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5 Bet

Introduction

5bet is a lottery game involving a draw of five balls out of 36. As opposed to the player picking five of his own numbers, there are hundreds of different bets to choose from. The game is offered by TvBet, a provider of live dealer games for Internet casinos.

Rules

  1. Every three minutes a live dealer will drawn 5 balls, without replacement, out of a hopper with 36 balls, numbered 1 to 36.
  2. The balls come in four colors — blue, red, yellow, and green. There are nine balls for each color.
  3. There are many different bets to choose from. Rather than list them all here, you may see each in the analysis sections below.
  4. All wins are on a "for one" basis.

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Selected Balls Drawn

This is the only type of bet that involving picking actual numbers. After the player chooses a type of bet, the game will ask him to choose the necessary balls.

Selected Balls Drawn

Bet Pays Combinations Probability Return
One selected drawn first 30 1 0.027778 0.833333
One selected drawn 6.8 52,360 0.138889 0.944444
One selected not drawn 1.103 324,632 0.861111 0.949806
Two selected drawn 55 5,984 0.015873 0.873016
Three selected drawn 650 528 0.001401 0.910364

Except for the bet on the first selected ball to be drawn, the probabilities are based on all combin(36,5)=376,992 ways of choosing five balls out of 36. The bet on the first ball drawn is based on 36 combinations.

Even-Odd

This is the only type of bet that involving picking actual numbers. After the player chooses a type of bet, the game will ask him to choose the necessary balls.

Even - Odd

Bet Pays Combinations Probability Return
Fewer even numbers 1.9 188,496 0.500000 0.950000
More even numbers 1.9 188,496 0.500000 0.950000
Sum of even balls higher than sum of odd balls 1.835 195,115 0.517557 0.949718
Sum of odd balls higher than sum of even balls 2.002 178,870 0.474466 0.949882
Total even numbers over 2.5 1.9 188,496 0.500000 0.950000
Total even numbers exactly 2 2.868 124,848 0.331169 0.949792
Total even numbers under 1.5 5.6 63,648 0.168831 0.945455
Total odd numbers over 2.5 1.9 188,496 0.500000 0.950000
Total odd numbers exactly 2 2.868 124,848 0.331169 0.949792
Total odd numbers under 1.5 5.6 63,648 0.168831 0.945455

One Color Bets

The player may choose any of the four colors and bet a variety of ways on the number of balls that will be drawn of that table.

One Color Bets

Bet Pays Combinations Probability Return
At least one ball drawn 1.208 296,262 0.785858 0.949316
Zero balls drawn 4.43 80,730 0.214142 0.948651
Over 1.5 balls drawn 2.589 138,312 0.366883 0.949860
Under 1.5 balls drawn 1.5 238,680 0.633117 0.949675
Over 2.5 balls drawn 10 33,012 0.087567 0.875668
Over 3.5 balls drawn 100 3,528 0.009358 0.935829
Under 3.5 balls drawn 1.001 343,980 0.912433 0.913346
5 balls drawn 1000 126 0.000334 0.334225
Exactly 1 ball drawn 2.267 157,950 0.418974 0.949815
Exactly 2 balls drawn 3.4 105,300 0.279316 0.949675
Exactly 3 balls drawn 12 29,484 0.078209 0.938503
Exactly 4 balls drawn 100 3,402 0.009024 0.902406
Exactly 1 balls not drawn 1.635 219,042 0.581026 0.949977
Exactly 2 balls not drawn 1.318 271,692 0.720684 0.949861

Two Color Bets

The player may choose any two of the four colors and bet a variety of ways on the number of balls of each color that will appear.

Two Color Bets

Balls of
First Color		 Balls of
Second Color		 Pays Combinations Probability Return
1 1 1.511 2 66,096 0.264916 0.264916
1 2 3.14 3 49,572 0.412890 0.412890
1 3 17 17 13,608 0.613636 0.613636
1 4 300 300 1,134 0.902406 0.902406
2 2 10 10 23,328 0.618793 0.618793
2 3 100 100 3,024 0.802139 0.802139

Sum of Balls

There are a host of ways to bet on the sum of all the balls drawn, the sum of the highest and lowest balls, and the difference between the highest and lowest balls.

