Probability Survey & Report 2016

As part of our luck and probability series, we challenged 1,500 people across Britain to compare the odds of seven likely and unlikely events - 99.5% got it wrong.

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Does Britain have a probability problem?

As part of our luck and probability series, we challenged 1,500 people across Britain to compare the odds of seven likely and unlikely events - 99.5% got it wrong.

Read our full in-depth report below or skip to our Britain at Odds infographic.

What are the chances of a 100 year old, six-fingered saint getting a royal flush while skydiving?

Ok, that was a bit tough. What do you think your own chances are of living to 100?

Still not sure? What if we told you that a baby girl born today in Britain has a one in three chance (3/1) of reaching a century - would you be surprised?

While we may think we understand probability and odds, we often fall short when asked to quantify the chance of an event happening.

To test this, we asked 1,500 people across England, Scotland and Wales to compare the odds of seven unique events.

Just 0.5% of people answered correctly.

The events in question were:

  1. Dying in a British road accident this year
  2. Getting a royal flush in poker
  3. Being born with six fingers or toes
  4. Dying in a skydiving accident
  5. Getting a hole in one in golf
  6. Living to 100
  7. Being declared a saint

To ensure the consistency of answers, we chose dying in a British road accident as the control event, and asked people to select the remaining events that they believed were more likely to happen. Want to know the odds? Click here to scroll.

From their answers, we have been able to draw conclusions about how Britain understands probability as a whole and how people's perceptions of relative events varies by age, country and gender.

Below are the most significant insights from our probability survey. If you'd like to see what the results said about road safety specifically, please visit our road safety awareness report.

We have included comments from David J. Hand OBE, senior research investigator and emeritus professor of mathematics at Imperial College, London. He is also a non-executive director of the UK Statistics Authority and the author of The Improbability Principle. You can read our full interview with David Hand here.

Britain is terrible at judging probability

99.5% of Britons judge probability wrong

  • Just 1 in 188 people across England, Scotland and Wales have an accurate perception of probability
  • Only 0.5% of those surveyed correctly selected just the four more likely events from our list

The headline statistic from our survey is the almost complete failure of Britain to correctly judge probability.

But, while this figure is interesting, it doesn't offer any specific insight into why people's perceptions are so wrong.

We asked Professor Hand for his thoughts:

"I wasn’t surprised that the survey showed that so many people were unable to judge probabilities accurately. Mistakes typically occur when we are asked to judge something that we have no experience of or haven’t studied, but it also applies more generally to numbers in other contexts.

"We’re particularly bad at judging very low probabilities - obviously because we will have very little experience of such events. Indeed, the only rational thing is to treat events with very low probabilities as impossible."

It is clear that experience (or lack of) can be influential in determining a person's ability to perceive the likelihood of an event, but what other factors could be at play?

Here are a few of our own thoughts on what else might have affected how people answered our survey:

  • A respondent’s exposure to media / the recency and scale of a related news report
  • The recency of an event happening and a respondent being aware (ie. local paper reporting on amateur playing getting hole in one in weeks before)
  • A respondent’s quality of life, mental state and outlook on the future - optimistic vs pessimistic
  • A respondent’s lifestyle and hobbies - are they an active golfer, poker player, skydiver?
  • A respondent’s parental status - do parents perceive risks to be higher due to worrying about their children?

We hoped to uncover evidence of these influences when examining our data. And we did...

% of people who answered correctly
(selected just the four more likely events)

Correct - 0.5% (8/1500)
Incorrect - 99.5% (1,492/1,500)

Scottish people worse at judging probability than English

Scottish people are the worst at judging probability in Britain

  • Five times more English people answered our survey correctly than Scottish people
  • 11.6% more Scottish people wrongly selected none of the events as more likely than 36,000/1 than English people (6.8% more than Welsh)

Of everyone who completed our survey, it was the Scottish who were consistently the worst at perceiving probability. Not only did fewer Scottish people answer correctly than English or Welsh, but they also most excessively misjudged the relative chances of individual events.

However, it is important to consider the impact of the control event in Scottish responses. As we cover in more detail in our road safety awareness report, you are actually more likely to die as a result of your injuries as a road accident casualty in Scotland than anywhere else in Britain.

With this is mind, it is perhaps not surprising that many Scottish answers reflected an overestimation of road accident risk and consequently, a more general failure to judge probability. Would changing the control event to one which people were perhaps more positive about have changed the outcome?

It is possible that the negativity of the control event (a road accident) combined with the real additional danger of Scottish roads, could have influenced the pessimism of Scottish perceptions.

% of people who answered correctly, per country

England - 1% (5/500)
Wales - 0.4% (2/500)
Scotland - 0.2% (1/500)

Chance of being born with six fingers or toes - Polydactyly

88.3% of Britons underestimate the odds of polydactyly

  • The chance of a baby being born with an extra finger or toe (polydactyly) is just 500/1

Being born with an extra finger or toe is far more common than you might think. Worldwide, a child has a 1 in 500 chance of being born with an extra digit. Even in the UK, there is a 1 in 1,000 chance that a child will be born with polydactyly.

