Becoming a National Lottery millionaire could provide the financial freedom to do as you please. But only a few people win the highest prizes of £1 million or more. From millions of players, will you win the jackpot?

Perhaps not today, but could you ever win a large amount, and soon? Is it feasible, and if so, how? Or will it remain just a pipedream?

We shall try to find out how you might fulfil this aspiration. But, until we understand how the National Lottery works, we cannot hope to answer the question, “How Can I Win the National Lottery?” adequately.

To get a better grasp of the problem, let us begin at the beginning.

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Estimated reading time: 50 minutes

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Thank you and welcome

Welcome to my website about the UK National Lottery. I hope it answers your search adequately and interestingly, whether you are a keen player or just innately curious.

Over time, I want to discuss the theory, history, operation and mathematics of lotteries clearly to whet the appetite of any enthusiast. Step inside; there is more to the National Lottery than meets the eye, as I think you will begin to see and appreciate soon!

Scratchcards not included

Before going further, let me stress that we shall not consider National Lottery Scratchcards (Instant Win Games). Our concern lies primarily with the game known now as Lotto.

How did you get here?

If you arrived here by typing keywords into Google or a similar search engine, you have done well since this website is barely one year old and currently has low search rankings. I value your call highly.

Alternatively, you may have come by typing the URL https://coulditbeyou.net into the search bar of your browser or through a social media link such as Facebook, Twitter, or LinkedIn.

Thank you for visiting, no matter how you have found this site. Its purpose is to provide accurate, impartial and trustworthy information based on evidence obtained from experiments.

Contact Me

Feel free to ask questions or seek clarification on anything. I welcome constructive criticism and any suggestions that you have to enhance the content of this website. Please use the contact form provided.

I look forward to hearing from you. Thank you.

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Financial Freedom

Experience suggests that many people long for the sense of security that a lot of money can bring at some point in their lives. Thus, there is an appetite for easy money; undoubtedly, windfalls are very appealing.

I am not suggesting that the pursuit of money should be our top or sole priority; far from it! Some things in life are far more precious and meaningful, but sufficient money makes some choices easier, particularly at critical times.

In a liberal democracy like ours, there is respect for the law. The wealthy in Britain have always been free to do as they please without undue restraint legally. Life can be sweet and satisfying when you are unfettered from the urgent and compelling need to meet living costs day in, day out. Freedom from such constraints offers room for manoeuvre to indulge whims, follow dreams and fulfil personal ambitions.

After World War II, the sum of one million pounds represented the pinnacle of financial aspiration for most people, as witnessed by songs like “Who Wants to Be a Millionaire?” penned by Cole Porter and the popularity of the game show of the same name. The latter^[1] aired on ITV for over 15 years between 1998 and 2014. The show produced a total of six millionaires.

Legal Routes

There are many ways to acquire riches; some are lawful, others not! Schemes to acquire large amounts of money tend to be illusory and are often fraudulent. Legal avenues to become wealthy include:

• inheritance,
• working for a high salary,
• saving and investing surplus cash prudently,
• setting up and pursuing a thriving business (from which to draw dividends and an income), and
• good fortune.

The British Government, led then by Prime Minister John Major, set up the National Lottery to support a few Good Causes^[2]. Its foundation rested on the principle of additionality^[3].

Since 1994, winning the lottery has been added as another way to acquire wealth legitimately, but this is no more than a fantasy for most people. Such winnings are usually beyond their reach.

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What is a Lottery?

The National Lottery game of Lotto is a modern example of a lottery.

In general terms, a lottery is a game of chance, not skill, in which buyers of tickets receive prizes chosen by lot, according to a set of predetermined rules.

Lotteries are not new; the underlying ideas have existed for a long time.

Early, modern lotteries began as raffles in the Low Countries^[4] in the 15^th century to supplement taxation. They became common in England from 1567 until 1826, when they ended abruptly.

Over many generations, lotteries have raised vast amounts of money for many different organisations. Presently, most state-run lotteries, including the National Lottery, have adopted a system based upon one developed in the Italian city of Genoa between 1620 and 1643.

Initially, the method involved drawing five numbered balls from 90 in a wheel without replacement, similar to the one used in bingo today (see above); it produced more immediate results than raffles which were long, drawn-out affairs then.

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Looking to Luck

Anecdotally, it seems that good things happen to people during their lives irrespective of their abilities or actions. Examples include a sudden windfall or an unexpected inheritance. We regard this as good luck and welcome it with open arms when it comes our way.

Luck need not be good; it is considered bad luck when circumstances affect us adversely. e.g. financial ruin, accidental injury or death, or affliction by a life-threatening disease. However, there are also times when good luck and bad luck coincide. e.g. surviving a catastrophic accident unscathed.

With lots in mind, some people talk of the luck of the draw, referring to events over which they have no control and are governed by chance. When playing a lottery game, are we reliant on luck entirely, whatever it might be, or can we adopt a more rational approach?

Speaking for myself, I prefer not to rely on luck alone. I will try and find another better and more reliable way, though it might be challenging. Is this problem soluble?

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Launching the National Lottery

The possibility of winning £1,000,000 featured prominently in a tri-fold promotional leaflet, entitled It Could Be You, circulated throughout the UK before the National Lottery began in November 1994. It accompanied advertisements on independent television channels, in magazines and on hoardings.

The leaflet (© Camelot Group Plc. The National Lottery, PO Box 287, Watford WD1 8TT) forms part of my personal collection of lottery memorabilia.

To this day, the creation of new millionaires remains one of Camelot’s declared aims in its role as operator of the National Lottery. They have been much more successful than the popular TV show mentioned earlier, producing more than 6,100 millionaires between the launch of the National Lottery and October 2021.

In the early days, the hope was that the jackpot might reach as much as £2 million from time to time to rival the record set by the pre-dominant football pools^[5]. As events would show later, the lottery exceeded those expectations by far and did so consistently. The nation had taken the National Lottery to heart; this was no mean feat!

As the National Lottery grew more popular, the football pools companies^[6] took a hammering financially, from which they never really recovered.

