The Perils of Probability – The Monty Hall Problem

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?

Monty Hall - Game Show Host, from ABC TV
Monty Hall – Past Host of Let’s Make a Deal.

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!

Shelf Promotion – Branding for Librarians

Do you have a personal brand?

You can be forgiven for believing that branding is the sole domain of businesses selling a wonder product or influencers marketing themselves in the quest to obtain millions of followers. However, personal branding is not restricted to large companies or individuals with lofty online dreams. Developing a personal brand is a practical approach that any professional can take to advance their career and expand their network.

This week at the Florida Library Association conference, I am presenting a breakout session titled, Shelf-Promotion: Crafting Your Brand in the Digital Age. The session will outline a non-influencer approach to developing a personal brand. Below is the description in the conference agenda.

Building a brand is not just for influencers. Professionals of all types benefit from creating an engaging online presence to drive their career. This interactive workshop provides practical tools and a personalized action plan to confidently build an authentic, effective brand while maintaining professional boundaries. Presented by the Efficient Librarian.

Laptop displaying Alex Chen creative director branding alongside matching notebook, business cards, mug, and stamp on wooden desk
Image created with WordPress AI.

In the breakout session, I’ll guide participants through a simple series of steps to create the foundation of their brand. One concept that will be shared is known as “Skill Stacking.” Here is how the website, Indeed, defines it.

Skill stacking is the concept that individuals can make themselves more valuable by gaining a wide range of skills instead of pursuing one skill or talent. Try pursuing complementary skills that may support each other and create a unique new set of skills. Doing so can offer a more realistic path to success and may provide more professional opportunities in various fields.

In my case with the Efficient Librarian, I have matched the skills of productivity, leadership, and librarianship together to forge my unique brand.

Go ahead and try this for yourself. Make a list of all the skills you are good at and enjoy doing. The trick is you don’t need to excel at any one of them. A high level of competency is good enough. Review the list and then match together skills that complement each other as the basis of your brand.

To learn more about creating a personal brand, please attend the Florida Library Association conference in Orlando this week. I hope to see you there.

On the Town in the Palm Beaches

Media Alert!

In the most recent episode of On the Town in the Palm Beaches with Frank Licari, I was interviewed while showing off the new Canyon Branch library. In case you are not familiar with the series, On the Town takes viewers through a series of unique local points of interest in Palm Beach County. The host, Frank Licari, is a pleasant and engaging guide who takes the viewer on a whirlwind tour of fascinating places, events, and people in the Palm Beaches.

The library hosted Frank and the South Florida PBS team at Canyon Branch earlier this year. During the visit, I highlighted how libraries have become important community hubs and undergo constant change to match the needs of our residents. We toured the new library branch, with stops in our Children’s area, front reading room, and creation/maker spaces. A highlight for Frank was using our sorting machines for library item returns.

The segment is second on the episode after a tour of the new Canyon District Park. If you live in Palm Beach County or close by, I invite you to visit the Canyon Town Center to experience both the library and the park. It is well worth the visit.

Thank you to our friends at South Florida PBS and Frank Licari for being wonderful community partners by highlighting the library in their latest episode.

How Libraries Make Life More Affordable and Why It Matters More Than Ever

Are you worried about affordability? Nowadays many people are concerned about inflated costs for life’s necessities as pay checks fail to grow. What can be done to help those caught in this financial crunch?

I recently posted a new article to highlight the important role that libraries have in the affordability crisis. Based on a Medium post authored by a group called Reimagining the Civic Commons, I highlight five distinct ways that libraries help make life more affordable for communities. Here’s the opening of the article.


With gas, housing, and food costs rising, affordability is on everyone’s mind. Yet, in the quest to save money, is the solution to invest in our social infrastructure? In the April 2026 article 5 Ways Public Spaces Make Everyday Life More Affordable, the writers at Reimagining the Civic Commons reframe that conversation by highlighting how shared spaces like parks, community centers, and libraries reduce household costs in meaningful and often overlooked ways.

