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Lucky 6 35/48

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

Lucky 6-35-48 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

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.

Written by: Michael Shackleford