Only 11.7% of people surveyed selected being born with an extra finger or toe as more likely than 36,000/1, suggesting that the vast majority of the country (88.3%) believes the condition is at least 72 times less likely than it actually is.

What is polydactyly?

Polydactyly or polydactylism, also known as hyperdactyly, is a congenital physical anomaly in humans, dogs, and cats having supernumerary fingers or toes. Polydactyly is the opposite of oligodactyly (fewer fingers or toes). The condition can present itself on one or both hands. [Source: Wikipedia]

Odds of getting a royal flush - Texas Hold'em Poker

People underestimate their chances of being dealt a Royal Flush

  • 84% of Britons did not select being dealt the rarest hand in poker as a more likely event
  • English men are more optimistic about getting a royal flush than Scottish men

In Texas Hold'em poker, a royal flush is achieved when a player holds a run of an Ace, King, Queen, Jack and 10, of the same suit, from the seven cards available (two in hand, five in community).

A royal flush is the rarest hand in poker (there are only four possible combinations) and it guarantees victory for the player lucky enough to have it. The odds of being dealt a royal flush are 30,939/1 - 14% more likely than dying in a road accident and a common occurrence in poker games throughout the world - yet only 16% of those surveyed correctly identified this.

Could this be an example of people's experience determining perception? How many people from our survey knew what a royal flush was or had even played poker before answering our question? It seems likely that much of this misunderstanding was a result of limited exposure to the event in question.

The most unlikely royal flush ever?

In a game of the 2008 World Series of Poker, professional poker player, Justin Phillips held a royal flush, while opponent, Motoyuki Mabuchi, held quad aces (all four aces in the deck). The odds of this particular coincidence occurring have been calculated as 165 million to one! Read the full story (and watch the video) of the world's most unlikely royal flush.

Odds of getting a hole in one - Women more optimistic than men

Women are more optimistic about getting a hole-in-one than men

  • 3% more women (than men) correctly predicted the probability of scoring an ace
  • Younger people aged 18-34 are most positive about achieving a hole-in-one of all age groups

An amateur golfer has a 1 in 12,500 chance of scoring a hole-in-one, which is just under three times more likely than the odds of dying in a British road accident. Despite this, a huge 79% of Britons believe it is actually a less likely event. 

Our survey also revealed that 3% more women than men judged the chances correctly, with 22.7% selecting it as a more likely event, compared to just 19.7% of men. However, in a skill-based game such as golf, there are a number of ways you can positively influence the odds.

These include:

  • Your golfing experience and ability (handicap)
  • The length and difficulty of the course/hole being played
  • The weather and wind conditions

But, of course, understanding how you could swing the odds in your favour, requires a wider understanding of probability to begin with. We asked Professor David Hand how he thought this could affect a person's behaviour:

"I think that raising awareness of probability could affect how open people are to creating fortunate circumstances and luck. There are classic studies along these lines, showing that outgoing people tend to be luckier.

"In fact, of course, they are simply putting themselves in more situations and giving themselves more opportunities for good things to happen. Understanding how you can affect the odds can be empowering and motivational."

Are people limiting their opportunities and experiences by underestimating their chances of success? Could the country's probability problem be directly affecting the potential happiness of its population?

Stroke of luck: The man who scored three aces in one round

In 2015, amateur golfer, Patrick Wills, hit three holes-in-one in a single round, while playing in Virginia. Because of his ability, Patrick's odds of scoring one ace were lower at just 5,000/1, but not even he expected to do it three times. The odds? Over one trillion to one. Read more of Patrick's story here.

Odds of living to 100 in Britain

79% of Brits completely misjudge their chances of living to 100

  • Just 21% of people believe that the odds of living to 100 are less than 36,000/1
  • A child born today actually has up to a 3/1 chance of reaching a century

Living to 100 has never been more likely. A newborn girl has a one in three (33.7%) chance of becoming a centenarian, with a newborn boy’s chances slightly behind at 26%. In contrast, the odds of a current 65 year old reaching 100 are around one in 10.

Predictions released by the Office of National Statistics (ONS) in 2011, estimated that there will be over half a million people aged 100 or over in the UK by the year 2066.

Yet despite the optimism of the statistics, 78.9% of Britons surveyed did not select living to 100 as a more likely event than dying in a road accident (1,183 vs 1,500), with Scotland specifically underestimating the odds the most (83.6%).

Could the culture of a particular location cause this inconsistency in British perceptions?

"Culture can have an impact. For example, if you ask people to measure their level of wellbeing out of 10 in the West, you’ll get a basic level of around seven. In some other countries this basic level is lower. It’s influenced by cultures, religions and ways of life, and all of these can also affect a person’s perception of chance." - David Hand.

Living to 100 was the most likely event on our list by a significant margin. Is the country prepared for the impact of such widespread public misconception? With the pension crisis already a reality and an ageing population to support, could people's attitude to old age further compound the problems Britain faces?

