or may not fly, and even if it does, it is likely accomplishing that in a much more basic mode than for the real airplane.

How does the model of probabilistic randomness, as explored in several of my earlier posts, and using the example of common games that use six-sided dice, mesh into the concept of human volition or choice, as explored in more recent posts, in determining the course of our lives? Well, let’s try another dice game as a new model, the popular game of Yahtzee®.

As noted earlier, simple games using one six-sided die illustrate uniform randomness (an equal chance of rolling one through six), while the addition of a second die adds a more complex probabilistic randomness (with a roll of seven much more likely to occur than the roll of a two). However, in the game Yahtzee®, introduced in the 1940s by Milton Bradley (and now owned by Hasbro), another level of complexity is added with its own possible analogue to our life experiences.

In this game, the player throws five dice at once, which instantly brings us up to 7,776 different possible dice combinations, the lowest totaling five (all ones, for one chance in 7,776) and the highest totaling 30 (with the same odds as rolling that five). The statistical mean (average) settles in over many throws at 17.5, although you can never actually throw a 17.5. [1]

But the critical difference comes next, as the player can select one or more of the dice to throw a second time to try to achieve a particular sequence, many of them similar to poker hands, say, four dice with the same value, or a “full house” (three of one value and two of another). And if failing that second time, the player can repeat the same process for a third try at achieving the goal, rolling one or more dice, and thus improving the odds of claiming the assigned game points for that achieving that target sequence.

Different Yahtzee sequences have different odds of occurring, and the odds change given the state of your dice after the first or second throws. Sometimes you have a better chance of achieving your goal than with other throws. Experienced players eventually develop a sense of (though rarely do they actually calculate) which combinations have the best odds given each current state.

We have now a concept I call probabilistic volition. That is, you get to exercise some choice in determining the future, but your choice does not guarantee a particular future outcome. You have only improved the odds of it occurring. By selecting the best set of dice to roll the second and third times, as well as selecting which sequence of dice you are trying to achieve, you are “nudging the odds” toward your preferred outcome.

This is, to extend our model into the real world, a way of thinking about what is happening when you step into your automobile and drive down the street. You have dozens of volitional ways at hand to drive more safely (or not). Practicing each of these “safe driving” techniques substantially lowers the probability (often by several orders of magnitude) that you will get into an accident, but there are still no guaranteed outcomes. [2]

While following all safe driving practices, and safely stopped at an intersection for a red traffic signal, it is possible, although with a very low probability, that an out-of-control ambulance could careen around the corner and aim right at your stopped car. That happened once to me many years ago, the careening ambulance seeming to randomly “select” my car from a dozen other stopped cars at the intersection. But much more likely, you will get home safely today, and most traffic accidents have some “unsafe driving” factor involved, such as excess speed, bad weather, alcohol. etc.

This is probabilistic volition at work. You “play the odds” every time you walk outside your door, but most people, most of the time, learn the lowest-risk ways to get through the day. Sometimes they don’t, and that may actually be why you walk this Earth today. Human conception itself is usually a process of probabilistic volition. [3]

The Yahtzee® model and determinism

In an earlier post I discussed hard determinism, the idea that there is no “free will” because all natural events, including human “choices,” are completely determined by previously existing “states of nature,” with each state preceded by an earlier state, walking all the way back to the beginning of the universe as we know it. Many philosophers and physicists make a strong case for this concept. Yet you and l (and even those philosophers and physicists) go through life every day assuming that “I have free will over most of my actions, and I choose to eat this chocolate doughnut right now!”

The compatibilist model of free will acknowledges some very basic deterministic realities. There is a sense, and a scale of existence, that determinism is undeniable. The seeds of the Earth’s eventual cosmic destruction have likely already been sown. This may be from an asteroid “with our name on it,” traveling through space on an eventual trajectory toward Earth. It may occur if our Sun goes into a supernova state. We just don’t know if that end is next year or a billion years from now. The young Alvy Singer, portrayed in the Woody Allen film Annie Hall, fretted about the expansion of the universe (see the video clip below), causing him to “lose hope.” And I hate to break it to you, but your own death will likely happen well before that point. Our bodies are “destined” to die.

But the compatibilist model leaves some room for human volition despite our fate. How does this “Yahtzee® choice model” come into play here?  You at least appear to have some measure of control over your destiny, and it so appears that you can often nudge the odds of good things and bad things happening to you, perhaps by several orders of magnitude. However, sometimes a lottery-level probability event comes from out of nowhere to bite you in the rear end. And what God has to do with it (or not) still remains a mystery. [4]

Whether that “appearance” of free will has a biological basis remains a topic of a subsequent post. The real-life “identical” triplet brothers in the film Three Identical Strangers had three very different “fates.” My contention is that, from the moment they emerged from the womb, “life was new each moment” for each child, with some events and apparent choices facing different “Yahtzee-odds” outcomes as compared with others. In the meantime, how do you think you can “nudge the odds” of events facing you today?



  1. The probability of throwing a 17 or an 18 through some combination when all dice are thrown is equal, at just over one in ten.
  2. An “order of magnitude” is usually defined as a power of ten. In other words, if you have reduced the odds of a traffic accident from one in 100 to one in 1000, then you have reduced your risk by an order of magnitude (which, in this case, is quite significant).
  3. For more on this idea, see this earlier post about the probabilities around your own conception.
  4. I started this blog looking at Albert Einstein’s contention that “God does not play dice.” Dr. Einstein and I have a debate over that statement in this early post.
  5. “Life is new each moment” is a concept from process philosophy, of which I only scratch the surface in this post.

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