# Mark Six

For a former lottery in Hong Kong which is known as "多重彩" in Chinese, see Mark Six (1975–1976).

Mark Six (Chinese: 六合彩) is a lottery betting organised by the Hong Kong Jockey Club.

Mark Six advertisement outside a betting branch of Hong Kong Jockey Club

## The game

The front of a used Mark Six ticket
The back of a used Mark Six ticket

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 coloured balls numbered 1 to 49. The cylinder is rotated to provide randomisation 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'.

As of 2011, prizes are awarded as follows:

Prize – Numbers color chosen
1st division prize – All six drawn numbers
2nd division prize – Five drawn numbers and the extra number
3rd division prize – Five drawn numbers
4th division prize – Four drawn numbers and the extra number
5th division prize – Four drawn numbers
6th division prize – Three drawn numbers and the extra number
7th division prize – Three drawn numbers

The payout for the 1st – 3rd division prizes depend on the sales of that draw, and the presence of Jackpots and Snowball (see below). The 1st prize is guaranteed to be at least HK$8 million. Where there are multiple winners for a division, the prize is shared. The lower order prizes are fixed as shown below: 4th division prize – Fixed at HK$9,600
5th division prize – Fixed at HK$640 6th division prize – Fixed at HK$320
7th division prize – Fixed at HK$40 ## Jackpots and Snowballs If nobody wins the 1st and 2nd prizes, the money that would have been paid out for the prizes will be added to a Jackpot (多寶獎) in the next draw. If there are winners of the first prize, these winners take the jackpot fund as well. If again there is no winner, the process continues until there is, and in such cases 1st division winnings can build up to about HKD$60 million (compared to the normal HKD$8 million 1st division prize), as seen several times in 2004 and 2005. For each draw, a certain percentage (see below for details) of the entry money is deducted and placed into a Snowball Pool. On selected draws, the Snowball Pool is added to the 1st division prize as well. These draws are known as Snowball Draws (金多寶). The HKJC decides which draws are snowball draws. Usually the date is chosen to match a public holiday or festival, and the draw is named accordingly. For example: These draws are very popular due to their large 1st division prizes. ## Allocation of entry money Similar to most lottery systems in the world, Mark Six is used as a method of raising money for the Hong Kong government. The game is also used to raise money for charitable purposes. Every dollar spent on Mark Six is distributed as follows: 25% – Lottery Duty – paid to the Government 15% – Lotteries Fund – used for financing social welfare capital projects 6% – Commission – used to cover operating costs of the HKJC 54% – Prize Fund – used to fund prize As with all lottery systems, the expected winnings is lower than the entry cost, making this an unfair game. In the presence of Jackpots or Snowballs, the payout ratio of Mark Six can be much higher. The amounts required to pay the guaranteed prizes (divisions 4–7) are deducted first from the prize pool. Then, 7% is placed into the snowball fund and the remainder is shared as follows: 1st division prize – 45% x ( Prize Fund – total amount payable to 4th, 5th, 6th & 7th division prizes – Snowball Deduction* ) / winning units 2nd division prize – 15% x ( Prize Fund – total amount payable to 4th, 5th, 6th & 7th division prizes – Snowball Deduction* ) / winning units 3rd division prize – 40% x ( Prize Fund – total amount payable to 4th, 5th, 6th & 7th division prizes – Snowball Deduction* ) / winning units • Effective from 1 July 2006, Snowball Deduction means a sum equivalent to 9% x (Prize Fund – total amount payable to 4th, 5th, 6th & 7th division prizes). Note: The third division prize is allocated a larger proportion of the prize fund than the second division prize, but the winnings for this division are usually much smaller since many more people win the third division prize than the second. ## Winning probability As of 2011, the winning probability for each prize division is as follows:  Prize Criteria Dividend (HKD) Probability Expected investment for a win (HKD) 1st