Let’s calculate the probabilities of the septuagenarian presidential candidates making it through a full term or being diagnosed with dementia. The probabilities are expressed as rolls of the dice.

Regardless of who wins the 2020 election, America may soon have its oldest president ever. Ronald Reagan currently holds the record at 77 years, 349 days, but Joe Biden will pass that mark two weeks before the election. If Donald Trump wins re-election and serves his full second term, he’ll reach that milestone in 2024, his final year in office. 

The age of the candidates has raised questions. Will the next president live long enough to finish his term? Will he remain fit enough to see out a full term? After all, it’s a physically and mentally demanding job. Jimmy Carter claimed that by the age of 80, he would have been unable to carry out the duties of the Oval Office. So, what are the chances that the next president will be able to cope for the full four years? 

To find out, consider two probabilities. First comes the question of whether the next president will survive a full term. Second, assuming he does survive, will he have the capacity to carry out the duties of the office for four years. Luckbox doesn’t have access to the full medical history of either candidate, so let’s simply consider both candidates representative of other men their age. 

Term limits?

Of the eight presidents who have died in office, four did not die of natural causes. They were assassinated. Security may have tightened in modern times, but some degree of risk inevitably remains. And the president is still disproportionately exposed to several other sources of risk, such as a helicopter accident, as an inevitable consequence of an unusually busy schedule. Nonetheless, let’s assume the main threat to presidential life expectancy comes from a medical condition and not the risks of the office. 

A 75-year-old American male, as Trump will be in 2021, has a one in 30 risk of dying in a given year. For Biden, who’s slightly older, annual risk increases to one in 20. The cumulative risk of death during the four-year term works out to be around 15% for Trump and 19% for Biden.

These figures (which are both one-die risks ) contrast sharply with that faced by Barack Obama when he took office, which was only around 2% (a two-dice risk ). 

Mental acuity

The greater concern is perhaps not whether the president will survive the full term but whether he will retain his mental faculties—whether he will remain the same person the public saw on the campaign trail and in the televised debates. If the president’s ability to think and act rationally is compromised by aging, it could pose a significant risk to national security. 

One of the major causes of decline in mental capacity is dementia, a neurological disease that disproportionately affects older people. In the United States, approximately 7% of those over 65, and around 17% of those over the age of 80 are believed to have the condition. What do those figures mean for the next president?

Let’s estimate the probability that someone will become symptomatic over a four-year period. That’s calculated by looking at how the incidence of dementia changes with age and tells how many cases emerge as people get older. Men are at a slightly lower risk of dementia than women of the same age, so the projection should take gender imbalance into account. The cumulative risk that the president will develop dementia within a four-year term is approximately 5% for Trump and 7% for Biden.

But dementia is not the only neurological risk they face. Mild cognitive impairment (MCI) is a condition with a similar level of prevalence. While MCI does not adversely affect daily life to the extent dementia does, its symptoms of loss of memory or concentration may mean that carrying out presidential duties is too much to ask. The chances of the president becoming unfit to serve because of cognitive decline in the next term are in the region of 10%-15%.

Decline and death 

The probability that the president will die or suffer cognitive decline is a combination of the 15%/19% mortality risk for Trump/Biden, and their 10%/15% cognitive risk. Simply adding the cognitive and mortality numbers together would be an overestimate. Still, it’s reasonable to estimate the chances of an incomplete term in office at around 23% for Trump and 30% for Biden—almost twice the chance of throwing a single six. 

Because of the significant chance that either candidate will fail to see out a full term in office—10 times higher than with Obama—their running mates may be subject to closer scrutiny than the public usually exercises with vice-presidential candidates. While the vice president has had to step in to take power on nine occasions, it hasn’t happened since Gerald Ford took over for Richard Nixon in 1974. But will there be a President Mike Pence or a President Kamala Harris within the next few years? 

First woman president?

Despite the media focus on Trump and Biden, the chances that America will soon see its first female president have rarely been higher. Given a 60% chance of Biden winning the election, coupled with an estimated 30% chance of stepping down during his first term, suggests the odds of Harris being sworn into office before 2025 are as high as 4-1. Meanwhile, the odds of President Pence taking office before 2025 currently sit at around 10-1. 

Throwing bones 

What are the chances they all land on a six? Well, with two dice, the chance of that happening is just one in 36, or 2.8%. Roll more dice at the same time, and the numbers rise quickly. With six dice, the chance of rolling all sixes rises to a little over one in 50,000.

For simplicity, let’s refer to levels of risk in terms of “two-dice risk” and “six-dice risk.” Note that the risk of throwing six dice is much lower and hence safer than throwing just two. The more dice, the safer it becomes.

Fergus Simpson, Ph.D., a machine-learning researcher from Scotland, focuses on probabilistic models and information theory at Prowler.io, a business-decision platform. @frgsimpson