Lucky 6
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Introduction
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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.
6 Lucky Lottery Numbers
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
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 |
Lucky 6 Numbers
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
Lucky 6 Guns Livingston Wi
| 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.