% of people who didn’t select living to 100 as more likely, per country

Scotland - 83.6% (418/500)
Wales - 77.4% (387/500)
England - 75.6% (378/500)

Odds of dying in skydiving accident

Skydiving is almost three times safer than driving

  • 8.3% of Britons believe skydiving to be more dangerous than travelling by road
  • Skydiving is actually 2.8 times safer with odds of dying standing at 100,000/1

You are almost three times as likely to to die driving to work than if you parachuted into the office.

8.3% of those surveyed incorrectly selected dying in a skydiving accident as more likely than dying in a road accident. But, while this represents a portion of the population, the more significant statistic is that 91.7% of people actually recognised this, despite logic suggesting otherwise.

It is unlikely that all of these people had enough direct experience of skydiving to enable their more accurate judgement, so what else could be responsible?

Could it simply be because skydiving accidents are so rarely reported on by the media that when put up against a more common event such as a road accident, the comparative risk seems so much less?

It undoubtedly takes longer for 100,000 skydives to occur than it does for 100,000 road journeys, so not only is the event less likely, the probability is stretched over a much longer time-frame.

Also, the lack of skydiving experience may actually benefit the accuracy of people's perception if they are personalising the situation. Ie. Instead of judging the risk based on if they were to skydive, they judged the risk based on never intending to skydive, reducing their own odds from unlikely to impossible.

% of people who selected dying in a skydiving accident as more likely, per age group

18-34: 11.1%
35-54: 6.5%
55+: 6.8%

Odds of being declared a saint

5.7% of Brits completely overestimate their chances of becoming a saint

  • The odds of being declared a saint are 20 MILLION to one

Becoming a saint is the least likely event on our list by a considerable distance - it is 200 times less likely than dying in a skydiving accident and 555 times less likely than dying in a road accident.

In fact, your chances are so slim, they are equal to scoring 1,600 holes-in-one or getting 646 royal flushes, both of which would be truly miraculous in their own right.

But despite this, 5.7% of those surveyed (86 out of 1,500) selected ‘becoming a saint’ as more likely than dying in a road accident. That equates to one in every 17.4 people.

If they were right, there would be at least 1,777 saints living in Britain today. To put that into perspective, Pope John Paul II canonised just 482 saints, throughout his entire twenty-six-year reign.

Did you know? Despite the extremely long odds, you are actually over twice as likely to be declared a saint than you are to win the UK National Lottery, at odds of 45 million to one!

A chance to put things right?

Our survey has showed a complete failure of Britain to accurately judge the relative probability of independent events.

As we mentioned previously, there are a variety of factors that can influence and impair a person's ability to perceive chance, but our results indicate that people are mostly unable to account for these when asked to make a judgement.

We asked Professor David Hand whether he thought enough was being done to educate schoolchildren in probability:

“Getting people to have a gut feeling for chance can be done much better than it is at the moment. People aren’t getting enough maths education in general.

“Numeracy and quantitative skills are essential and influence many decisions in adult life. And they are becoming more and more important in the modern world. A sound grasp of chance and probability is increasingly important."

While misjudging the odds of some events may be trivial, not accounting for living longer or underestimating the risks of the road can have far more serious and permanent consequences.

How long before our luck runs out?

Think you would have answered correctly? Let us know in the comments.

Summary of odds

- Living to 100 - 3/1 (for a newborn girl) [1] [2]
- Being born with an extra digit - 500/1 [3] [4]
- Scoring a hole-in-one - 12,500/1 [5] [6]
- Being dealt a Royal Flush in Poker - 30,939/1 [7] [8]
- Dying in a road accident - 36,000/1 [9]
- Dying in a skydiving accident - 100,000/1 [10] [11] [12]
- Being declared a saint - 20,000,000/1 [13] [14]

Also in our probability series...

Our Britain at Odds survey is just one part of our wider content series on luck and probability. 

Follow the links below to see more.

- View our Britain at Odds summary [Infographic]
See what our survey said about British attitudes to road safety
View our Hazard Perceptions summary [Infographic]
Read our full interview with Professor David Hand
- Discover why the number 13 is considered unlucky



  1. ^ "How likely are you to live to 100?". The Guardian. August 2011.
  2. ^ "10 Surprising Clues You'll Live to 100".
  3. ^ "What Causes Polydactyly?". Bright Hub. August 2009.
  4. ^ "11 things more likely to happen than winning the Powerball jackpot". NBC News. November 2012.
  5. ^ "Want to know your odds for a hole-in-one?". Golf Digest. November 2013.
  6. ^ "What Are the Odds of Making a Hole-In-One?". June 2015.
  7. ^ "The odds of being dealt a royal flush". MindSports. December 2014.
  8. ^ "Beating the odds in poker".
  9. Number of UK road fatalities 2014 divided by Total population of the UK 2014
  10. ^ "What are the odds of dying while skydiving?".
  11. ^ "How skydiving works". HowStuffWorks
  12. ^ "Which risks of dying are worth taking?". Spencer Greenberg. October 2013.
  13. ^ "The odds are against you". Forbes. January 2016.
  14. ^ "What are the odds?". WCPO Cincinnati. March 2012.

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