Odds and UK National Lottery

I have found a competition that seems to have pretty good odds of winning a car. Basically they are selling 2,900 tickets for a spot the ball competition which seems good when compared to things like the Lottery.

There are a few places doing competitions like this do you think they are a good bet ?


This was the question I received a few weeks ago from David. Since I thought this might be of interest to our readers I'm publishing the answer here:

Risk vs Reward

The UK National lottery is long odds and high return. Chance to win jackpot is 1 in 13,983,815.

This is closer to the other end of the scale. Chance to win car 1 in 2,900.

NB: "Each entry has a 1 in 362 chance of winning a prize !" This isn't referring to the car and those prizes are probably worth less than the £15 cost of the ticket.

Just because the odds are shorter doesn't make it a good bet. It still has negative expectation, i.e. if you kept playing until you finally won the statistical probability is that you would have lost more money than the car is worth.

To be exact £43,500 to win a £26,000 car = profit - £17,500.

If you're looking for a game of random chance, that requires no skill and the odds are as short as possible (although still against you) go to a casino and bet on black or red (it's approximately 49% to win) .

I always like to remember the fact that you are statistically more likely to be struck by lightning than win the National Lotto jackpot. Remember that next time you are all walking up during a thunderstorm.

Found this handy odds calculator for any lotto game around the world.

It also explains the maths as to why the odds for winning the lottery are approximately: 14 million to 1.

I always wondered how they arrived at the figure 14 million to 1 for the UK lotto, as when I tried to work it out I arrived at:

You can choose 1 of 49 numbers for your first pick
You can choose 1 of 48 numbers for your second pick
You can choose 1 of 47 numbers for your third pick
You can choose 1 of 46 numbers for your fourth pick
You can choose 1 of 45 numbers for your fifth pick
You can choose 1 of 44 numbers for your sixth pick

Therefore 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520.

So, a 1 in 10 billion chance roughly.. However, this obviously isn't right, as the jackpot is won by at least one person most weeks, and the chance of winning is quoted as *only* 1 in 14 million.

Anyway, I found the reason for the difference in calculations, is that you can pick your numbers is any order. This increases your chance by 720 times, and gives you a 1 in 13,983,816 chance

Here's the webpage for those interested: Lottery Odds Calculator for UK Lotto

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