Sum of Balls

Bet Pays Combinations Probability Return
Under 92.5 1.9 188,496 0.500000 0.950000
Over 92.5 1.9 188,496 0.500000 0.950000
Difference between highest and lowest ball under 25.5 1.862 192,280 0.510037 0.949690
Difference between highest and lowest ball over 25.5 1.938 184,712 0.489963 0.949548
Sum of highest and lowest ball under 36.5 2.05 174,624 0.463203 0.949567
Sum of highest and lowest ball over 36.5 1.769 202,368 0.536797 0.949593
Sum of all even balls under 46.5 1.85 185,010 0.490753 0.907893
Sum of all even balls over 46.5 1.952 191,982 0.509247 0.994050
Sum of all odd balls under 43.5 1.906 179,321 0.475663 0.906613
Sum of all odd balls over 43.5 1.893 197,671 0.524337 0.992571
Difference between lowest and highest balls odd 1.891 187,680 0.497835 0.941407
Difference between lowest and highest balls even 1.908 189,312 0.502165 0.958130
Sum of lowest and highest balls odd 1.891 187,680 0.497835 0.941407
Sum of lowest and highest balls even 1.908 189,312 0.502165 0.958130

Divisibility

The player may bet on whether any balls are divisible by 5, 7, or 10. I suspect TvBet may not know how many numbers between 1 and 36 are divisible by 7 *ahem*.

Divisibility

Bet Pays Combinations Probability Return
Any number divisible by 5 1.386 258,237 0.684993 0.949401
No numbers divisible by 5 3.01 118,755 0.315007 0.948170
Any number divisible by 7 1.729 207,081 0.549298 0.949736
No numbers divisible by 7 2.107 169,911 0.450702 0.949629
Any number divisible by 10 2.564 139,656 0.370448 0.949829
No numbers divisible by 10 1.509 237,336 0.629552 0.949994

Lowest/Highest Ball

The player may bet on how low or high the lowest or highest ball will be.

Lowest/Highest Ball

Bet Pays Combinations Probability Return
Lowest ball under 4.5 2.039 175,616 0.465835 0.949837
Lowest ball over 4.5 1.778 201,376 0.534165 0.949746
Lowest ball odd 1.769 202,368 0.536797 0.949593
Lowest ball even 2.05 174,623 0.463201 0.949562
Highest ball under 32.5 1.778 201,375 0.534163 0.949741
Highest ball over 32.5 2.039 175,616 0.465835 0.949837
Highest ball odd 2.05 174,623 0.463201 0.949562
Highest ball even 1.769 202,368 0.536797 0.949593

Color of First Ball

The player may bet on the color of the first drawn ball.

Color of First Ball

Bet Pays Combinations Probability Return
First ball will be chosen color 3.8 9 0.250000 0.950000
First ball will not be chosen color 1.266 27 0.750000 0.949500

Strategy

The game obviously endeavors to achieve close to a 95% return on most bets. However some, like all two-color bets, are much lower. So be careful what you bet on, staying close to 95%, if you must play.

Math

As long as I took the trouble to calculate the odds for this game, I may as well post the combination tables behind them.

The following table shows the number of combinations for each possible total of all five balls.

Sum of all Balls

Sum all Balls Combinations
15 1
16 1
17 2
18 3
19 5
20 7
21 10
22 13
23 18
24 23
25 30
26 37
27 47
28 57
29 70
30 84
31 101
32 119
33 141
34 164
35 192
36 221
37 255
38 291
39 333
40 377
41 427
42 480
43 540
44 603
45 674
46 748
47 830
48 916
49 1,010
50 1,108
51 1,214
52 1,324
53 1,442
54 1,564
55 1,694
56 1,827
57 1,968
58 2,112
59 2,263
60 2,417
61 2,577
62 2,739
63 2,907
64 3,076
65 3,250
66 3,424
67 3,602
68 3,779
69 3,959
70 4,137
71 4,316
72 4,492
73 4,668
74 4,839
75 5,009
76 5,172
77 5,332
78 5,484
79 5,631
80 5,769
81 5,900
82 6,021
83 6,134
84 6,236
85 6,329
86 6,410
87 6,481
88 6,540
89 6,588
90 6,624
91 6,648
92 6,660
93 6,660
94 6,648
95 6,624
96 6,588
97 6,540
98 6,481
99 6,410
100 6,329
101 6,236
102 6,134
103 6,021
104 5,900
105 5,769
106 5,631
107 5,484
108 5,332
109 5,172
110 5,009
111 4,839
112 4,668
113 4,492
114 4,316
115 4,137
116 3,959
117 3,779
118 3,602
119 3,424
120 3,250
121 3,076
122 2,907
123 2,739
124 2,577
125 2,417
126 2,263
127 2,112
128 1,968
129 1,827
130 1,694
131 1,564
132 1,442
133 1,324
134 1,214
135 1,108
136 1,010
137 916
138 830
139 748
140 674
141 603
142 540
143 480
144 427
145 377
146 333
147 291
148 255
149 221
150 192
151 164
152 141
153 119
154 101
155 84
156 70
157 57
158 47
159 37
160 30
161 23
162 18
163 13
164 10
165 7
166 5
167 3
168 2
169 1
170 1

The following table shows the number of combinations for each possible total of all even balls.

