I. INTRODUCTION1. The game

A lottery is a form of gambling which involves the drawing of lots for a prize. Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. In several countries, lotteries are legalized by the governments themselves.

The Hong Kong Mark 6 lottery is the principal lottery game found in Hong Kong and is run by the Hong Kong Jockey Club – founded back in 1884 – and is one of the largest horse racing organizations in the world.

The HKJC is authorized by the Hong Kong Government to operate the Hong Kong Mark 6 alongside its primary business of horse racing – the most popular spectator sport throughout Hong Kong.

The Jockey Club operates as a non-profit organization and donates approximately HK $1 billion annually, making them one of the most important philanthropic contributors worldwide. Additionally, the Hong Kong Jockey Club is Hong Kong’s largest taxpayer, paying about 6.5% of all federal taxes.

The largest Mark Six Lotto jackpot, HK$133.5 million ($17.2 million), was split between three winners in May 2011.  Undoubtedly this is an impressive sum.  

2. Hong Kong Mark Six – Overview

The Mark Six Lottery is a traditional jackpot style lotto game which is incredibly popular amongst the people of Hong Kong. It was first launched back in 1975 and is a standard part of everyday life in Hong Kong with a large number of the population regularly playing.

The Hong Kong Mark Six is administered by the HKJC Lotteries Ltd., which is a subsidiary of the famous Hong Kong Jockey Club.

3. Mark Six Lotto Statistics

The Hong Kong Jockey Club only takes a fraction of the lottery proceeds, allocating the rest for prize money and charity. Fifty four of lottery sales money goes directly into the prize pool, of which 9% is allocated to the Snowball Fund.  

The funds generated by the lottery benefit both the government and local charities. 15% of all proceeds go straight to the Lotteries Fund, which is distributed amongst social

welfare capital projects in Hong Kong. 25% of all funds are used to pay the lottery duty to the government and the Hong Kong Jockey Club keeps 6% as commission.

The lottery’s most frequently drawn numbers are currently: 4, 12, 20, 46, and 49.

The lottery’s most least frequent numbers are currently: 1, 14, 23, 27, and 32.

4. Mark Six Anecdotes

Lucky Patriotism- The people of Hong Kong love the Mark Six so much that it is often said that one who does not enter the lottery is not a true citizen. Unlike other Asian lottery draws, Hong Kong broadcasts the drawing live on public television which creates national interest and making it a favorite in the region. When the jackpot rises to staggering heights after weeks of rollovers, such as in Spring 2011, long lines form at lottery offices, oftentimes wrapping around the block. Many superstitious Hong Kong residents travel to the other side of the city to purchase their tickets from an office where a previous winning ticket was bought.

II. STASISTIC OF TOTO LOTTERY1. Mark Six Lotto Rules

The Mark Six Lotto utilizes a traditional single drum lottery system and offers a bonus ball, called an extra number. To play, participants select 6 numbers from a guess range of 1 to 49. During the draw, seven numbers are randomly selected from the single transparent cylinder. The first six are called drawn numbers and the seventh bonus number is called the extra number.

The bonus number (extra number) is drawn from the same drum as the regular guess set and counts towards the second, fourth and six prize categories. Players can win the jackpot regardless of the bonus number by correctly guessing 6/49 numbers.

Four or five times a year, the Hong Kong Mark Six Lotto holds seasonal Snowball Draws. On these occasions, extra funds are added to the jackpot. Part of each Mark Six ticket price is allocated for the Snowball Pool and this money is added to the first prize on designated dates. Snowball draws are traditionally held during seasonal festivals, including Chinese New Year, Easter, Dragon Boat Festival, Mid-Autumn Festival and Christmas.

Hong Kong Mark Six drawings are held on Tuesdays, Thursdays, and Saturdays at 13:30 GMT. The six drawn balls and one extra ball are randomly selected from a plastic cylinder and broadcast on live television in Hong Kong. Mark Six invites notable citizens, justices of the peace, and beneficiaries of their lottery charity fund to supervise the televised drawing.

2. How it Works

The Hong Kong Mark Six Lottery game uses what’s called a 6/49 matrix which means that when playing the Mark 6 – you need to select 6 numbers from a number range of 1 to

49. If you match all 6 numbers drawn then you will win a 1st division prize – the Mark 6 jackpot.

For every – game 7 numbers are drawn using a traditional ball drawing machine that contains 49 numbers. Firstly the 6 main numbers are drawn then a 7th number – the Extra Number – which is used to determine winners on prize levels 2, 4 and 6.

As well as the jackpot itself – there are 6 more ways that you can win on the Hong Kong Mark Six – which means that are a very large number of prizes to be won 3 times every single week.

The Mark 6 jackpot prize starts off at HK$ 8 MILLION and will rollover – rising in size each time it is not won. With 3 potential rollover draws every week and no limit to how big it can grow – some incredibly large Mark 6 jackpot figures have been won.