Photo by cottonbro studio on Pexels.com

If you’re a lifelong library lover, this won’t come as a surprise. The article explicitly positions public spaces as shared infrastructure that helps families navigate financial pressure and improve quality of life at limited expense. Let’s break down what that really means.

1) Libraries Are Cost-Avoidance Engines

When Reimagining the Civic Commons notes that public spaces can “meaningfully lower the cost of living,” it’s recognizing how much households save when they don’t have to buy what can instead be borrowed. Think about the resources available with a library card: books, movies, digital subscriptions, databases, and even streaming. These are items most families would otherwise purchase, subscribe, or have to go without if libraries did not exist. This is affordability in action by avoiding expenses before they ever occur.

2) Libraries Expand the Idea of “Access”

One of the article’s strongest insights is around shared assets. These are things households don’t need to own because they’re available in the public realm. Many libraries operate a “libraries of things” where residents can check out tools, equipment, and technology. This saves a household from buying and storing items used only occasionally. Another example are the Birding Backpacks at the Palm Beach County Library System. Accessibility is an essential element of affordability.


Discover the other three ways that libraries help with affordability, along with the name of a great book that explains the concept in further detail, by reading the rest of the article.

Make 2026 the Year to Rediscover Reading

Are you ready to Rediscover Reading?

Below is a copy of my recent op-ed in the Palm Beach Post encouraging people to take part in the new Rediscover Reading.

Rediscover Reading helps locals realize the benefits of books

When was the last time you read a book for sheer enjoyment?

If you are like most people, it has been a while since you cracked open a novel. You may think that reading for pleasure is simply one entertainment option out of many. However, reading for pleasure is more than a possible pastime. It’s a story driven public-health prescription. That’s the rationale behind the Palm Beach County Library System’s 2026 yearlong initiative, Rediscover Reading.

As our communities wrestle with loneliness and frayed social ties, returning to pleasure reading, and the libraries that sustain it, offers an affordable, evidence-based path to improve lives. The scale of the challenge is striking. A 2025 study of more than 230,000 Americans found the reading for pleasure dropped from 28% in 2003 to just 16% in 2023. That decline isn’t just a worry for the publishing industry. It has public-wellness concerns. When a large part of the population stops reading for pleasure, we lose a simple, low-barrier route to better mental health.

A growing body of research finds that reading for pleasure delivers measurable benefits such as reduced stress, better sleep, enhanced empathy and improved cognitive well-being. At the same time, shared reading like book clubs and read-aloud sessions activate regions in our brains tied to social cognition and emotional connection. This helps counter feelings of isolation and distrust.

That’s where Rediscover Reading comes in. The Library is inviting Palm Beach County residents to pick up a favorite book, sample a new novel, and set a reading goal for the year. What would happen if we all committed to reading one book a month? How much more restful would we feel by exchanging 15 minutes of mindless scrolling before bed with the narrative delight of a story? The sense of wonder, escape or solace found in the written word can bring peace of mind, greater life satisfaction, and a more empathetic understanding of the world.

Reading for pleasure combines the best of both worlds: the private delight of losing yourself in a narrative and the social lift from shared reflection. Libraries, with our welcoming spaces and community activities, transform solitary reading into a communal experience. As research suggests, the path to improved well-being doesn’t require expensive interventions. Instead all we need is a book in hand and a comfy spot to read it.

The invitation is extended. Dust off that old beloved title or pick up a new bestseller, be it a physical book, e-book or audiobook. Rediscover Reading isn’t just about books. It’s about opening your mind to a world of unlimited possibilities through the simple, but powerful ritual of reading for pleasure.

Grab your library card and visit your local branch of the Palm Beach County Library System or a municipal library to access free materials. Check out free e-books and e-audiobooks online through our website: www.pbclibrary.org.

