The Zen of Yahtzee
What is Yahtzee
Summary of the rules of Yahtzee if you haven’t played
Yahtzee is a light hearted and quick game, including elements of both skill and chance. Within a few games, you can develop enough understanding to play reasonably well. Due to the large element of chance, it’s hard to invest too much of your ego in the game.
Recently, I spent some time writing a Yahtzee solver [1]. My solver isn’t very sophisticated, but it gave me some valuable insight into the game.
My baseline strategy (named “random”) was to generate random choices for each turn in the game, without any application of the relevant probabilities.
Next, I tried a strategy (named “all Yahtzee”) in which all decisions are made to maximize the chance of achieving a Yahtzee (all 5 dice matching) on each turn.
Finally, I tried a strategy (named “human-ish”) based on a precomputed table of the relevant probabilities and some heuristics that I typically use while playing.
The following table summarizes my results. I have also included the results for the optimal single player Yahtzee strategy developed by Tom Verhoeff [2].
| Strategy | Average Score |
|---|---|
| Random | 46.5 |
| All Yahtzee | 151.2 |
| Human-ish | 226.1 |
| Optimal | 254.6 |
As you can see, my strategy is not that bad!
What is Zen?
Here is the best encapsulation of the concept I can find from Alan Watts’ “What is Zen”.
“Truly there is nothing else — and never was anything else — except the present. There never will be anything but the present”
Living “in the moment” seems all well and good, and I do find some peace in moments where I can focus on my senses. However, for someone who spends most of his time trying to learn from the past and plan for the future, Zen is not an easy concept to wrap my head around. It does not seem practical to spend time living only in the present.
The Zen of Yahtzee
The main obstacle for me incorporating Zen ideas into my life is the worry that living solely in the moment is not sufficient for leading a life of meaning. I spend most of my time trying to use rationality to maximize my success at work, increase the quality of my relationships, and improve at my hobbies.
Yahtzee, while one of my less important hobbies, is probably the most Zen activity I engage in.
My Yahtzee strategy only requires considering the current state of the game and dice roll. I act on what seems right in the moment without much deliberation or worry about the future. The empirical results from my Yahtzee solver demonstrate that this in-the-moment strategy vastly outperforms the random strategy [3], and comes reasonably close to the performance of the optimal one.
Is it possible to export my attitude while playing Yahtzee to other facets of life? Are there other areas where simply taking the next best step, right now, leads to a perfectly acceptable outcome? I think it’s easy to overestimate how much control we actually have over how life unfolds, and worrying has no more value than hoping for a Yahtzee on your next roll.
[1] I’ll open source the solver, which is essentially a table of probabilities and a few SQL queries, soon.
[2] http://www-set.win.tue.nl/~wstomv/misc/yahtzee/trivia.html
[3] Nihilism?