Learning risk management by playing a game

Updated: Feb 22

Jeff Hulett, November 6, 2020

I’ve often thought of backgammon as one of my best risk management teachers.

Backgammon is deceptively simple. While the rules are simple, the application of probability and risk management principles are what makes the game very interesting. Also, game success isn’t just about applying probabilistic knowledge*. Game success is also about understanding how to hedge positions and how to manage your risk of ruin. Long term winning strategies include emotional control, like control of greed, fear and pride. Also, long term winning strategies include knowing when to take a small game loss to protect yourself from ruin and to maximize match winnings. Backgammon helps one think about the difference between ergodic and non ergodic systems. Meaning, one can play a probabilistically “perfect” game and still lose big. Backgammon, as in life, has some elements of both systems. Understanding the relative ergodicity of the game and the dynamics between both systems is helpful. See heuristic 7 below for an example.

Also, backgammon has elements of a classic dynamical (chaotic) system, subject to higher sensitivity to initial conditions. (I.e., the butterfly effect) My ability to forecast whether I will win or lose increases significantly after the initial 5 to 10 moves. Why? There are 2 distinct chaotic system analogues.

  1. Each die roll outcome is not linearly related to the incoming information. By definition, a roll outcome is random and with no relationship to the opponent's last move. (energy independence)

  2. Future moves have a high degree of influence from previous moves. That is, feedback (or recurrency) is endemic to backgammon, like most games. (decision information dependence) As such, positioning myself in the initial stages of the game is important for determining the game outcome.

Below are several good backgammon heuristics provided by Bilal Bach, I found on his blog post. I do appreciate his reference to Taleb:

  1. When to hedge a position in an opponent's territory for protection, even though you have the dice and luck to advance a fortified position: Hedging and taking defense.

  2. When to open up a position to be vulnerable for a calculated valuable potential outcome: When to take a risk.

  3. Choosing which vulnerable position to open up when you must. Minimizing what can hurt you most long term: Risk management, as you choose among different alternatives.

  4. When and where to fortify a position: Timing.

  5. When to add on an established fortified position instead of taking other choices: Risk aversion, saying “no”, and perhaps, averaging out.

  6. When to open up a position as a bait. As Nassim Taleb says, “It is a very powerful manipulation to let others win the small battles.”

  7. When to drop an unnecessary risk: Probability of ruin. When one of your blots go bust, it will have to restart from scratch. If a black swan occurs and your investments plunge 50%, you will need to make 100% to go back to even.

  8. When to make use of an opportunity and/or good luck.

  9. When to drop a ‘lucrative’ opportunity if the risk/reward is concave.

  10. When to delay taking the checkers out while winning to decrease the risk of having a vulnerable position or going bust due to the randomness of the other player’s dice. Perhaps this translates to delaying gratification and profit taking at the same time.

  11. With the doubling cube introduced, one has to learn when to take a loss, and resign a game for the sake of the match.

  12. No matter how skillful I’d think I am, a beginner could always get to humble me. “No matter how sophisticated our choices, how good we are at dominating the odds, randomness will have the last word” as Taleb puts it.

Finally, Einstein’s suggestion to honor the intuitive mind is certainly relevant to backgammon and risk management.

"The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift."

For backgammon, our "faithful servant" applies probability, the "sacred gift" provides for long term winning strategies. Both are necessary for backgammon success!

2 dice probability
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