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Origins

When it began in November 1994, the National Lottery consisted of a single game. The cost to play one game in a single draw was £1.

Then, you could only play anonymously through the dedicated computer terminals installed in many newsagents, post offices and shops throughout the UK and the Isle of Man, like the one shown above.

The National Lottery provided Play Slips, pre-printed slips of paper, to mark your choice of numbers which you hoped would match those drawn to win a prize. The Play Slips have changed many times since 1994 to reflect the evolution of the game.

During the first year of operation, jackpots rose with increasing ticket sales, giving a bumper financial harvest for the good causes. Top prizes over £10 million had become commonplace to the disdain of many people who thought that they were excessive.

Despite the loud cries for action that had ensued, Camelot was reluctant to tinker with the prize structure since it might reduce revenue detrimentally, having established the National Lottery brand and encouraged people to play regularly.

Deftly, Camelot quietened the criticism by introducing Lucky Dips, which lowered the frequency of those jackpots considerably and made it easier for hesitant people to play.

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The Design of the Original Game

The National Lottery designed its first game around 49 numbered balls, drawing seven balls in turn without replacement.

The prizes fell into five tiers, four of which depended only on the first six balls drawn. The remaining tier relates to the seventh ball drawn combined with any five of the first six (typically, with a prize of £100,000 or more); otherwise, the seventh ball, the bonus, has no further role.

• A consolation prize of £10 lay at the bottom of the prize structure.
• The winners and prize pool for each tier determined the rewards at the higher levels, which varied widely.
• In practice, jackpots would exceed £1 million regularly. 

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Underlying Mathematics

Mathematically speaking, there are ⁴⁹C₆ combinations when choosing any six from 49 numbers, like Lotto balls in the original game, for instance.

$$ \begin{split}^{49}C_6& = \frac{49!}{6! × 43!}\\ \\&=\frac{(49×48×47×46×45×44×43×\dotso×6×5×4×3×2×1)}{(6×5×4×3×2×1)×(43×42×41×\dotso×3×2×1)}\\ \\&=13983816 \end{split} $$

The exclamation mark ! indicates a factorial number, and the ellipsis … means and so on until.  e.g. 6! = 6×5×4×3×2×1 = 720. 

Many factors in the numerator and denominator above cancel out.

Mathematicians have a shorthand for combinations. Two are in everyday use; they mean the same thing, are identical and interchangeable.

$$ ^{49}C_6 ≡ \binom{49}{6} $$

As you can see, it is tedious to write out the process in longhand; the abbreviation makes things much more straightforward.

Since each combination consists of 6 of the 49 balls, it follows each ball appears (13,983,816 × 6) ÷ 49 times. i.e. 1,712,304 times. This fact may be interesting, but it is not particularly helpful in our quest for success; we need better insights.

The total number of combinations is slightly less than 14 million. Only one contains all of the six main numbers. What about the rest? How many of the others are prize-winning combinations?

The following table shows how many combinations match the main numbers drawn.

The number of combinations of six main Lotto numbers using 49 balls.

Category	Combinations	Winning Combinations
Match 0	6,096,454	0%
Match 1	5,775,588	0%
Match 2	1,851,150	0%
Sub-total:	13,723,192	0%
Match 3	246,820	94.7%
Match 4	13,545	5.2%
Match 5	252	0.10%
Match 5+	6	0.002%
Match 6	1	0.004%
Sub-total:	260,624	100%
Total:	13,983,816	100%

In the case of Match 5+, it is pretty straightforward to see that six combinations are possible since each of the six main numbers can be replaced by the bonus number.

To summarise, only 260,624 (1.86%) of the 13,983,816 combinations possible win prizes. In other words, over 98% of them win nothing at all! The pie chart on the left below demonstrates this vividly; winning combinations account for the minuscule blue slice.

Most of the winning combinations (almost 95%) qualify only for the minimum Match 3 prize; about 5% match four of the six main numbers. Less than 0.1% produce the best outcomes (Match 5, 5+ and 6) – much too small to observe in the pie chart on the right.

The figures in the table confirm our belief, wrought from experience, that it is difficult to win any prize in Lotto, let alone one of the higher ones, which are the most attractive and desirable.

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The First Draw

It is instructive to examine the first draw held on 19 November 1994, which set the pattern despite later reforms. Let us imagine the scene at that time and re-enact it.

To play, you need to pick six unique numbers between 1 and 49. This selection is the minimum entry you can make. It is the unit of play, called a board. To be eligible for a prize, Camelot must record the details of the board in its computer system before the draw takes place.

Conduct of the Draw

• Forty-nine numbered balls are dropped from hoppers into the drum of a machine that resembles a tumble-drier. Geometrically speaking, the drum is a transparent spherical frustum. One of its circular ends faces an audience, allowing us to see what is happening inside.
• Behind the front face is a three-legged rotor with feet, sculptured like scoops, which spins anti-clockwise about the central, radial axis of the drum.
• At the same time, an impeller at the rear with three oblique vanes at right angles to its plane rotates clockwise about the same axis concentrically.
• The counter-rotation jumbles the balls as they tumble chaotically inside and ensures random mixing. The movement of the vanes appears to lag behind the rotor legs by an angle of 60°.
• The lightweight balls are tough enough to withstand mechanical agitation without damage and are indistinguishable, apart from their colour and number.
  

  

• Once the draw master is satisfied that the machine is behaving correctly, an independent person starts the selection process by pressing a button.
• A mechanism at the base of the drum withdraws seven balls at intervals. A camera records their escape singly along a chute to form a stationary row. Once removed, they play no further active role since they make no return to the drum.
• The first six balls are the main balls. The order is immaterial since it does not affect how they qualify for a prize.
• Events follow this sequence. The first ball is drawn from 49 in the drum, the second from 48, the third from 47, the fourth from 46, the fifth from 45 and the sixth from 44.
• Finally, the machine draws the seventh ball, called the bonus ball, from the remaining 43 left inside the drum. The bonus ball becomes significant if a player matches any five of the main balls.