Division All 6 drawn numbers 45% of prize fund after deduction $\frac{1}{{49 \choose 6}} = \frac{1}{13,983,816}$ 139,838,160 2nd Division 5 out of 6 drawn numbers, plus the extra number 15% of prize fund after deduction $\frac{{6 \choose 5}}{{49 \choose 6}} = \frac{1}{2,330,636}$ 23,306,360 3rd Division 5 out of 6 drawn numbers 40% of prize fund after deduction $\frac{{6 \choose 5}{42 \choose 1}}{{49 \choose 6}}\approx\frac{1}{55,491.33}$ 554,913 4th Division 4 out of 6 drawn numbers, plus the extra number 9,600 $\frac{{6 \choose 4}{42 \choose 1}}{{49 \choose 6}}\approx\frac{1}{22,196.53}$ 221,965 (23 times the dividend) 5th Division 4 out of 6 drawn numbers 640 $\frac{{6 \choose 4}{42 \choose 2}}{{49 \choose 6}}\approx\frac{1}{1,082.76}$ 10,828 (17 times the dividend) 6th Division 3 out of 6 drawn numbers, plus the extra number 320 $\frac{{6 \choose 3}{42 \choose 2}}{{49 \choose 6}}\approx\frac{1}{812.07}$ 8,130 (25 times the dividend) 7th Division 3 out of 6 drawn numbers 40 $\frac{{6 \choose 3}{42 \choose 3}}{{49 \choose 6}}\approx\frac{1}{56.7}$ 567 (15 times the dividend) The overall odds of Mark Six, i.e. the probability of winning something is approximately 1:53.655. Compared to the biggest two lotteries available in the United States, Powerball (the overall odds are approximately 1:35) and Mega Millions (the overall odds are approximately 1:40), players have lower chance to win a prize in Mark Six. The odds of getting 2 out of 6 drawn numbers plus the extra number are approximately 1 in 81.207, less likely than getting 3 out of 6 drawn numbers. However, there is no prize for only getting 2 out of 6 drawn numbers plus the extra number, which explains why Mark Six has lower overall odds. If one day this became the 8th division of the game, the overall odds of Mark Six would reduce to 1:32.208, comparable to counterparts in the United States.  Prize Criteria Dividend (HKD) Probability Expected investment for a win (HKD) Imaginary 8th Division 2 out of 6 drawn numbers, plus the extra number N/A $\frac{{6 \choose 2}{42 \choose 3}}{{49 \choose 6}}\approx\frac{1}{81.207}$ N/A Imaginary 9th Division 2 out of 6 drawn numbers N/A $\frac{{6 \choose 2}{42 \choose 4}}{{49 \choose 6}}\approx\frac{1}{8.33}$ N/A ## Fairness The draws are broadcast live by one of the two free-to-air television stations in Hong Kong. To ensure the fairness of the draws, the HKJC invites outsiders to supervise the draw. They usually invite 2–3 people of high social status. For example, Justices of the Peace are often invited. A few years ago, the HKJC started to invite representatives from the beneficiaries of its lottery fund as supervisors. ## Popularity The game is immensely popular in Hong Kong. It is considered normal for Hong Kong people to play Mark Six. When the prize jackpot is very high, it is not uncommon for a total in excess of HKD$120 million to be spent on Mark Six (this is 24 million games from a total population of 7 million in Hong Kong).

Although the game is only available in Hong Kong, some people play it illegally in other countries, particularly in Mainland China. The reason for such popularity is because the draw takes place in Hong Kong and is broadcast live on television to ensure that no one can manipulate the draw. This is contrary to many lotteries in mainland China, where the draws are not broadcast live and there are many reports indicating that the draws are manipulated.

Apart from choosing the 6 numbers, people can make various side bets. Some of them are:

• the color of the extra number (the numbers are drawn in the form of coloured balls)
• the parity (even or oddness) of the extra number

Outside of Hong Kong, the bet can be less than HK\$5 to increase sales (inside Hong Kong it is illegal to make bet with parties aside from the HKJC).

## Trivia

The new drawing machine, introduced on 2 December 2010, is the Halogen II designed and built by Smartplay International, Inc.

The previous drawing machine was the "Stresa" built by French company Ryo-Catteau.

To ensure the unpredictability of the draw, the drawing machine is replaced once every few years.

The background music featured in the television broadcasts of the draws is a version of Inkpot, a song written by the Dutch rock band from The Hague Shocking Blue.