This year, reclaim the joy of literature as a daily act of self-care and community building. Join us as we invite you to Rediscover Reading.

Libraries are at the Heart of the Reading Ecosystem

When I say libraries, what is the first thing to come to mind?

It was probably books.

The purpose of libraries for thousands of years was to collect and preserve the written word. Of course, having books alone is not enough without people who know how to read them. That is why libraries have always strived to expand literacy. This is especially true today, even in the digital age.

Brooks Rainwater, CEO of the Urban Libraries Council, understands the important role that public libraries play in expanding literacy. In a recent article on the EdTrust website called Libraries are at the Heart of the Reading Ecosystem, Rainwater shares how libraries are important to literacy while at the same time facing a very challenging environment.

Without public libraries, it is much harder to solve the problem of illiteracy. At a time when only 31% of U.S. fourth graders are reading proficiently, a continuing downward trend from previous years, it is especially worrying that public libraries — critical to helping children and their families begin the important process of reading and writing fluently to gain on-grade skills — are under attack.

Rainwater stresses how libraries play a bigger role in our communities beyond just acquiring books.

Libraries are more than just passive repositories of books; they are indispensable neighborhood resources. Libraries are learning hubs at the very heart of community literacy, anchor spaces providing essential support to our youngest readers and their families, teachers, and other literacy providers, helping to build out a strong “literacy ecosystem” across communities.

From his leadership position at one of the largest library organizations in North America, Rainwater understands the challenges and knows how libraries are making a difference in their communities.

I am the president and CEO of the Urban Libraries Council (ULC), an organization dedicated to strengthening and advancing the essential role of public libraries as dynamic, accessible places for opportunity, learning and innovation. I’m proud to say that, despite the challenging environment we are in, our member libraries are still stepping up to meet the needs of our developing readers and their families in numerous ways that are aligned to all that we know about how young brains learn to read. 

To learn more about how libraries support literacy, please read the full article.

How People are Really Using ChatGPT

Are you concerned that AI is coming for your job?

Since it exploded onto the scene in 2022, ChatGPT and its AI cousins have created a sensation. Aspects of knowledge work that were always assumed to be the province of humans can now be done in mere moments with the proper prompt. This has led many prognosticators to assume that AI will take over all white-collar work. After three years of these AI tools, what is the actual truth?

A recent post from Daniel Pfeiffer on the website Choice360 sheds light on what people are actually doing with ChatGPT. In a review of a study of 1 million conversations, Pfeiffer discovered that the assumed absorption of knowledge work by AI tools is not what it seems. For starters, more people are using ChatGPT outside of work than at the office.

One of the key takeaways from this report is that, though work-related usages of ChatGPT continue to grow, they are wildly outpaced by nonwork-related usages, which have grown from 53 to 73 percent of all ChatGPT messages. This finding raises two important questions: Given its ostensible economic promises, why isn’t work-related usage growing faster, and why is nonwork usage growing so much? 

Pfeiffer speculates that the clean AI interface has become preferable for regular searching than the messier Google page. The results are also easier for the average person to interpret, saving them time previously used to click through to other websites.

Another assumption is that most people are using ChatGPT to write the original copy of documents. However, actual use appears to be different.

Given the prized role of writing in educational environments, many academics might assume that when people use ChatGPT “for writing,” they’re using it specifically to generate new text from scratch—hence, the return of blue books. What this report finds, however, is that about two-thirds of all writing tasks have ChatGPT modify existing text, e.g., editing it for errors, adjusting the tone, or offering critiques, rather than generating new text. 

On closer inspection, Pfeifer wonders if this finding holds for all types of users.

As we await more data, I think it behooves us to keep in mind that “writing” encompasses a range of activities. While we might imagine that students are asking ChatGPT to “write a seven-page essay on the Civil War,” for instance, they might well be using it to “make this email sound more professional.” 