If the draw has followed the rules correctly, the winning numbers are confirmed in ascending order, with the bonus number last. The first draw met the rules, and the numbers picked were: 3, 5, 14, 22, 30 and 44, and bonus 10. 

How to Win a Prize

The aim is to predict in advance which numbers will be drawn. The minimum entry, called a board, is a selection of six different numbers. There are five categories for each board played, and a winning board receives a prize in the highest category for which the numbers qualify.

Original Prize Categories in Lotto

Category	Condition	Example(s)	Possibilities
Match 3	Any 3 main balls	(3, 5, 14) or (5, 30, 44)	6C3 = 20
Match 4	Any 4 main balls	(3, 5, 14, 22) or (5, 22, 30, 44)	6C4 = 15
Match 5	Any 5 main balls	(5, 14, 22, 30, 44)	6C5 = 6
Match 5+	Any 5 main balls & bonus ball	(5, 14, 22, 30, 44) and 10	6C5 = 6
Match 6	All main balls	(3, 5, 14, 22, 30, 44)	6C6 = 1

You will not be surprised to learn that it is harder to match six main numbers than five, five more than four, and four more than three. Therefore, in general, the cash value of the prizes increases with the number of balls that match, reflecting the degree of difficulty. However, the amount won depends also upon the number of prize winners in each category for a pari-mutuel game. We shall see how this works later.

The figure below is an artist’s impression, showing how the six winning main numbers (shown in red) appear on the play slip displayed earlier.

Filling seven blocks would have caused the retailer’s lottery machine to reject the play slip – to the player’s dismay and those in the queue behind him (or her) in the shop.

Results

Despite the media hype, razzmatazz and the hopes and expectations of the public, the first draw failed to create any millionaires. Instead, seven winners shared the jackpot, each receiving £839,254. I can recall a palpable sense of disappointment in the one-hour show hosted by Noel Edmonds after the draw.

Winners, prizes and prize pools in each category for Draw 1 on 19 November 1994

Category of prize	Number of winners	Prize	Prize Pool
Match 6 (jackpot)	7	£839,254	£5,874,778
Match 5 plus bonus ball	39	£46,349	£1,807,611
Match 5	2,139	£528	£1,129,392
Match 4	76,731	£32	£2,455,392
Match 3	1,073,695	£10	£10,736,950
Total:	1,152,611		£22,004,123

There should have been no cause for concern or dismay since there were 1,152,611 winners who collected prizes worth £22,004,123 from ticket sales of £48,965,792. Winners accounted for 2.35% of tickets sold, and most winners (99.8%) belonged to the Match 3 and Match 4 categories. That figure did not fall below 99.6% in 2,065 draws played with 49 balls between 19 November 1994 and 7 October 2015.

• Ticket sales fund the prizes. In this case, the total prize pool (£22,034,606) came from 45% of tickets (£48,965,792).
• Match 3 prizes were fixed at £10 each, giving a total of £10,736,950, which was deducted from the total prize pool of £22,034,606.
• The deduction produced a residual prize pool amounting to £11,297,656, which was shared across the pari-mutuel prize tiers of Match 4, Match 5, Match 5 plus bonus and Match 6 in the following proportions: 22%, 10%, 16% and 52%.

Calculation of pari-mutuel Prizes in Draw 1

Sales	£48,965,792
Prize Fund	45% of Sales	45% of £48,965,792	£22,034,606
	less Match 3 prizes	1,073,695 × £10	£10,736,950
		leaving	£11,297,656
Category	Allocation	Prize Pool ÷ Winners	Prize
Match 4	22% of £11,297,656	£2,485,484 ÷ 76,731	£32
Match 5	10% of £11,297,656	£1,129,765 ÷ 2,139	£528
Match 5+	16% of £11,297,656	£1,807,624 ÷ 39	£46,349
Match 6	52% of £11,297,656	£5,874,781 ÷ 7	£839,254

Keen observers will notice two totals for the prize fund, namely £22,034,606 and £22,004,123. The difference of £30,483, known as breakage, arose from ignoring pennies when calculating pari-mutuel prizes and went towards a general-purpose fund.

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Building on Success

Afterwards, no one could have doubted that the National Lottery had begun successfully, exceeding all expectations triumphantly, and had made a good start in raising colossal sums of money for charities – its raison d’etre. The first draw contributed about £14 million to the charitable funds alone.

Excluding Superdraws^[7] and Rollovers^[8], the primary method of calculating prizes shown above continued to draw 1856 on 5 October 2013. As part of the New Dawn for Lotto initiative, Camelot increased the board price to £2, stepped up the Match 3 prize from £10 to £25 and introduced a raffle to rejuvenate the game.

Two years later, the raffle was dropped, and Lotto began to use 59 balls instead of 49, accompanied by a reformed prize structure.

In Conclusion

The lottery enterprise has produced spectacular results in 25 years. Between November 1994 and September 2019, according to Camelot, it raised £43 billion for Good Causes, paid out £56 billion in prizes and created 6,100 millionaires – benevolence on a large scale. This performance is impressive by any standard.

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Playing a Single Board – a logical approach

I will continue to focus my attention on the original game, played with 49 balls.

In a Single Draw

Including the bonus ball, (43 × ⁴⁹C₆) combinations can be drawn. i.e. 601,304,088^[9]. There are only six fixed outcomes, regardless of the numbers chosen to comprise a single board. They are summarised in the table below.

Possible outcomes for a single board of Lotto using 49 balls

ID	Match 3	Match 4	Match 5	Match 5+	Match 6	Probability(%)	Occurrence
1	0	0	0	0	0	98.14	590,097,256
2	1	0	0	0	0	1.765	10,613,260
3	0	1	0	0	0	9.686×10-2	582,435
4	0	0	1	0	0	1.802×10-3	10,836
5	0	0	0	1	0	4.291×10-5	258
6	0	0	0	0	1	7.151×10-6	43
					Totals:	100%	601,304,088

Only five win a prize, not including the most probable outcome (shown in red). Overall, the probability of winning any prize is 1.86% in any one draw.

