You’ve seen it in the news, all your friends are talking about it, the Euro millions jackpot is over £150m. You start to imagine what it would be like winning all that money; houses, cars, yachts and planes fill your mind. You don’t care what the odds of winning are, some has to win it and as Camelot says “it could be you!”
Sound familiar? Then you have a classical case of probability blindness.
The human brain is not really wired to calculate things. It has evolved to catch prey, grow crops and generally make living easier. So when the chance of all up wildest dreams coming true is up for grabs the smart part of the human brain shuts down. For example take this simple maths question, which you are going to get wrong.
A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost?
Got the answer?
Even though I forewarned you about your error, you still think the answer is 10p. Don’t feel too bad, almost everyone answers this question wrong. The reason being is the brain sometimes jumps to the answer without reviewing the calculation. We often have to force ourselves to do the calculation.
So, if the ball costs 10p and the bat is £1 more, then bat is £1.10 which totals £1.20. But if the ball cost 5p and the bat is £1 more then the bat is £1.05 totalling £1.10. Not rocket science, but we have to force ourselves to do the calculation and it is the same case with the lottery. The brain thinks “there is a chance of winning £150m, the ticket only costs £2 - it’s a good deal”. We have to stop ourselves becoming emotional about the lottery, stop ourselves imagining what it would be like to win and start thinking about why we are throwing away £2 every week?
To help break through this irrationality you can use a simple tool, Expected Monetary Value (EMV), which is the probability of winning times the winning amount.
EMV
To know weather your ticket is good value or not, first you must consider the odds of winning.
To calculate this, you take the odds of guessing a single number correctly, that is 1 in 50. Guessing the next ball is slightly easier since one ball has been removed. So 1 in (50 x 49). You will need to match 5 numbers. But you don’t need to match them in any order, so you divide by the number of permutations factorial (5x4x3x2x1).
So far we have (50x49x48x47x46) / (5x4x3x2x1) = 2.1million to one
Not bad you might think, but in the Euro millions they add another set of numbers, ironically called ‘Lucky Stars’. Here you have to guess another two numbers from a pool of numbers. So an additional (11x10) / (2x1) = 55 but we are not adding we are multiplying (55x2.1milion) = 1 in 116.5million!!!!!
But the jackpot could be massive; a few weeks ago it was £166m (which it was capped to)! So is it worth it?
The EMV is the probability of wining (in decimal form) times the winning value. If the EMV is lower than the cost of the ticket, it is not a good investment.
EMV = (1/116.5million) x £166million = £1.42
The ticket cost if £2.
There are of course other prizes to be one, (not that you really care about those), if we included those it only increases the EMV to £1.80.
So the highest ever jackpot for Euro millions was still not worth buying.
There was one case where a ticket was worth buying. In 1992 some Australian investors noticed that the Virginia state lottery had an EMV of $3.95 when the ticket only cost $1. So they quickly found 2500 investors, investing $3000 each and set about buying every possible combination of tickets. The problem they had was trying to them all in a week (they had to buy over 7 million tickets). They hired 125 people to fill out the tickets manually in stores across Virginia, but it wasn’t enough. By the time the draw went ahead the investors had only 60% of all possible combinations. They also had another fear, what if they had to share their jackpot? In both cases the investors were massively exposed to a big loss. They watched the draw nervously, to their delight there was only one winner and it was them.
Ambition Depressor
On a concluding note, the lottery is only £2, it’s not a massive amount of money to throw away, but I do have concerns that the lottery inhibits ambition. Dale Carnegie, author of How to Win Friends and Influence people writes that one of the main hungers we have is for ‘money and things that money buys’, in other words ambition. Ambition however can be satisfied without actually encountering the money, so long as you’re moving in the right direction. For example when looking for a new job you have an ambition to move on, a hunger, but when you send off your CV to a company you feel satisfied that you are moving in the right direction. For people buying lottery tickets, I believe the hunger for ambition is being satisfied, even though there is practically no chance of winning. How many times have you herd someone who is unhappy with their job or in a bit of financial trouble part jokingly say “I’m hoping to win the lottery”?
If everyone stopped buying lottery tickets, stopped fanaticising about the event which will never happen and instead focused on practical ways of improving their life, 99.999999% of people would be a lot better off.
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