Decision Theory: Simulating Decisions

This is part 5 of our series on Decision Theory, previous segments are available in our archives.

Gambling Can Be Good

Even with the tools we have discussed this week, it can still be hard to make tough decisions. If your decision tree has a lot of uncertainty or your expected values are hard to predict even these frameworks can offer little aid.

The good news is that you can cheat! You can run through the same decision thousands of times and see how it turns out before you make your decision for real. That process is called a Monte Carlo simulation, which uses software to simulate making the same decision many times and, using the probabilities you provide, determines the outcomes. By studying the outcomes across so many tests, you can understand the most likely outcomes and use that as part of your decision making.

For example, let us return to our decision about whether to buy a lottery ticket. Remember, the ticket cost $1 and the payout for winning is $100M, but the chances of winning are only 1 out of 175M. What if that same ticket also provided a 1 in 20 chance of winning $5 and a 1 in 50 chance of winning $20? How do we make the decision then?

For this simple of an example, we could calculate the expected values directly, but for fun, I ran a Monte Carlo simulation, which generated the following winning outcomes:


I ran the simulation 500 times, of which I made nothing 467 times, $5 15 times, $20 16 times and, sadly, $100M 0 times. The mean outcome was winning $0.79 – still less than the price of the ticket!

However, considering the probabilities involved in this simulation 500 times is probably not enough to have a consistent result. As with any probability simulation, the more times you run it the more your resulting distribution of results will reflect the true probabilities so always run it as many times as possible.  I re-ran this same simulation another 500 times and got a mean value of $0.54 which is vastly different! This highlights the dangers of this kind of approach, where you need to use the results as guidance but not fact since there is so much variability in the results.

To Review: We’ve covered the basics of decision theory this week, including how to visualize decisions to ensure you capture all possible choices and outcomes (decision models and trees) and account for uncertainty in the outcomes (expected values). I hope this gives you a start in approaching your decisions in a systematic way that will help you make better decisions!

Next Week: All of the decisions we have covered this week assume you are the only one making the decisions. But what happens when your decisions will affect others and their decisions will affect you, such in a negotiation? Game Theory comes to our rescue by helping us understand how to make decisions when we have opponents (or teammates) making decisions at the same time.  

Quote of the Day: “The gambling known as business looks with austere disfavor upon the business known as gambling.” ― Ambrose Bierce