Lucky 6
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Introduction
Lucky 6 35/48 is a lottery game in which 35 balls are drawn, without replacement, out of a drum of 48. Before the draw, the player chooses six balls and is paid according to how many balls it takes to draw all six of the players chosen balls. I'm aware of two providers offering this game. The rules of each shall be addressed.
Lucky 6 35/48 should not be confused with another lottery game titled Lucky 6.
Lottery Instant Win
Lottery Instant Win offers the following pay table. The lower left cell shows an expected return of 84.31%.
Lottery Instant Win Pay Table
| Balls | Pays | Probability | Return |
|---|---|---|---|
| 6 | 100000 | 0.000000081 | 0.008149 |
| 7 | 10000 | 0.000000489 | 0.004889 |
| 8 | 5000 | 0.000001711 | 0.008556 |
| 9 | 2000 | 0.000004563 | 0.009127 |
| 10 | 1000 | 0.000010268 | 0.010268 |
| 11 | 500 | 0.000020535 | 0.010268 |
| 12 | 300 | 0.000037648 | 0.011294 |
| 13 | 200 | 0.000064540 | 0.012908 |
| 14 | 100 | 0.000104877 | 0.010488 |
| 15 | 90 | 0.000163142 | 0.014683 |
| 16 | 80 | 0.000244713 | 0.019577 |
| 17 | 70 | 0.000355946 | 0.024916 |
| 18 | 60 | 0.000504257 | 0.030255 |
| 19 | 50 | 0.000698202 | 0.034910 |
| 20 | 40 | 0.000947560 | 0.037902 |
| 21 | 30 | 0.001263414 | 0.037902 |
| 22 | 25 | 0.001658231 | 0.041456 |
| 23 | 20 | 0.002145946 | 0.042919 |
| 24 | 15 | 0.002742042 | 0.041131 |
| 25 | 10 | 0.003463632 | 0.034636 |
| 26 | 9 | 0.004329540 | 0.038966 |
| 27 | 8 | 0.005360383 | 0.042883 |
| 28 | 7 | 0.006578651 | 0.046051 |
| 29 | 6 | 0.008008793 | 0.048053 |
| 30 | 5 | 0.009677292 | 0.048386 |
| 31 | 4 | 0.011612750 | 0.046451 |
| 32 | 3 | 0.013845971 | 0.041538 |
| 33 | 2 | 0.016410040 | 0.032820 |
| 34 | 1.5 | 0.019340404 | 0.029011 |
| 35 | 1 | 0.022674956 | 0.022675 |
| 36 to 48 | 0 | 0.867729421 | 0.000000 |
| Total | 1.000000000 | 0.843068 |
Merrybet
The next table shows the return for the pay table in use at the Merrybet casino. This is before considering the Clover multiplier, which I will explain after the table. The lower right cell shows an expected return of 101.94%.
Merrybet Pay Table — Before Clover Multiplier
| Balls | Pays | Probability | Return |
|---|---|---|---|
| 6 | 10000 | 0.000000081 | 0.000815 |
| 7 | 7500 | 0.000000489 | 0.003667 |
| 8 | 5000 | 0.000001711 | 0.008556 |
| 9 | 2500 | 0.000004563 | 0.011409 |
| 10 | 1000 | 0.000010268 | 0.010268 |
| 11 | 500 | 0.000020535 | 0.010268 |
| 12 | 300 | 0.000037648 | 0.011294 |
| 13 | 200 | 0.000064540 | 0.012908 |
| 14 | 150 | 0.000104877 | 0.015732 |
| 15 | 100 | 0.000163142 | 0.016314 |
| 16 | 90 | 0.000244713 | 0.022024 |
| 17 | 80 | 0.000355946 | 0.028476 |
| 18 | 70 | 0.000504257 | 0.035298 |
| 19 | 60 | 0.000698202 | 0.041892 |
| 20 | 50 | 0.000947560 | 0.047378 |
| 21 | 40 | 0.001263414 | 0.050537 |
| 22 | 30 | 0.001658231 | 0.049747 |
| 23 | 25 | 0.002145946 | 0.053649 |
| 24 | 20 | 0.002742042 | 0.054841 |
| 25 | 15 | 0.003463632 | 0.051954 |
| 26 | 10 | 0.004329540 | 0.043295 |
| 27 | 9 | 0.005360383 | 0.048243 |
| 28 | 8 | 0.006578651 | 0.052629 |
| 29 | 7 | 0.008008793 | 0.056062 |
| 30 | 6 | 0.009677292 | 0.058064 |
| 31 | 5 | 0.011612750 | 0.058064 |
| 32 | 4 | 0.013845971 | 0.055384 |
| 33 | 3 | 0.016410040 | 0.049230 |
| 34 | 2 | 0.019340404 | 0.038681 |
| 35 | 1 | 0.022674956 | 0.022675 |
| 36 to 48 | 0 | 0.867729421 | 0.000000 |
| Total | 1.000000000 | 1.019353 |
At the Merrybet casino, the game will randomly place two clovers on the scored board for the 6th to 35th chosen balls by the game, before the ball draw. If one number that is drawn in one of those positions matches a player pick, then any win will be doubled. If two numbers in clover spots match the player's picks, then any win will be tripled.
