Olympic Euromillions: the best lottery ever

EuromillionsMost lotteries are a rip-off, but maths proves that the July 27th Euromillions superdraw will be sensational!

It's often said that lotteries are "for mugs" and are nothing more than "a tax on people who are bad at maths". As a former mathematician, I would almost always agree.
For example, I know that the UK's National Lottery pays out only 50p for every £1 of ticket sales. In other words, the Lotto has a 'negative expectation' of 50%. This means that -- with average luck and playing over long periods -- you should expect to lose roughly half of your stake money.

As proof, lottery organiser Camelot Group had sales of £6,526 million in 2011/12, but paid out only £3,389 million in prize money. As a result, British punters lost £3,137 million in the 12 months ending 31 March 2012. This is more than three billion pounds, which averages to almost £121 for each of the UK's 26 million households. Ouch!
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The UK and the EuroMillions
The EuroMillions lottery draws -- which take place on Tuesday and Friday evenings -- have a similar minus 50% expectation, because they too pay out only half of the stake money in prizes.

Sometimes, however, certain EuroMillions draws are well worth playing -- and the biggest of these rare opportunities arrives later this month.

As the UK is not part of the euro zone, the British pound creates a headache for the EuroMillions organisers. Over here, we pay £2 per ticket, but exactly the same ticket costs €2 in other European countries. As €2 is worth below £1.60, we Brits pay a quarter (25%) more to enter EuroMillions draws than European punters do.

To tackle this British overpayment, Camelot has a special UK Millionaire Raffle open only to tickets sold in Britain. Each EuroMillions draw includes a raffle into which all UK participants are entered, with a guaranteed prize of £1 million. In other words, with two draws per week, the UK Millionaire Raffle guarantees to create at least 104 extra British millionaires each year.

One enormous EuroMillions payout
Every so often, in order to boost ticket sales and prize money, Camelot promotes special EuroMillions superdraws.

For example, on Friday, 23 December 2011, the UK Millionaire Raffle paid out 25 million-pound prizes, handing 25 new millionaires a cash-rich Christmas. In fact, the UK Millionaire Raffle paid out no fewer than 50 million-pound prizes that month, making December 2011 a bumper month for British gamblers.

Even better, the biggest-ever EuroMillions superdraw is on the horizon. To celebrate the opening of the London 2012 Olympics, Camelot is organising a huge payout to coincide with the opening ceremony on Friday, 27 July.

As the sporting festivities get under way on 27 July, that Friday evening's EuroMillions draw will include 100 -- yes, one hundred -- £1 million prizes to be paid out by the UK Millionaire raffle. In other words, as well as the usual EuroMillions prizes on offer that night, there will be another £100 million paid out to lucky Brits.

This will be one of the biggest-ever prize funds to be widely shared by British punters. In addition, it will set a new world record for the largest number of millionaires created in a single draw.

Why this is a super superdraw
As I explained earlier, most lottery draws are pants, because they pay out only half of what is collected in ticket sales. The 27 July EuroMillions superdraw is very, very different, as it is set to pay out many times what Camelot will collect in ticket sales.

For example, let's say that gambling-mad Brits buy 10 million tickets for the 27 July draw. These would cost £20 million and boost the usual EuroMillions prize pot by £10 million. However, the total paid out will be whatever we Brits go on to win in the main EuroMillions draw, plus another £100 million on top.

Therefore, in this example, the payout to UK gamblers could be, say, £110 million on sales of £20 million. In effect, this would be 5½ times as much as we paid in, which is a payout ratio of 550%. Statistically speaking, this would make the 27 July draw a terrific gamble, because payout ratios above 100% mean that the odds are firmly in the punters' favour.

What are your odds of winning £1 million?
Of course, the odds of winning £1 million in this Olympic UK Millionaire Raffle superdraw depend entirely on the total number of tickets sold for that particular draw.

Unfortunately, Camelot could not give me a figure for expected sales for the 27 July draw. This is because ticket sales vary dramatically, not least because of the weather and time of year.

Also, ticket sales soar for draws with bumper payouts, especially those with huge jackpots above £100 million following multiple rollovers.

Even so, here's a table showing a possible range of outcomes for British punters. Please note that these apply only to that one night (27 July) and not any other EuroMillions draws. Also, these numbers are purely a general guide and the actual outcome on the night is certain to be different to these figures.

Tickets

sold

Ticket

cost

Odds of

winning

£1 million

Possible

UK prize

fund

Payout

ratio

10,000,000

£20,000,000

100,000 to one

£110,000,000

550%

12,500,000

£25,000,000

125,000 to one

£112,500,000

450%

15,000,000

£30,000,000

150,000 to one

£115,000,000

383%

17,500,000

£35,000,000

175,000 to one

£117,500,000

336%

20,000,000

£40,000,000

200,000 to one

£120,000,000

300%

22,500,000

£45,000,000

225,000 to one

£122,500,000

272%

25,000,000

£50,000,000

250,000 to one

£125,000,000

250%

As you can see, the more tickets are sold, the higher the odds against winning £1 million become. This is because the number of UK Millionaire Raffle winners is fixed at 100, but the odds against winning increase as the number of tickets entered in this raffle soars.

Even so, if 20 million tickets are sold, then the odds against winning £1 million will be 200,000 to one -- making this much better than a fair gamble. Indeed, the payout for 20 million tickets sold could be £120 million, which is three times as much as the £40 million cost of these tickets. This equates to a payout ratio of 300%, which is three times the break-even point of a 'fair gamble' 100% payout.

A mathematical marvel
Of course, the chances of you winning a million are still very low, but the high payout ratio means this is the best lottery that I've found since I started loving maths more than 40 years ago. That's why I'll be buying a ticket or two for this Olympic superdraw.

In summary, the 27 July EuroMillions superdraw is the best lottery that I have found since I started loving maths more than 40 years ago. That's why I will be buying a ticket or two for this Olympic superdraw!

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