Some of the kinds of things successful people often say are: "I've got to where I am because I’ve made my own luck” or “The harder I work, the luckier I get!” This is a way of saying it’s not because of luck that they got to where they are. It’s because of their own abilities, hard work and determination. This suggests we control our lives and what happens to us is entirely a matter of choice not chance. 

But we can’t choose where we’re born or who we’re born to. That is entirely random. Most of us probably agree that it’s, say, bad luck to be born in a refugee camp or a country torn apart by civil war. But it’s good fortune to be born in a stable, developed country where we can take food, shelter, clean running water, access to good healthcare and security for granted. 

Can someone ever be lucky in a car accident?

Suppose you’re in a car accident and you live - are you lucky for surviving or unlucky to be in an accident in the first place? How you view this may depend on what sort of person you are and the stories you tell about yourself e.g. “that’s just my luck!” or “I had a lucky escape there”. How you see this could be affected by previous life experiences - what makes you who you are, says Paul Russell, Professor of Philosophy at the University of British Columbia. How do you think you might feel?

In a podcast for the Philosophy Bites website, Paul Russell talks about what philosophers call consequential (or moral) luck. If someone drinks over the alcohol limit then drives home and nothing happens, this is known as consequential/moral luck. They did a bad thing but got away with it. But if they’d had an accident because their driving was badly affected and they killed a child, they would be responsible. After all they chose to drive while drunk. It wasn’t bad luck, it was a bad choice. And the child who died was very unlucky to be in the wrong place at the wrong time. It was a random event that the child unfortunately had no control over. This is an example of how external events outside our control may affect us.

So what is luck exactly?

What do we mean when we talk about luck and how does this differ from fate and destiny? The Oxford English Dictionary defines luck as the chance occurrence of situations or events that are either favourable or unfavourable to a person's interests. The word used before luck often indicates the type of luck referred to. So bad luck, good luck, hard luck, ill luck, pot luck, rotten luck and tough luck. Can you think of anymore?

How does fate differ from luck?

Fate has its roots in Greek and Roman mythology - originating from the Latin 'fata' which means a prediction. It’s the belief, according to some philosophical thought, that all or some events are unchangeable and predetermined. So your life is set by fate and you have no control over it. If something is meant to be, it will happen. “Let’s leave it all to fate,” you might say. But is this giving away responsibility for your life choices?

Is this your destiny?

Destiny is very similar to fate - it’s what is meant to be. So a professional sportsman or woman might say it’s their destiny to win top titles and a singer might say the same for headlining Glastonbury or topping the charts. Your destiny is where fate takes you. 

Is it better to be lucky or rich?

When we talk about luck, we might think about gambling. Some types of gambling involve an element of skill or knowledge such as playing poker or picking winning horses (you might study the horses’ form beforehand). But winning the lottery is down to pure chance. The phrase, “I feel lucky,” is often used by gamblers when placing a bet. They know for all their knowledge about horses and cards, luck is what they most need to win. And so luck is highly valued by gamblers as it can quickly bring further success.

Luck is at the centre of D.H. Lawrence’s short story, and modern fable, ‘The Rocking Horse Winner’. The story poses the question - is it better to be lucky than rich? The hero, a young boy called Paul, knows his mother, Hester, has big money worries. She explains, “If you're lucky you have money. That's why it's better to be born lucky than rich. If you're rich, you may lose your money. But if you're lucky, you will always get more money.”

The boy on the rocking horse 

Hester says she has no luck. But she’s beautiful, happily married and has three lovely children. However, because she never has enough money, she says she’s unlucky. In the walls of the house where they live, Paul hears a constant whisper: “There must be more money.”

When Paul is given a rocking horse for Christmas, he discovers, by chance, that if he rides it frantically a strange power comes over him and he can see the names of winners in horse races. His uncle, Oscar, gives him money and places bets on his behalf. Paul gives his winnings to his mother, pleased that he can help her pay her debts and buy all the nice things she wants. But he falters when trying to “see” who will win The Derby, one of the biggest and most important races. (And one that attracts a great of betting). He keeps riding his rocking horse, going all night long till the name of the winning horse finally comes to him. The horse wins, making a fortune for his family. But Paul dies from a fit at the end. What point do you think the author may be trying to make here? 

Are you lucky?