A Quick Pick facility is available when you play the Hong Kong Lottery very much the same as the “Lucky Dip” option that is used in the UK National Lottery or Europe’s Euro Millions or nearly all USA Lottery games – which means that you can ask the lottery retailer or computer to randomly select all your numbers for you.

Mark Six is a lottery style game where players guess what numbers will be drawn out of a lottery machine. The lottery machine is a transparent plastic cylinder which contains colored balls numbered 1 to 49. The cylinder is rotated to provide randomization in the drawing process. Each drawing occurs on 9:30PM (Hong Kong Time) every Tuesday, Thursday, and Sunday, while bets are accepted until 15 minutes prior to the drawing.

Players choose six numbers out of a possible 49. Each selection of the numbers costs 10 HKD and is one selection of the results of the lottery draw. In the draw, 7 numbers are drawn. The first six numbers drawn are called the "drawn numbers". The last one drawn is called the "extra number". Often, in Cantonese this number is called a 'half number'.

The cost of playing the Mark 6 Lottery is HK$ 10 for one entry.

So – playing the Mark 6 is very easy – simply select your own 6 numbers or request them to be automatically chosen for you by either the computer or HKJC agent's random number generator.

The front of a used Mark Six ticket

The back of a used Mark Six ticket

3. Who Can Play?

As with most lotteries around the world – previously only citizens living in the country itself were allowed to play in any of the Hong Kong Lotto games including the Mark Six Lottery – you used to have to purchase

your Hong Kong Lotto tickets from an authorized HKJC retailer based within Hong Kong.

Today though – this is not a concern as there are a good number of online lottery ticket sales retailers such as Coral and The Lotter who are both authorized and genuine – you are now easily able to select your Mark 6 numbers online and purchase your Mark 6 tickets from almost anywhere in the world that you may be living.

This is good news of course if you live outside of Hong Kong and want to play the Mark 6 Lottery and ensure your entry into the next draw or even if you want to have the convenience and ease of being able to buy lottery tickets online from your own home.

You need to be 18 years of age to be eligible to purchase a ticket for any Hong Kong Lotto game including the Hong Kong Mark 6.

4. How to Play Mark Six [1]

In each Mark Six draw, the Mark Six Draw Machine (Figure 1) will randomly draw six numbers from 1 to 49, called the “Drawn Numbers”, by letting go six of the 49 balls that are inside the machine (Figure 2), with each ball representing a different number.

After that the machine will draw another number, called the “Extra Number”, to allow some winners to get a bigger prize. In each unit bet, costing five dollars, the bettors choose six numbers before the Mark Six draw. If any three or more of the chosen numbers match the Drawn Numbers, prizes will be awarded. The more chosen numbers match the Drawn Numbers and the Extra Number, the bigger the prize is.

5. The Probability to Win the First Prize

In order to win the Mark Six first prize, all of your chosen numbers have to match the six Drawn Numbers. No doubt it is a rare case -but how rare is it? When the Mark Six Draw Machine draws the first number, out of the 49 possible results, six of them will match the chosen numbers. Therefore the probability that the first Drawn Number matches any chosen number, denoted by P1, equals 6/49.

When the machine draws the second number, out of the 48 possible results (it is 48 because one ball has previously left the machine), five of them will match the chosen number (it is now five because one of the chosen numbers has already been matched). So the probability that the second Drawn Number matches any chosen number, denoted by P2, equals 5/48. After using the same technique to find out P3, P4, P5, and P6, it becomes clear that the probability of all the Drawn Numbers matching the chosen number, i.e. the probability of winning the first prize, equals

This probability is so small that one needs to bet nearly 14 million times on average in order to win the first prize just once! The probability of winning other prizes can be calculated by using similar technique, and are listed in Table 1 for reference.

Misconception about Mark Six Many bettors like to study the statistics of the Mark Six lottery (Figure 3) to help them predict the results of the coming draw. Suppose the number 20 has been drawn consecutively in the past ten lotteries. Some bettors will think, “The number 20 is on fire and it is very likely to be drawn again.” Others will say, “The number 20 has already exhausted all its luck and it is unlikely to be drawn again.” Who are correct?

In fact, both are wrong. As the Mark Six Draw Machine and the balls inside “do not contain any memory”, each draw result does not depend on the previous results and is completely random. Therefore studying the statistics to predict results will not help at all.

Conclusion

After calculating the probability of winning different prizes of Mark Six, it can be seen that Mark Six actually is not a fair lottery. Take the first prize as an example. It has been shown before that it requires, on average, 14 million bets, i.e. 70 million dollars, to win the first prize once, while the prize money is usually only around 10 million dollars. As studying the statistics does not help predict draw results, gambling on the long term will definitely result in loss of money. Therefore do not indulge in betting Mark Six!