Image generated with WordPress AI

A third issue considered in the study is the economic impact of generative AI on workers. The media discussion often assumes that AI will take away jobs, especially lower-level knowledge work. Again, that may not be the case yet.

To get a more granular picture, researchers ran all the work-related messages through a different taxonomy based on common work activities, e.g., communicating with supervisors, scheduling events, and training others. They found that 57.9 percent of work-related messages fell into two broad categories “1) obtaining, documenting, and interpreting information; and 2) making decisions, giving advice, solving problems, and thinking creatively”. In other words, people are using ChatGPT less as a replacement worker and more as an advisor and research assistant. 

Reflecting on this finding, Pfieffer comes to this conclusion.

“ChatGPT likely improves worker output by providing decision support, which is especially important in knowledge-intensive jobs where productivity is increasing in the quality of decision-making.”  

Finally, Pfieffer speculates on the impact of hallucinations. As librarians have long complained, it is easy for people to believe what AI says rather than confirm that it is true. The study does not measure the effect of wrong information on people’s productivity and decisions.

The full blog post is worth a read. You can find it on the Choice360 website.

Supporting Florida Libraries

This week I am sharing an important message from the American Library Association in support of Florida Libraries. Please consider offering your support to ensure that the Florida Library Association is able to continue its mission of connecting libraries and library staff across the state.


Imagine a Florida without libraries—no story times, no safe study spaces, no free access to books, technology, or community programs. That’s the future our colleagues at the Florida Library Association (FLA) are working hard to prevent.

FLA has been a steadfast advocate for libraries across your state, but today, they need your help. Like many organizations, FLA has faced serious financial challenges in the wake of the COVID-19 pandemic. While their recent conference in Orlando was a success, they continue to face declining membership and the loss of key funding sources, including Library Services and Technology Act grants (through the Institute of Museum and Library Services).

Yet, we remain hopeful—and they remain active. In the past year alone, FLA:

  • Successfully lobbied against the “Material Harmful to Minors” legislation
  • Secured full base funding for Public Library State Aid
  • Achieved a 25% increase in funding for library cooperatives
  • Hosted a dynamic and educational 2025 conference
  • Made membership more affordable and accessible

Now, on behalf of our friends at FLA, we’re asking for your support to keep their momentum going.

📚 Donate: Every dollar helps them continue our collective mission to support and advocate for Florida’s libraries.
📚 Join or Renew: Personal memberships are 50% off through December—there’s never been a better time to get involved.
📚 Share: Help them spread the word by forwarding this message to your colleagues, friends, and family and posting to social media.

Donate to the Florida Library Association

Your contribution will help ensure that libraries remain strong, inclusive, and essential to every Florida community. 

On behalf of their friends at ALA’s Public Policy and Advocacy office, thank you for showing up for the Florida Library Association.

Warm regards,

Lisa R. Varga, MLS
Associate Executive Director, Public Policy & Advocacy

Can ChatGPT Write a Speech Better Than a Toastmaster?

Just say you need to give an important speech, but only have a few minutes notice. Can an AI chat service bail you out?

For my upcoming Toastmasters meeting, I was challenged to write a speech titled, “AI – Friend, Foe, or Tool?” As a fun experiment, I decided to see what ChatGPT would do with this topic. Would it be honest about its limits, share it deep dark secrets, or in the end just give me an okay speech.

Created with WordPress AI Image Tool

On the Efficient Librarian website, I wrote an article showing the prompts and output from this process. For reference I used a free ChatGPT account, which still provided enough access for delivery of a speech, but a few limitations on its output options. The whole process took less than five minutes from start to finish.

Overall, this quick dip into the AI waters showed that for all its versatility there are still some weaknesses. For example, I asked for a 5 to 7 minutes speech, but what was provided took only four minutes to speak. Also, it ran into some issues with suggestions that in the end I couldn’t do with the free service.

To see the entire process and read my other thoughts on this AI exercise, please read the article on the Efficient Librarian website.