Subsequently, the next pertinent question is: How might I fare over an extended period? 

2,065 Draws with 49 Balls

To answer the question above, I carried out some experiments covering the period when Lotto was played with 49 balls and then drew a bar chart of the results^[10].

The bar chart shows that you are most likely to succeed between 31 and 45 times in 2,065 draws, with 38 the most probable at 6.50%.

Most prizes are likely to be £10 (or later £25, after the New Dawn^[11]) with a few Match 4 wins and possibly a Match 5 win, too. Winning a jackpot or Match 5 plus bonus prize is improbable, but not impossible; it becomes a reality only for some lucky players.

Looking at the total cost calculated below, clearly, you need to win at least one sizeable Match 5 prize to stand a chance of making a profit.

Total cost over 2,065 draws:  (1855 × £1) + (210 × £2) = £2,275

For example, if I had played the following numbers throughout (4, 7, 9, 23, 28, 37), I would have won prizes on 46 occasions, collecting a total of £582, but making me a loss of £1,693.

Lotto prizes won over 2,065 draws with the board: (4, 7, 9, 23, 28, 37).

Category	Prize Breakdown	Amount
Match 3	(40 × £10) + (4 × £25) = £400 + £100	£500
Match 4	£40 and £42	£82
Match 5	None	£0
Match 5+	None	£0
Match 6	None	£0
	Totals:	£582

This stark finding demonstrates how difficult it is to win randomly a sum of money that will be life-changing.

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The Lotto Experience

Step by step, let us go through the standard procedure when playing Lotto in the next available draw only, using a play slip in-store. It has applied since the National Lottery began.

1. Decide how many boards you wish to play.
2. Choose six numbers for each one.
3. Mark the play slip accordingly, clearly and unambiguously.
4. Give the play slip to the retailer with your stake.
5. The retailer accepts your payment, inserts your play slip into the reader on his machine.
6. The machine reads your play slip and returns it, along with a printed ticket. 

Shown below is my play-slip, stake of £5 and the retailer’s ticket to take part in the draw on Wednesday, 28 September 2005.

Unless the machine rejects your play slip due to an error, you will have made a successful official entry at this stage.

• Then, you await the draw and check your ticket against the results declared officially.
• Have you been lucky?
• Either you have won a prize by matching sufficient or all of the numbers, or you have not.
• If you have won nothing, your ticket is spent and worthless, which is the fate of most of them. Your current Lotto journey has ended without reward. You are in the company of many.
• For a small minority, things are different. How you receive payment depends upon the amount you have won. You should return to the retailer who will validate your ticket and pay small cash prizes. But, for more considerable sums, contact the National Lottery to check the eligibility. To learn how the National Lottery will settle payment with you, refer to its website for details.

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Example of Play

On Wednesday, 28 September 2005, I played five boards of Lotto in the hope of improving my chances of winning. You can see a copy of my play-slip, my stake of £5 and the ticket that the retailer gave me above.

For draw 1019, held that evening, the winning balls were 21, 32, 41, 42, 43 and 46, with 17 as the bonus ball. I did not match a single ball and lost £5.

It was as well that my losses were so low. Losing £5 is undesirable but not severe under normal circumstances. In a casino, some people playing on slot machines can quickly lose a lot of money. Although most people hope not to lose too often, losses are inherent in gambling.

Long Term Performance

Sometimes combinations of balls that fail in most draws succeed, making a usually worthless ticket valuable at that time.

Let us suppose that I had entered the same five Lotto lines in all draws using 49 balls between 19 November 1994 and 7 October 2015. i.e. 2,065 draws. How might I have prospered?

Expenditure

There is a slight complication in that Camelot doubled the price of a Lotto board during the period. We need to account for this change – see below.

1,855 draws	5 boards @ £1 per board, costing	£9,275
210 draws	5 boards @ £2 per board, costing	£2,100
2,065 draws	Total cost:	£11,375

Winnings

The table below summarises how much I might have won if I had played the same ticket in 2,065 draws. Also, it shows the breakdown of the prize money. With the most likely at the top, I have listed the outcomes in decreasing order of probability.

Outcomes observed in 2,065 draws using 49 balls – buying 5 Lotto boards per draw

ID	Match 3	Match 4	Match 5	Match 5+	Match 6	Probability	Count	Prizes
1	0	0	0	0	0	94.39	1,955	£0
4	1	0	0	0	0	3.142	69	£810
3	2	0	0	0	0	1.443	30	£690
2	3	0	0	0	0	0.5243	6	£225
9	4	0	0	0	0	0.1021	1	£40
7	3	1	0	0	0	5.750×10-2	1	£89
5	2	2	0	0	0	5.707×10-2	1	£76
6	4	1	0	0	0	3.690×10-2	1	£76
11	0	1	0	0	0	2.789×10-2	1	£43
					Others:	0.22% total	0	£0
					Totals:	100%	2,065[12]	£2,049

Of 38 outcomes possible with this ticket, nine appeared in total, and only 8 won a prize.

In this scenario, the probability of winning a prize in any tier is 0.0561 (or 5.61%, expressed as a percentage). i.e. (100% – 94.39%) = 5.61%.

Buying five boards instead of one has multiplied the probability of winning by three approximately, rather than producing the five-fold increase (5 × 1.86% = 9.3%) that we might have expected intuitively. This observation implies that the probability of winning a prize is not directly proportional to the number of boards bought but that some other subtle relationship applies.

Now, I have to make an admission! The five boards I chose were not random but were related to each other. In trying to make improvements, I made matters worse. Had I chosen five Lucky Dips, I would have fared better with a winning probability of 9.00% ± 0.13%, close to the 9.3% expected.

Summary

Maximum winnings:	£89
Total winnings:	£2,049
Loss:    £11,375 – £2,049	£9,326
Average prize over 110 successes:	£18.63
Average winnings over 2,065 draws:	£0.99

So much for prosperity with that plan of playing five boards! I would have made a significant loss.

