The Birthday Paradox

The Birthday Paradox

May 23, 2025

Probability is a funny thing. Sometimes it squeezes the magic out of coincidence.

I remember sitting in class in a calculus course at Duke. There were 23 students in class. The professor bet us $1,000 that someone in the room shared a birthday with someone else. He promised he hadn’t looked at our birthdays beforehand.

365 days, 23 kids…sounds like fairly low odds, right?

Wrong. Turns out someone shared my birthday. Also, turns out the probability of two out of 23 people sharing a birthday is over 50%. He had stacked the deck in his favor. It also turns out that the probability of someone sharing a birthday is almost 100% with just 100 people…despite only 27% of the days in a year.

Probability can play mind games on us. And in the financial planning world, there are several instances I can think of that tend to trip up advisors and clients alike. We are going to talk about just one today.

It is a different kind of birthday effect. This mind game is about life expectancy.

The average life expectancy in the US according to the CDC is 77.5 years. Most people know that. When I start the financial planning process with clients, I tell them one of the most important things in the plan we need to estimate is how long they will need money for. In other words, we need to guess their life expectancy.

Some people are pretty quick to answer–others really aren’t sure what to say. Family longevity is often referenced, which is a good place to start. Sometimes health issues pop up, which can affect their guesses. Some of the more thoughtful folks ask me what I think they should estimate.

I tell them this: “For a married couple, husband and wife, who walk into this room who are currently 65 years old, there is a 50% chance at least one of you will live to at least 92.”1

Even more mind-blowing, you can take a couple who is 65 now, husband and wife who don’t smoke and are in good health, and there is a 1 in 4 chance one of them lives another 33 years. That is a 1 in 4 chance of someone living to at least 98 years old. This is from the Society of Actuaries, my friends.

What is going on? How can average life expectancy paint such a different picture?

Answer: probability. this is the 2-person version of that birthday paradox, in many ways. Be glad you don’t have 3 people in a marriage–the probabilistic implications look even crazier (though that would probably be the least of your problems).

There is more to it than this. Even people who are not married need to pay attention here. If you live to age 60 or 65, you have successfully avoided many of the accidents, tragedies, and poor life choices that bring US life expectancy down. Your prize: the grateful opportunity to pay for significantly more years of retirement. I semi-morbidly joke around that people with low life expectancies have the silver lining of worrying way less about running out of money. Interestingly enough, clients in that position actually laugh along with me (turns out they usually aren’t sensitive about the prospect of a shortened life, having come to terms with it long before meeting with me).

So what can we take away from this?

First, we are not that calculus professor I had: the stakes in financial planning are not betting students $1,000. Life expectancy is an average, and you don’t want to bet on living to the average. It is misleading and tells only a small part of the story–especially if you are married and/or in good health, planning to live to 77.5 is an easy way to run out of money long before you die. We have clients finishing marathons, traveling the world, and outpacing grandchildren at 77.5 years old. For even somewhat healthy people, you need to plan to live longer.

Second, we need to stress test: when we run financial plans with you, we run extra analyses to see what happens if you live another 5 or even 10 years. For some clients, it won’t matter–we have many clients with positive cash flows in retirement. For others, it may break the plan, in which case we may need to reduce withdrawal rates from investment accounts to ensure you don’t outlive your money.

That said, even those of you with positive cash flow no matter how long you live need to keep this in mind: you living an extra 5 or 10 years can also affect your estate planning. You may need to think about how to avoid paying estate taxes to the state (or even federal estate tax for those with really high net worth). You may need different estate documents to navigate that properly. If your net worth continues to compound an extra half decade or more, you could wind up paying an eye popping amount to the state rather than your cherished family and causes.

Third, be careful about your lifestyle. I am blessed to work with wonderful, caring, generous clients. Quite a few have family and friends, children and grandchildren, even parents they want

to help. That generosity can take the shape of Christmas presents or birthday gifts, or helping with a mortgage downpayment or weddings. Sometimes it is buying a house, car, college education, or fronting the cost to start a business. Other times they want to pay for medical expenses or long term care. These gifts can range from nominal to extravagant. The challenge is making sure you don’t overextend yourself—over-generosity is a difficult risk to plan for. Clients don’t want to let family down.

But when we do planning, we consider the other side of life expectancy. Your children probably don’t want to feel burdened by income shortfalls you might have when you are 85 because you gave too much earlier in life. There is a delicate balance to strike here. And perhaps one of the most common wishes I hear from clients is not wanting to be a burden to their family. Under-estimate how long your retirement may be and you certainly run that risk.

Last but not least, do not limit yourself to simple rules of thumb when it comes to withdrawal rates. You might hear that 4% or some other value is the “correct” amount you can spend per year of your portfolio and be fine. That is the beginning of the conversation, but certainly misleading if you don’t do the planning. In reality, clients spend different percentages each year. Some years you spend more, and others you spend less. The key is doing the planning so we can model it all and see if your means can sustain your goals. The devil is in the details.

We haven’t even mentioned anything that might come along and increase life expectancy over the next 20,30, or even 50+ years depending on your age. We do not want to ignore that: already we have many clients across Conestoga who have outlived their parents because their lifestyles and healthcare are dramatically better than prior generations could access. With all the technology and medical advances ahead of us, we almost certainly can expect improvements in the future.

While death comes for us all eventually, we have the privilege of living in a time when more and more people experience long, wonderful, rewarding, beautiful retirement lifestyles. Provided we don’t allow probability to hoodwink us, we can properly plan for sustainable, successful retirement living. We want you to look forward to, not dread, all those future birthdays.



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