Have you ever pondered any of these questions?

• Should I buy that airline ticket now or wait to see if the price will drop?
• Should I buy the extended warranty on my used car or risk possible repair costs?
• Should I buy a ticket for the lottery since the jackpot is very high?

Day after day we have to make decisions based on probabilities. Some choices are as simple as packing an umbrella when it’s an 80% chance of rain. Others are more complicated like how to invest retirement account money amongst many fund options. With the rise of prediction markets, more and more people are putting their money down on sports gambling without fully understanding the odds. Alas, many of those people are losing their bets because humans are very bad at understanding probability.

To learn more about the risks of sport betting, listen to the latest season of the excellent podcast, Against the Rules, from Michael Lewis. (Note – as much as the sports betting commercials try to sell you on it, think twice before betting a parlay!)

I explored the challenges we have with understanding probabilities in an article several years ago called Deal or No Deal, Mr Hall! – How We Misunderstand Probability The centerpiece of the article concerns a much-discussed probability puzzle called The Monty Hall Problem. Here is how the problem is described.

You are a contest on Let’s Make a Deal. Your game is to pick one of three doors. Behind one is a new car and behind the other two are goats. (For purposes of play assume you want the car.) Monty Hall invites you to pick a door, so let’s say you choose Door #1. Monty, who knows what is behind each door, opens Door #3 to reveal a goat. Then he gives you the opportunity to switch your choice to Door #2. The question: Are your chances of winning the car better, worse, or no different if you switch doors?

What is your answer?

To learn the right choice, please read the full article on the Efficient Librarian website. Just know in advance that even the smartest college professors got the logic wrong when they first pondered it!

If you are thinking The Monty Hall Problem is merely a fun little puzzle, know that the ramifications of logic errors in other aspects of our lives are significant. Failing to understand probabilities can lead to poor decisions. As I state in the article:

We face a whole host of probabilistic situations throughout our lives. For example, is it worthwhile to buy extended warranties on appliances? To make an informed decision we have to know the probability that the appliance will fail and the projected cost of an uncovered repair. How about the weather? The accuracy of a five-day forecast is much lower than tomorrow’s forecast. Yet we often treat the two forecasts with the same value. Is it a better investment to buy stock in a single company or purchase a market index fund? The truth is that individual stocks are statistically more volatile than a weighted market index, yet most of business articles focus on finding the next home run stock pick.

If you enjoyed reading about The Monty Hall Problem, then I invite you to explore the follow-up article focusing on the logic behind the game show, Deal or No Deal. In that piece, we learn the important lesson that possibilities are not probabilities!

Enjoy and good luck with your next decision!