Spread over 21 years, I might not have felt the full impact, unlike someone playing with more immediacy in a casino, for example. However, a loss is undoubtedly a loss regardless of its time frame.

Probability of Winning

The bar chart below shows the likelihood of success in 2,065 draws by persevering with my five boards. With a probability of 3.81% at its peak, the most likely result would be 115 successes; I had 110 – see above.

The width at half-maximum is a common way of measuring overall success. By this measure, between 104 and 128 wins account for more than 75% of those observed in practice.

The truth is that I would have been more successful if I had chosen five boards at random – see the table below.

Five Lotto boards chosen at random

(1)	14	21	28	30	37	44
(2)	10	11	20	25	30	37
(3)	5	10	22	23	40	41
(4)	2	3	8	22	37	43
(5)	10	14	16	18	36	46

They would have given me a probability of success of 8.99%, winning between 171 and 200 times at half-maximum and peaking at 185 times (rather than 115). In total, I would have collected £2,385 in prize money by spending the same amount on Lotto tickets, making me a net loss of (£11,375 – £2,385). i.e. £8,990

This finding encourages me since it implies that it is possible to achieve better results from the same expenditure of £5 per draw by tweaking the boards somehow. You can be sure that we shall follow this line of inquiry later since it looks promising.

What If?

It is pertinent to consider what might have happened if I had deposited the money I would have spent on the lottery weekly in a building society savings account^[13]. I have calculated the total amount I would have accrued by 14 October 2015, using several specimen interest rates.

Savings Interest Rate	Amount saved
1%	£11,396.40
2%	£11,417.85
3%	£11,439.35
4%	£11,460.91
5%	£11,482.52

Considering this alternative shows what a mountain we must climb to make reliable gains by playing the lottery. The result pours cold water on our dreams. They might be unrealistic with riches beyond our grasp.

Interest rates on savings plummeted sharply over the period due to the impact of the worldwide financial crisis that began in 2008. The bar chart^[14] below illustrates the change.

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Facing failure head-on

Repeated failure begs the question of what can you do to succeed. Perhaps, we can give luck a nudge? This question, or one like it, led you to my website, if I am not mistaken. Am I right?

We need to find a viable approach, rejecting the dubious and spurious along the way.

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Surfing the Internet for Advice

The World Wide Web has made research much more straightforward, although sometimes not always for the best. As a springboard, it makes an excellent tool with which to begin, but we must take care not to become complacent and accept only superficial answers to the questions we ask. Therefore, we must be discerning.

Early in the history of the National Lottery before the New Dawn, I did a quick trawl of the internet using terms like “how to win the lottery”. As I expected, it threw up many results – some of a very doubtful value, most notably when I added the word “guaranteed” to my search.

Some results contained advice and comments from journalists and writers with a particular interest in lotteries. Some advice was tongue-in-cheek, but in many cases, the authors were trying to throw some light on certain aspects, such as the peculiar behaviour of players, and events that seem bizarre, to attract readers’ attention.

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Early Advice for Players

I have prepared a list of 26 pieces of advice that I took from several websites and books. The order is not significant, nor have I verified any advice given. I have included the counsel because it attracted my attention, whether serious or frivolous.

1. Never spend more money than you can afford to lose.
2. Buy Lucky Dips.
3. Choose numbers yourself; do not buy Lucky Dips.
4. Try to take part in every draw even if you only buy one board.
5. You should keep your ticket in a safe place that is known to you; do not lose it.
6. Check your ticket against the published results carefully.
7. If you have won a prize, claim before the deadline has expired. You have 180 days after the draw has taken place to file your claim before you forfeit your prize.
8. Open an account with the National Lottery and buy your tickets online. If you do this, Camelot will check your tickets and will notify you automatically if you have won a prize.
9. Adopt a system of your own and stick to it.
10. Buy more boards than usual when there is a rollover.
11. Play only when there is a rollover.
12. Join a syndicate to spread the financial burden.
13. Do not join a syndicate since you will have to share the winnings^[15].
14. Never base your selection entirely on birthdays, since prizes are likely to be extremely low.
15. Avoid picking a board that contains small prime numbers^[16], especially 7.
16. Avoid multiples of small numbers^[17].
17. Do not make patterns on the play slip or construct arithmetic patterns^[18] when choosing your numbers.
18. Pick a board with 2 or 3 consecutive numbers. e.g. 11, 15, 24, 39, 40, 48.
19. Do not squash the numbers on each board too closely – the difference^[19] between the largest and smallest should be 25, at least.
20. Ensure that the numbers comprising each board add up^[20] to more than 177.
21. It is better to buy 20 boards in one draw than one board on 20 separate occasions.
22. Trust in cosmic forces. e.g. Look into a crystal ball, interpret dreams, or use clairvoyance.
23. Move to Dumfries in Scotland, which has one lottery millionaire for every 8,288 adults.
24. Include 38 in your selection but avoid 13. The number 38 has been drawn more often than any other so far, and 13 less frequently than all others.
25. Take no notice of the results of previous draws. The balls are inanimate objects with no sense of their history. They do not have form like racehorses. Every combination of 6 numbers has an equal chance of being drawn^[21], and there are 13,983,816 of them.
26. Use a Perm
    Players who play several boards per Lotto draw regularly use a perm^[22]. To play, you pick more than six numbers and then construct Lotto boards using six of them at a time. The cost of covering all the combinations possible rises quickly with the overall number chosen^[23]. Reduced perms are cheaper, but coverage is compromised. Avoiding some combinations may mean missing out on some prizes.

Finally, there is what might be loosely termed a gambler’s prayer. It stems from a catchphrase used often by Bob Monkhouse during his tenure as host of The National Lottery Live show broadcast on Saturday evenings on BBC1 and BBC One between 1996 and 1998.

This funny catchphrase carries a faint echo of a supposed long-standing link between the divine and humanity.

I know I’m a sinner, but make me a winner!

Bob Monkhouse on The National Lottery Live show

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Devising a Strategy

For many people, playing one board per game is not enough. They spend more to improve their chances.

