Have you ever wondered about the odds and statistics of winning the lottery? Most lotteries involve selecting a fixed set of numbers from a larger collection of numbers by drawing numbers at random. Let’s take the UK National Lottery as an example. This requires 6 numbered balls to be drawn at random from a total of 49 uniquely numbered balls and the declared odds are 14 million to 1. You can easily calculate these odds using Microsoft Excel. Simply type the following into a cell:

=COMBIN(49,6)

The numbers in the brackets represent the total number of balls from which to draw and the number of balls which are drawn, respectively. In this case we are drawing from a total of 49 balls and we are drawing 6 balls in total, so we use 49 followed by 6; the larger number is always placed first. The number you should see in the cell is 13,983,816 or just under 14 million to 1.

We can experiment with this to find different odds and the results can be surprising. For example, which odds are higher, drawing 6 balls correctly from 50 or drawing 7 balls from 49? Using the COMBIN function in Excel tells us that the odds are 15,890,700 and 85,900,584 respectively. In other words it is 5.4 times harder to pick 7 from 49 than it is to pick 6 from 50. This goes some way to explain how the odds quickly escalate as the number of balls drawn increases. For example, the odds of picking 1 correctly from 49 are clearly 1 in 49. The odds of picking 2 from 49, however, are 1176 to 1. Even then the UK lottery pays nothing. So what about 3 from 49, paying a heart stopping £10? Again the mathematics tells us that the correct odds of doing this are 18,424!

The full odds of correctly predicting an increasing number of balls are as follows:

1 in 49: 49 to 1

2 in 49: 1176 to 1

3 in 49: 18424 to 1

4 in 49: 211876 to 1

5 in 49: 1906884 to 1

6 in 49: 13983816 to 1

This probably explains why you probably know someone who has matched 3 or even 4 numbers but it’s very unlikely that you know a jackpot winner.

We can use this information to select which lottery to enter, since there are hundreds of different lotteries available across the world. Not all of them allow non residents to take part, but many of them do. The important thing to remember is that the fewer numbers you have to predict and the fewer you have to pick from, the higher the chance of success. Let’s take an example to prove the point.

Consider the following lotteries and select which one has the best odds of success, based on the calculated odds.

UK Lottery – selecting 6 from 49 means odds of 13,983,816 to 1

USA Mega Millions – selecting 5 from 56 and 1 from 46 means we have to calculate each probability separately using the COMBIN function in Excel and then multiply them together to get the overall odds. This reveals that the odds of selecting 5 correct numbers from 56 is 3,819,816 to 1 and the odds of selecting 1 from 46 is obviously 46 to 1. Multiply them together and we can see the total odds are a massive 175,711,536.

Spanish “El Gordo de La Primitiva” – selecting 5 from 54 means odds of 3,162,510.

EuroMillions – selecting 5 from 50 and 2 from 9 means we have to carry out a similar calculation to that in the USA Mega Millions. In this case the total odds are 76,275,360.

So, based on the calculated odds, you have the most chance of success in the Spanish “El Gordo de La Primitiva” Lottery draw with odds of 3,162,510 to 1. Unfortunately you will also find that generally the lower the odds the lower the prize funds available, particularly the jackpot prize. The trick here is to decide how much you want to win to change your life and then find the lottery with the lowest calculated odds of winning this amount.

A word of warning about the so called “hot numbers” This is the theory that some numbers are hot and therefore have more chance of being selected. The truth is that a lottery is just that – a lottery. This means that selection of the winning numbers is random, which means that each number has an equal chance of being selected. Evidence of “hot” numbers usually centres around short periods of time. For example, it is easy to argue that a particular number is hot if it has been drawn in the last three draws. In reality, it is no more and no less likely to be drawn than any other number and is certainly not capable of remembering that it has been drawn on the last two occasions and therefore it will ensure it is available to be drawn a third time!

You can prove this for yourself by looking at the number of times a particular number has been drawn over a period of time. The longer the time period in question, the more likely it is that each number will be drawn a similar amount of times. In other words the concept of “hot” numbers is a complete fallacy.

There are only two ways of increasing your chances of winning the lottery. The first is to pick the appropriate lottery which has the best calculated odds of winning the jackpot prize, assuming this is sufficient to change your life. The second is simply to buy more tickets either as an individual or via a Lottery Syndicate!