The direct math was rather messy in calculating the probability of the Clover multipliers, so I did a random simulation of 644,500,000 games to determine the average Clover multiplier for any given number of balls required to match all six player balls. The following table shows those multipliers and the adjusted wins after considering the multiplier. The lower right cell shows an expected return of 134.60%, assuming the clovers are randomly distributed between the 6th and 35th positions of the scoreboard and that the ball draw is fair, meaning each ball in the bin is equally likely to be drawn.
Merrybet Pay Table — After Clover Multiplier
| Balls | Pays | Average Multiplier | Probability | Return |
|---|---|---|---|---|
| 6 | 10000 | 1.065217 | 0.000000081 | 0.000868 |
| 7 | 7500 | 1.087087 | 0.000000489 | 0.003986 |
| 8 | 5000 | 1.173752 | 0.000001711 | 0.010043 |
| 9 | 2500 | 1.199587 | 0.000004563 | 0.013686 |
| 10 | 1000 | 1.221471 | 0.000010268 | 0.012542 |
| 11 | 500 | 1.231463 | 0.000020535 | 0.012644 |
| 12 | 300 | 1.251580 | 0.000037648 | 0.014136 |
| 13 | 200 | 1.258473 | 0.000064540 | 0.016244 |
| 14 | 150 | 1.270126 | 0.000104877 | 0.019981 |
| 15 | 100 | 1.280259 | 0.000163142 | 0.020886 |
| 16 | 90 | 1.288411 | 0.000244713 | 0.028376 |
| 17 | 80 | 1.295503 | 0.000355946 | 0.036890 |
| 18 | 70 | 1.301718 | 0.000504257 | 0.045948 |
| 19 | 60 | 1.308082 | 0.000698202 | 0.054798 |
| 20 | 50 | 1.313961 | 0.000947560 | 0.062253 |
| 21 | 40 | 1.316674 | 0.001263414 | 0.066540 |
| 22 | 30 | 1.320792 | 0.001658231 | 0.065705 |
| 23 | 25 | 1.323907 | 0.002145946 | 0.071026 |
| 24 | 20 | 1.326784 | 0.002742042 | 0.072762 |
| 25 | 15 | 1.330749 | 0.003463632 | 0.069138 |
| 26 | 10 | 1.333275 | 0.004329540 | 0.057725 |
| 27 | 9 | 1.336543 | 0.005360383 | 0.064479 |
| 28 | 8 | 1.338122 | 0.006578651 | 0.070424 |
| 29 | 7 | 1.340937 | 0.008008793 | 0.075175 |
| 30 | 6 | 1.342334 | 0.009677292 | 0.077941 |
| 31 | 5 | 1.344725 | 0.011612750 | 0.078080 |
| 32 | 4 | 1.346001 | 0.013845971 | 0.074547 |
| 33 | 3 | 1.348010 | 0.016410040 | 0.066363 |
| 34 | 2 | 1.349547 | 0.019340404 | 0.052202 |
| 35 | 1 | 1.350959 | 0.022674956 | 0.030633 |
| 36 to 48 | 0 | 1.235865 | 0.867729421 | 0.000000 |
| Total | 1.250024 | 1.000000000 | 1.346022 |
Colors Completed
Lottery Instant Win offers a set of five side bets on the number of completed colors in 35 balls. The 48 balls are in eight different colors, six balls per color.