If you play for fun and to help Good Causes, staking a pound or two^[24] per draw regularly in the slight hope of winning a prize is neither here nor there. It is of little consequence if you lose since this expense is almost insignificant to most people.

However, matters are not so straightforward for the more seriously minded player. i.e. a gambler. We face a tricky question to answer. How much should be spent to make a significant improvement?

Unfortunately, many players take an over-optimistic view of their chances of success. They expect to win higher prizes and win more often when they increase their stakes. Often, there is disappointment and frustration when the winnings (or rather, the lack of them!) fail to match expectations with a danger that more money will be committed to seeking an imminent but elusive, big win to compensate.

Undoubtedly, higher stakes are less affordable. Unlike National Savings Premium Bonds, the stake is forfeit if we fail. Regular players of Lotto should question whether they can afford to lose the money, given only a tiny proportion of boards win prizes.

Our Goal

As far as we are concerned, although an occasional win might bring a feeling of well-being and satisfaction, a winner is a player who collects more money in prizes than they have staked, which is no mean feat!

In devising a strategy, we seek to minimise risk and expenditure but maximise gain, which will not be easy. Two approaches spring to mind.

1. Try to find sets of six numbers that will always win a prize, however small.
2. Acknowledging that winning is rare, try to maximise a good result should one occur.

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Buy More Boards

Playing a single board in every Lotto draw is unlikely to result in a substantial gain for most players; success is not guaranteed. The cost is minimal, rising from £104 to £208 per year based upon 52 weeks with the New Dawn, playing a single board on Wednesdays and Saturdays.

But How Many?

There arises the question of how much to spend, weighed against what can be afforded. How can we make that decision? If I buy two boards per draw instead of one, will I double my chances of winning a prize? i.e. achieving 3.72% rather than 1.86%.

Outcomes versus number of prizes

Playing more than one board per draw raises the possibility of winning more than one prize. Therefore, it becomes clear that we need to distinguish between a successful outcome and the number of winning boards.

Successful Outcomes

A successful outcome implies winning one or more prizes. From now onwards, we shall base our discussion primarily on successful outcomes rather than focus on the number of prizes won.

Suppose I buy 54 boards; multiplying 1.86% by 54 gives 100%. Does this mean that winning is guaranteed? I am afraid not.

What’s Going On?

To understand what is happening:

1. Let us choose five boards randomly from 49 balls.
2. Compare them against 43 x ⁴⁹C₆ combinations of the bonus and main balls, making a tally of each outcome.
3. Repeat the exercise 100 times.

Repeat steps 1 to 3 several times using different numbers of boards, build a table (see below), then plot the results from columns 1 and 2 on a graph – see the blue curved line.

Mean Probability of Winning and Number of Outcomes of ‘n’ Lucky Dips over 100 trials.

Boards (N)	Probability of Winning (%)	Std Deviation (%)	Outcomes	Std Deviation
0	0	0	0	0
1	1.86	0	6	0
5	9.02	± 0.10	13	± 3
10	17.15	± 0.29	21	± 6
15	24.58	± 0.41	28	± 6
20	31.42	± 0.55	34	± 7
25	37.49	± 0.59	41	± 8
30	43.12	± 0.65	47	± 8
35	48.34	± 0.72	50	± 9
40	53.00	± 0.76	55	± 9
45	57.13	± 0.74	63	± 11
50	61.03	± 0.70	67	± 11
55	64.42	± 0.79	73	± 11
60	67.71	± 0.72	79	± 13
65	70.57	± 0.79	84	± 11
70	73.20	± 0.78	90	± 15
75	75.60	± 0.69	94	± 13
80	77.78	± 0.68	102	± 15
85	79.83	± 0.68	105	± 15
90	81.68	± 0.74	109	± 13
95	83.23	± 0.60	115	± 14
100	84.83	± 0.56	118	± 15
105	86.12	± 0.56	124	± 16
120	89.46	± 0.52	144	± 19
150	94.03	± 0.41	174	± 20
163	95.33	± 0.27	189	± 21
200	97.65	± 0.22	229	± 27

Looking at the blue curve, you can see that it rises steeply at first, then slowly approaches a plateau without reaching 100%^[25]. The curve’s path closely matches the red straight line for less than ten boards, which plots multiples of 1.86%. i.e. the probability of success playing one board. Then, it begins to diverge.

Only six outcomes are possible with a single board – 5 winning and one losing; the latter dominates. The number of outcomes increases sharply as more boards are played.

The following graph illustrates the growth with the standard deviation^[26], shown as hairline error bars, and plotted from columns 1, 4 and 5 of the table. Note that there is always one outcome for each data point that wins nothing; the others win various prizes, often more than one.

For instance, the number of outcomes for 20 boards is 34 ± 7. i.e. from 27 to 41.

Cover All Combinations

Now we enter the world of fantasy which is made possible by simulation.

With 49 balls, there are 13,983,816 combinations of the six main numbers. Initially, the cost of covering them all was £13,983,816, but this doubled to £27,967,632 after the New Dawn. Winning is guaranteed, but there will be a sharing of the total prize fund.

Practical Difficulties

Setting aside that it is unaffordable, many practical problems are associated with this scheme.

1. You would have the daunting task of completing 1,997,688 play slips accurately unless you could persuade Camelot to accept a letter of intent to play every available combination instead. Otherwise, it would be a tedious manual process likely to be riddled with many mistakes.
2. How long would it take to submit the play slips for a single draw? The answer is 116 days through one terminal at the rate of one every 5 seconds. The time is unrealistic since there are two draws per week.
3. The retailers would receive a whopping commission. At 10p per board, it would feel like winning the lottery! Indeed, that is our aim.
4. Even winning presents a formidable problem. How would you identify the winning tickets? No single retailer would be able to cope.
5. This scenario is unworkable without a concession from Camelot to be treated as a special case. Otherwise, you would be buried in paper!
   
   

   

6. To add insult to injury, you would be unlikely to make a profit. Losses would be catastrophic and unsustainable.

The inescapable conclusion is that buying all combinations has never been viable – before the New Dawn or after and not now^[27] for sure. Enhanced Lotto has more combinations with 59 balls. There is no point; it is a waste of time, effort and money, leading not to riches but impoverishment.