The phrase, “born under a lucky star” is often used about people who seem to have good fortune in life. Yet, what can look like luck on the outside may be due to other factors such as hard work and study. Some people prefer to put their successes down to luck in the hope they don’t come across as boastful. “Oh I was just lucky,” they might say or “I happened to be in the right place at the right time.” This is what’s called perception - how you view the world. What do you think - do you take responsibility for your successes and failures or put it all down to chance?
 

Maths uses numbers and mathematical ideas to make sense of chance.

Let’s look at some examples…

The birthday problem 

Suppose there’s a classroom full of students. What's the chances (or probability) that there are two people with the same birthday? 

Maths forces us to make the following assumptions:
1.    there are only 365 days in a year (for simplicity, let’s ignore leap years)
2.    all birthdays are equally likely and independent of each other (no-one’s birthday can affect another person’s)

With this in mind, the Laws of probability tell us that we need just 23 students to have a 50% chance that two of them will share a birthday. This number is very small and proved pretty surprising to some. So surprising that they have doubted that it is true at all. According to Geoffrey Grimmett, Professor of Mathematical Statistics (University of Cambridge) one talk show host denied this theory that 'he had asked an audience of 100 people whether anyone had the same birthday as him, and the answer was "no".

Can you see where the talk-show host has gone wrong in his understanding of the birthday problem?

…Got it?!... The host was asking a completely different question. The number of people required for there to be someone who shared his birthday is a whopping 253, which is 2.5 times the number of people present in his show. And so - from a mathematical point of view – it’s no surprise that no-one had the same birthday as him in an audience of 100! It would’ve been a lot more surprising if no-one in the audience shared a birthday with one or more other people.

The law of averages and the law of large numbers

The 'law' of averages and mathematical law of large numbers share some similarities but also look at things in slightly different ways. In fact, the law of averages is not a mathematical law at all. It’s more of a simple expression of wishful thinking. So - for example - it says that if I toss a fair coin six times and get heads over and over again, then it’s more likely that the seventh toss will show a tail. Somehow things will balance themselves out. 

This is, of course, false- at any stage in the tossing of a fair coin, the chance of getting a head is the same as the chance of getting a tail (50/50). What’s more, maths tells us that you can have a stretch of heads or tails of any length. 

The law of averages is often referred to in gambling, where it’s suggested that a long run of bad luck must end sooner or later. It’s often used to encourage people to continue gambling even as they’re going through a terrible losing streak. In contrast, the law of large numbers says - again using the tossing a coin example- if you toss a fair coin for a large number of times (1000 times, 1 million times etc. ), then there would roughly be as many heads as tails. It’s tempting to think that if we toss the coin 100 times (which is a pretty small number to be fair) we should get 50 heads and 50 tails. This is certainly suggested in the 'law of averages' but this this isn’t supported by research and mathematical theory. In reality, we're more likely to get something like 49:51 or 48:52 heads and tails. A difference of 1 or 2 is considered unimportant for large numbers like a million or more. 

Changing trains problem

So let’s explore another example of probability at work. Suppose you’re planning to travel from Oxford to Glasgow over Christmas. You learn that you have to change trains in London. You have a change over time of 15 minutes to catch your connecting train to Glasgow. But you learn to your disappointment, that due to engineering work, the two trains reach London independently of each other. 

Before making the journey, you want to know the chances that the two trains will be at the London station at a similar time. Should you take the risk, or should you give up on the journey altogether. Unfortunately, here gut feeling is not enough so it can be helpful to turn to maths... 

1. So the change over time is 15 minutes.This is 1/4 of an hour. 
2. You need to work out the probability of one train meeting the other. 
3. The probability of Train A not meeting Train B is 3/4, and the probability of train B not meeting train A is also 3/4.
4. To gain the probability of the trains not meeting at all, you need to multiply these together i.e. (3/4) x (3/4) = 9/16.
5. Then the probability of meeting becomes 1 -  9/16 = 0.4375, which is less than 1/2 (>50%)

In light of this, you may feel it's not worth taking the journey and risk being stranded in London. This and the examples above show us how maths can help us make better and more informed decisions. 