Lottery Instant Win Pay Table
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Exactly 0 | 3.5 | 46,948,206,528 | 0.243345 | 0.851709 |
| Exactly 1 | 1.7 | 94,168,766,160 | 0.488103 | 0.829774 |
| Exactly 2 | 3 | 45,626,036,400 | 0.236492 | 0.709477 |
| Exactly 3 | 20 | 6,012,429,360 | 0.031164 | 0.623281 |
| Exactly 4 or 5 | 800 | 172,810,848 | 0.000896 | 0.716581 |
In case you're wondering (or I forget myself at a later time) the formulas for each number of colors, here they are:
- Exactly 0 = COMBIN(48,35)-8*COMBIN(42,29)+COMBIN(8,2)*COMBIN(36,23)-COMBIN(8,3)*COMBIN(30,17)+COMBIN(8,4)*COMBIN(24,11)-COMBIN(8,5)*COMBIN(18,5) = 46,948,206,528
- Exactly 1 = COMBIN(8,1)*(COMBIN(42,29)-7*COMBIN(36,23)+COMBIN(7,2)*COMBIN(30,17)-COMBIN(7,3)*COMBIN(24,11)+COMBIN(7,3)*COMBIN(18,5)) = 94,168,766,160
- Exactly 2 = COMBIN(8,2)*(COMBIN(36,23)-6*COMBIN(30,17)+COMBIN(6,2)*COMBIN(24,11)-COMBIN(6,3)*COMBIN(18,5)) = 45,626,036,400
- Exactly 3 = COMBIN(8,3)*(COMBIN(30,17)-5*COMBIN(24,11)+COMBIN(5,2)*COMBIN(18,5)) = 6,012,429,360
- Exactly 4 = =COMBIN(8,4)*(COMBIN(24,11)-4*COMBIN(18,5)) = 172,331,040
- Exactly 5 = COMBIN(8,5)*COMBIN(18,5) = 479,808
Color Completed
6 Lucky Numbers For Today
The Merrybet casino has a set of eight proposition bets on whether a specific color, chosen by the player, will be fully covered in the 35-ball draw. In other words, the bet wins if every ball of the chosen color is drawn. Again, the balls are divided into eight colors of six balls each. A a win of 6 for 1, the table below shows an expected return of 79.36%.
Color Completed
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 6 | 25,518,731,280 | 0.132271 | 0.793623 |
| Loss | 0 | 167,409,518,016 | 0.867729 | 0.000000 |
| Total | 192,928,249,296 | 1.000000 | 0.793623 |
The Merrybet casino has a set of two proposition bets, odd and even, on whether more odd or even balls will be drawn in the 35-number ball draw. Wins pay 1.8 for 1. The bottom right cell in the following table shows an expected return of 90%.
More Odds or Evens
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1.8 | 96,464,124,648 | 0.500000 | 0.900000 |
| Loss | 0 | 96,464,124,648 | 0.500000 | 0.000000 |
| Total | 192,928,249,296 | 1.000000 | 0.900000 |
The Merrybet casino has a set of two proposition bets, odd and even, on whether more odd or even balls will be drawn in the 35-number ball draw.
More Odds or Evens
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1.8 | 24 | 0.500000 | 0.900000 |
| Loss | 0 | 24 | 0.500000 | 0.000000 |
| Total | 48 | 1.000000 | 0.900000 |
First Ball Odd or Even
The Merrybet casino has a set of two proposition bets, odd and even, on whether the first ball drawn will be odd or even. Wins pay 1.8 for 1. The bottom right cell in the following table shows an expected return of 90%.