It means that no multi-millionaire can hijack the lottery to increase their wealth effectively and so spoil the chances of others. While there is a guarantee of winning many prizes, hefty losses wipe out any prospective gains in almost all cases.

260,624 combinations win prizes; 13,723,192 do not. Can we improve this ratio? Yes, we can, but the real question is how much will it favour our cause?

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Current situation

The National Lottery has evolved since then, and now you can buy tickets readily:

• on the internet using a customer account with the National Lottery;
• with a Play Slip or Fast Play Card in a supermarket or shop;
• by Direct Debit, or
• through the National Lottery App on your smartphone.

A choice of six games

Presently, you can play six National Lottery games by staking a modest amount per play, depending on the game, provided that you are aged 18 years or over.

National Lottery Games available now

Game	Cost per play	Held Every
Lotto	£2.00	Wednesday and Saturday
Thunderball	£1.00	Tuesday, Wednesday, Friday and Saturday
Lotto Hotpicks	£1.00	Wednesday and Saturday
Euromillions	£2.50	Tuesday and Friday
Euromillions Hotpicks	£1.50	Tuesday and Friday
Set for Life	£1.50	Monday and Thursday

The current schedule means that you can play a National Lottery game every day of the week but Sunday if you want.

Each game is different with several prize tiers, some fixed, some variable and all tax-free. The games allow players to win top prizes ranging from £350,000 to several million pounds. Some games are won more readily than others. In general, higher returns are more challenging to obtain.

The table below shows the games with prize tiers of £1,000,000 or more to help you decide which games suit your intentions.

National Lottery Games with Prizes of £1 million or more

Game	Prize Tier	Prize	Odds
Lotto	Match 6	Share of at least £2,800,000 million	1 in 45,057,474
Lotto	Match 5 plus Bonus Ball	£1,000,000	1 in 7,509,578
Euromillions	Match 5 plus 2 Lucky Stars	Share of at least €17 million	1 in 139,838,160
Millionaire Maker	Raffle	One winner of £1,000,000	1 in 3,570,000
Euromillions Hotpicks	Pick 5	£1,000,000	1 in 2,118,760
Set for Life	Match 5 plus Life Ball	£10,000 per month for 30 years	1 in 15,339,390

The Set for Life jackpot is a 30-year annuity of £10,000 per month instead of a lump sum, common to the other games. Therefore, the game targets younger players specifically. Older players who may not live long enough to benefit fully from their annuity should probably avoid this game.

Although Lotto is the primary focus of my website, I wanted to make it clear that other games in the National Lottery portfolio offer a route to winning £1,000,000, too. Both Lotto and Euromillions have two prize tiers available with this amount and more for a stake of £2 and £2.50, respectively, but you should be aware that Lotto is my firm favourite.

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How can I win the National Lottery?

It is such a simple but burning question. However, there are nuances, and the question can be tricky to answer satisfactorily, like many similar questions.

What is your motivation?

The quality of the answer depends upon your degree of motivation.

• Are you just slightly curious, implying that a simple answer will suffice?
• Or, are you searching purposefully for a way to win large amounts that will change your life?

These two extremes lie at the ends of a broad spectrum of behaviour between an occasional light-hearted, harmless flutter and compulsive gambling.

Some pitfalls of gambling

Be under no illusions. To take part, you have to spend money to wager. It is the nature of the contract.

Playing the National Lottery is a form of gambling. The outcomes are uncertain; sometimes, you win, but mostly you lose. It is what happens! You should be clear in your mind about that.

Gambling can so quickly become addictive and destructive if you lose control. Never get so desperate that you must win!

By all means, if you choose to play, be focussed and systematic, but please take care not to jeopardise your financial security nor harm your mental health, and never gamble more than you can afford to lose.

Carry on undaunted but aware

Read on if you want to keep things on an even keel. Learn how to play responsibly to achieve better outcomes with a clear mind and your eyes wide open to the consequences.

With large, attractive prizes, you can support good causes, enjoy the thrill of taking part on a manageable budget and win, even with the unfavourable odds against you.

Such is the kind of answer I want. We can get good results based solely on mathematical and statistical experiments and avoid the pitfalls of marketing hyperbole and bogus claims. Get-rich-quickly schemes have no place here. Shall we resume?

Regulation keeps us safe

Losing large amounts of money is something you would not wish to repeat too often. However, a loss is inherent in gambling. There are obstacles placed to prevent misuse and unbridled play by problem gamblers. They include:

• Limiting the number of draws per week. e.g. Lotto has 2.
• Imposing cash limits on the amount spent weekly through the internet. The most you can add to your National Lottery account is now £350 per week.
• With seven boards per play slip, submitting many play slips to the reader in-store to pay for a large bet would be time-consuming and attract attention, to say nothing of the time taken to complete them accurately. Probably, this would be enough in itself to deter all but the most determined of players.

Of course, there are impediments to excessive and reckless play in other settings too, but they are beyond our concern here. Suffice it to say that Lotto does not lend itself so readily to excess as some other forms of gambling. You can live the dream without it becoming a nightmare.

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Where Do We Stand Now?

The discussion so far has related mainly to the original game of Lotto played with 49 balls, but things have moved on. What is the point of harping on about a game that you can play no longer? Furthermore, how does any of this relate to the current situation?

Recap

After remaining stable for 19 years, the National Lottery operator, Camelot, changed Lotto, affecting the dynamics of the game profoundly.

• In October 2013, Camelot modified the distribution of the total prize fund among the prize tiers and added raffle prizes. Most noticeably, the basic award for matching three numbers rose from £10 to £25.
• Two years later, Camelot enhanced Lotto to play with 59 balls instead of 49.

Now, it is much more difficult to win any prize, discounting the award of a free Lucky Dip in a future draw by matching just two numbers^[28].