Some of the ideas above are discussed further in:
•    David Williams (2001) Weighing the odds: a course in probability and statistics. OUP 
•    David Stirzaker (1999) Probability and Random variables: a beginner's guide. OUP
 

The power of our DNA

In a perfect world, success in a certain area comes from the amount of work you put in. The emotional and financial support from family, your education, access to resources and general quality of life, all have a part to play too. Your environment (both at home and at school) is extremely important to shaping who you are. But what if we don’t all start from the same baseline? In other words, what if we’re destined to have certain skills (and not others) before we’re even born? It’s in our genes. 

The DNA we get from our parents gives us all the features we can see, like hair colour and shoe size.  But also those that we can’t, like how fast our bodies transport oxygen around our blood or how the neurons (cells) in our brain connect to each other. 

The colour of your hair is unlikely to affect how fast you can run, but let’s take an obvious example: male vs female. We separate sports categories by sex because it just isn’t fair otherwise. A simple genetic difference means that males put on muscle more easily and release energy faster than females through the hormone, testosterone. 

To catch up on the biology behind this topic, take a look at the video below in which science writer, Jo Hanson explains the wonderfulness of DNA: 

https://www.youtube.com/watch?v=aeAL6xThfL8

We’re all mutants

As a species, humans share around 99.5% of their DNA with each other. In 1953, James Watson and Francis Crick famously discovered the structure of the DNA molecule known as the double-helix model. This is recreated below: 

Years later (2008-2015), the international 1000 Genomes research project worked out the exact sequence of our DNA code: a string of four letters (A, C, G, T) totalling 3.2 billion characters long! The scientists pinpointed exactly where all the differences between us are found in this string. Pretty impressive, right? The researchers realised that all of our personal features come from small differences at 4-5 million places in our DNA. Most of the time these differences are tiny, just one of the four possible letters is swapped for another. 

Journalist, Malcolm Gladwell famously said that 10,000 hours of hard work might be enough for someone to become an expert in something. Do you think this can ever be possible? 

But even a single letter change can have a big effect on how our genes work. The 20,000 genes in our DNA are like the important words in a sentence: they are the strings of letters that make our hair brown or our eyes green. When a letter change affects how a gene works, it's called a mutation. We all carry mutations in a handful of genes, but because we have two copies of the genome – one from each parent - most don’t affect our daily life. What about those that do though?

The “sprinter gene”?

One clear example where DNA affects our potential is the ACTN3 gene. ACTN3 is used to control how some of your muscles tense. Within the gene sequence, the letter C (short for cytosine) is swapped for a T (short for thymine) in 20-50% of people around the world. People with the letter T mutation are perfectly healthy but top sprint runners seem to perform a lot better with the usual letter C gene. This doesn’t mean that having two copies of the C gene destines you to be a record-breaking sprinter but it does give you an automatic advantage over anyone with the T mutation.

The endurance gene

Another example from the sporting world comes from the Erythropoietin (EPO) hormone. In you and me, the more EPO you have in your blood, the more new red blood cells you make. The more red blood cells you make, the more oxygen you can carry around your body and the harder your muscles can work. Usually, we only have a lot of EPO when we’re replacing red blood cells lost in an injury. But, for Finnish skier, Eero Mäntyranta, a single letter change in his DNA makes his body think that there’s always lots of EPO around. This means that he constantly makes more red blood cells than the rest of us, even though his body doesn’t need them! For endurance sports like swimming and cycling where your muscles use a constant supply of oxygen, this is like winning the DNA lottery! 

The creative gene

Sport isn’t the only area where we can pinpoint a single gene with a big effect. For example, Neureglin-1 is a gene involved in brain development. DNA mutations that disrupt this gene are associated with mental health conditions such as schizophrenia, psychosis and poor memory. But some people who have mutations in Neureglin-1 (and who don’t suffer from mental health problems) do better in tests for creativity than those with two copies of the working gene. 

Does one gene say it all?

The different potential outcomes of the Neureglin-1 mutation is a good example of why we can’t explain people’s potential with a single gene. Depending on the rest of the variations found in the DNA, the Neureglin-1 mutation can be a blessing or a curse: increasing the risk of disease or boosting creativity. We’re all products of the two copies of 20,000 genes we carry, and how they interact together. 

What we can take away

The bottom line? Yes, it’s true that we’re all different from the very beginning. And for some of us our genes work together to make us perfectly designed to be the next Pablo Picasso or Usain Bolt. But the rest of us are two copies of 20,000 genetic instructions all mixed together to make us who we are.

So what do you think? Does luck = DNA?