Sum of all Even Balls

Sum Even Balls Combinations
2 3,060
4 3,060
6 3,876
8 3,876
10 4,692
12 4,845
14 5,661
16 5,814
18 6,783
20 6,954
22 7,923
24 8,247
26 9,234
28 9,576
30 10,717
32 11,077
34 12,236
36 12,768
38 10,886
40 10,621
42 11,155
44 10,774
46 11,175
48 10,814
50 11,082
52 10,588
54 10,859
56 10,215
58 10,335
60 9,694
62 9,646
64 8,836
66 8,772
68 7,793
70 7,542
72 6,528
74 6,088
76 5,701
78 5,360
80 4,918
82 4,538
84 4,210
86 3,791
88 3,423
90 3,134
92 2,743
94 2,431
96 2,170
98 1,852
100 1,586
102 1,416
104 1,145
106 988
108 884
110 742
112 653
114 544
116 472
118 381
120 327
122 254
124 219
126 166
128 133
130 100
132 87
134 57
136 47
138 37
140 30
142 23
144 18
146 13
148 10
150 7
152 5
154 3
156 2
158 1
160 1

The following table shows the number of combinations for each possible total of all odd balls.

Sum of all Odd Balls

Sum Odd Balls Combinations
1 3,060
2 -
3 3,060
4 816
5 3,060
6 816
7 3,060
8 1,632
9 3,213
10 1,632
11 3,213
12 2,448
13 3,366
14 2,448
15 3,519
16 3,282
17 3,672
18 3,282
19 3,825
20 4,116
21 4,131
22 4,134
23 4,284
24 4,986
25 4,591
26 5,004
27 4,897
28 5,874
29 5,204
30 5,910
31 5,511
32 6,798
33 5,972
34 6,852
35 6,280
36 7,758
37 3,682
38 7,014
39 4,144
40 7,140
41 4,455
42 6,414
43 4,766
44 6,558
45 5,079
46 5,850
47 5,239
48 6,012
49 5,402
50 5,304
51 5,565
52 5,466
53 5,577
54 4,758
55 5,590
56 4,920
57 5,605
58 4,194
59 5,467
60 4,338
61 5,331
62 3,594
63 5,195
64 3,720
65 4,908
66 2,940
67 4,620
68 3,030
69 4,333
70 2,214
71 3,892
72 2,268
73 3,452
74 2,214
75 3,163
76 2,214
77 2,720
78 2,124
79 2,428
80 2,088
81 2,135
82 1,962
83 1,839
84 1,890
85 1,541
86 1,746
87 1,393
88 1,656
89 1,090
90 1,494
91 937
92 1,386
93 781
94 1,224
95 623
96 1,116
97 462
98 954
99 452
100 846
101 286
102 702
103 272
104 612
105 256
106 486
107 239
108 414
109 220
110 324
111 202
112 270
113 183
114 198
115 165
116 162
117 146
118 108
119 129
120 90
121 112
122 54
123 97
124 36
125 82
126 18
127 69
128 18
129 57
130 -
131 47
132 -
133 37
134 -
135 30
136 -
137 23
138 -
139 18
140 -
141 13
142 -
143 10
144 -
145 7
146 -
147 5
148 -
149 3
150 -
151 2
152 -
153 1
154 -
155 1

The following table shows the number of combinations for each possible sum of the lowest and highest balls.

Sum of Lowest and Highest Balls

Sum Combinations
6 1
7 4
8 11
9 24
10 46
11 80
12 130
13 200
14 295
15 420
16 581
17 784
18 1,036
19 1,344
20 1,716
21 2,160
22 2,685
23 3,300
24 4,015
25 4,840
26 5,786
27 6,864
28 8,086
29 9,464
30 11,011
31 12,740
32 14,665
33 16,800
34 19,160
35 21,760
36 24,616
37 27,744
38 24,616
39 21,760
40 19,160
41 16,800
42 14,665
43 12,740
44 11,011
45 9,464
46 8,086
47 6,864
48 5,786
49 4,840
50 4,015
51 3,300
52 2,685
53 2,160
54 1,716
55 1,344
56 1,036
57 784
58 581
59 420
60 295
61 200
62 130
63 80
64 46
65 24
66 11
67 4
68 1

The following table shows the number of combinations for each possible difference between the lowest and highest balls.

Difference Between Lowest and Highest Balls

Difference Combinations
4 32
5 124
6 300
7 580
8 980
9 1,512
10 2,184
11 3,000
12 3,960
13 5,060
14 6,292
15 7,644
16 9,100
17 10,640
18 12,240
19 13,872
20 15,504
21 17,100
22 18,620
23 20,020
24 21,252
25 22,264
26 23,000
27 23,400
28 23,400
29 22,932
30 21,924
31 20,300
32 17,980
33 14,880
34 10,912
35 5,984

Written by: Michael Shackleford