To answer the two questions posed earlier:

1. I had accumulated a large body of historical data that applied to Lotto played with 49 balls, covering 2,065 draws; there was too much to discard.
2. Many lotteries in the world still use 49 balls; some are similar to the UK National Lottery in their operation.
3. It is a sound general principle in science and mathematics to study simple cases first and then progress to greater complexity in due course. i.e. Start by considering 49 balls, then move on to 59. Often, some conclusions remain the same.

However, Lotto has changed irrevocably as a result. The two versions are distinct in many ways.

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How can I win the National Lottery? – revisited

Realistically, this is a difficult question to answer; there are nuances, as we have seen.

Here are some suggestions for you to consider.

1. First and foremost, prioritise your cost of living expenses. If you cannot meet them, don’t play but wait until you can.
2. Play regularly and deliberately but make it fun. Be consistent. It is better not to play out of desperation. Remember that you are helping good causes and might win. There are substantial prizes on offer in every draw. Sometimes you will win, but mostly you will lose.
3. Set a budget that you can afford that does not jeopardise your financial security.
4. By making modest changes to how you play, you can achieve better outcomes, whatever the size of your budget. 

As this website matures and becomes more comprehensive, you will see how to proceed more clearly. It bears repeating that you can live the dream without it becoming a nightmare.

Good luck. Watch this space!

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Notes

• [1] Revived in 2018, Jeremy Clarkson replaced Chris Tarrant as host. The show produced a total of six millionaires legitimately. A seventh, Major Charles Ingram, was later disqualified, suspected of cheating.
• [2] Originally, the Good Causes were: Arts, Charities, Heritage, Millennium Projects and Sports.
• [3] Principle of Additionality: the lottery should not relieve the burden from the taxpayer but instead provide additional funding.
• [4] Nowadays, the Low Countries comprise Belgium, The Netherlands and Luxembourg.
• [5] Players bet on the outcomes of a fixture list of top-level Association Football matches held on Saturdays during the season. The most popular game was the Treble Chance.
• [6] Littlewoods, Vernons and Zetters mainly.
• [7] Ticket sales determine the total amount of prize money, but occasionally, Camelot holds a Superdraw, boosting the value of the prize fund allocated to one category, usually the jackpot (Match 6).
• [8] Any draw that follows one with no Match 6 winners is called a Rollover. Usually, the previous prize pool is added to the next Match 6 prize, enlarging the jackpot.
• [9] From now on, we shall account for the bonus ball since it generates outcomes that we ought to consider.
• [10] The Binomial Distribution function allows us to calculate the probability of winning multiple times over several attempts. Fortunately, to simplify things, the Binomial Distribution function is available in Microsoft Excel through the worksheet function BINOM.DIST.
• [11] Camelot created a New Dawn for Lotto from 5 October 2013 by making changes to reinvigorate the game. The board price doubled to £2, and the Match 3 prize rose from £10 to £25. Also, raffle prizes of £20,000 and £1 million were added to spice up the higher tiers and arouse interest.
• [12] I would have won prizes in 110 of the 2,065 draws, and nothing in the remaining 1,955.
• [13] This brings to mind an account I read of Margaret Thatcher reproaching a woman she encountered buying a National Lottery ticket in a newsagent, urging her not to waste her precious coin. “Don’t waste it, dear, you should invest that pound instead. Invest it in the future of British manufacturing and industry. Watch your savings grow, dear”. Did this really happen, or is it just an urban myth?
• [14] I obtained a list of savings interest rates from swanlowpark stats for savers.
• [15] According to Camelot, syndicates win approximately 1 in 7 jackpots over £1 million.
• [16] A prime number is a number, greater than 1, that is divisible only by itself or 1 without a remainder. The prime numbers available on an original Lotto board are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. The small prime numbers appear in bold print.
• [17] e.g. 3, 9, 12, 36, 45, 48 – contains multiples of 3.
  5, 10, 15, 20, 25, 30 – contains multiples of 5.
• [18] e.g. 1, 8, 15, 22, 29, 36 – here, seven separates each number in the sequence (an arithmetic progression).
  1, 4, 9, 16, 25, 36 – the numbers are squares of 1 to 6 (a geometrical progression).
• [19] In the example quoted in item 18, the difference is (48 – 11) = 37.
• [20] In the example quoted in item 18, the sum is: 11+15+24+39+40+48 = 177.
• [21] Even 1, 2, 3, 4, 5, 6! Believe it or not, Camelot has reported that about 10,000 players use this combination in every draw. The jackpot would be ridiculously small if these numbers were to appear. Even with a guaranteed jackpot of £10 million, jackpot winners would be lucky to receive £1,000 each.
• [22] The term perm (short for permutations) is a misnomer since it would imply that the order in which the items are chosen is significant. For Lotto, the order in which the balls appear is irrelevant. Operators of the Football Pools in the UK used to promote perms to help punters. e.g. through Littlewoods Lit-Plans and Perms. To date, Camelot has made no provision whatsoever for perms. It is easy to see why they have not. A line in a Lit-Plan was a penny or fraction thereof but, each Lotto board cost £1 initially, making even the simplest perm expensive and at odds with the policy of discouraging gambling to excess.
• [23] For example, there are 28 ways of combining eight balls six at a time, and 84 ways of combining nine balls six at a time. You would need to play 28 and 84 boards respectively to cover these combinations.
• [24] On 5 October 2013, the cost of entry rose from £1 to £2 per board for Lotto, marking the beginning of the New Dawn for Lotto. This was the first rise in price since the National Lottery began in November 1994.
• [25] The curve reaches 100% around 800 boards per draw.
• [26] The standard deviation is a statistic that measures how a set of values are dispersed about the mean (average). The smaller the standard deviation, the closer the values are to the mean.
• [27] Enhanced Lotto has more combinations with 59 balls. i.e. ⁵⁹C₆ combinations ≡ 45,057,474. Buying all of them would cost a staggering £90,114,948!
• [28] Some people dispute whether this is a real prize! It seems little more than a sop to players to give the illusion of a better chance of winning when the odds of winning a cash prize have worsened actually.

Revision date: 18 December 2021