First Ball Odd or Even
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1.8 | 24 | 0.500000 | 0.900000 |
| Loss | 0 | 24 | 0.500000 | 0.000000 |
| Total | 48 | 1.000000 | 0.900000 |
First Ball Over or Under 24.5
The Merrybet casino has a set of two proposition bets, under and over, on whether the first ball drawn will be over or under 24.5. Wins pay 1.8 for 1. The bottom right cell in the following table shows an expected return of 90%.
First Ball Over or Under 24.5
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1.8 | 856,152 | 0.500000 | 0.900000 |
| Loss | 0 | 856,152 | 0.500000 | 0.000000 |
| Total | 1,712,304 | 1.000000 | 0.900000 |
Total of First Five Balls Over or Under 122.5
The Merrybet casino has a set of two proposition bets, under and over, on whether the sum of the first five balls drawn will be under or over 122.5. Wins pay 1.8 for 1. The bottom right cell in the following table shows an expected return of 90%.
Total of First Five Balls Over or Under 122.5
| Balls | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 1.8 | 856,152 | 0.500000 | 0.900000 |
| Loss | 0 | 856,152 | 0.500000 | 0.000000 |
| Total | 1,712,304 | 1.000000 | 0.900000 |
External Links
Discussion about Lucky 6 35/48 in my forum at Wizard of Vegas.
Lucky 628
Written by:Michael ShacklefordLucky 650
The Most Auspicious Numbers: 6, 8, 9:
Six, eight and nine are regarded as the luckiest numbers in China. All of their homophones have auspicious meanings.
The number 6 pronounced as 'Liu' means smooth and well-off. In Chinese people’s eyes, it stands for everything will go smoothly. So when choosing telephone numbers, people like more number 6s in it. Eight has the similar pronunciation with 发 (means wealth and fortune in Chinese), so Chinese people favor it very much especially for businessmen. The number 9 pronounced as Jiu (久) in Chinese means everlasting, longevity and eternality. In Chinese culture, it is associated with the Emperor of China. You can see the Emperor's robes have nine dragons and the Beijing Forbidden City has totally 9,999 and a half rooms. For lovers, 99, 999, or 9999 roses are usually sent to present the eternal love.
The most Inauspicious Numbers: 4, 7
Four is regarded as the unluckiest number as the word for 死（death）sounds similar to four in Chinese. So when mention the number 4, the Chinese people usually associate it with death. It is disliked by the Chinese people like the western people don’t like the number 13. But it also has a good meaning as it has the same pronunciation with the word发 (fortune) in Chinese.
Another inauspicious number is seven which have the meaning of gone. It also has the same pronunciation with 欺 (cheat) in Chinese. So in daily life, Chinese people usually avoid to use the number. You can see that when Chinese people choose a number for their telephone, 4 and 7 are most disliked by them.
Meanings for Other Numbers: 0, 1, 2, 3, 5
Zero - Means everything or nothing. It is limitless. Chinese people think everything begins with 0.
One – means the first. It is the simplest number but also the most complex one in terms of its cultural meaning in Chinese culture. It is neither auspicious nor inauspicious. People use it to name the winner. It also has the meaning of beginning, loneliness, single. For example: November 11th is the single’s day in China, as the date has four ‘1’ which stand for single.
Two - means ‘double’, ‘twinned’ and ‘again’. In most cases, it is a lucky number in Chinese culture as Chinese people think all good things com in pairs. But in some areas, people use this number to describe someone is stupid and reckless which is ironic.
Three – is a lucky number in Chinese culture as it sounds similar to the character of ‘birth’ (生 shēng). For a people’s life, there are three most important stages: birth, marriage and death. You can see the number 3 is greatly used in Chinese culture, history and more: There are three gorges of Yangtze River; Three Sages and Three Kingdoms in Chinese history; three halls of Forbidden City in Beijing…
Five – a neutral number in Chinese culture. It is lucky as it usually related to the Emperor of China. There are five blessings in China - wealth, happiness, longevity, luck and prosperity. Also in Chinese astrology, there are five elements - Metal, Wood, Water, Fire and Earth. There are Five Kinds of Main Grain in China. As it has the same pronunciation with ‘无’（means nothing in Chinese）, it has a negative meaning. It also used to mean ‘I’ because of the similar pronunciation with ‘我’ in Chinese.