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7 Bet

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Introduction

7bet is a lottery game involving a draw of seven balls out of 42. 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 seven balls, without replacement, out of a hopper with 42 balls, numbered 1 to 42.
  2. The balls come in four colors — blue and black. There are 21 balls for each color. The even balls are blue and the odd balls are black.
  3. There are many different bets to choose from. Rather than list them all here, you may see each in the analysis sections below. The way I title them is not necessarily the same as by TvBet.
  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

7bet img 2

Even/Odd

This category features two bets only, on whether there will be more odd or even balls drawn.

Even/Odd

Bet Pays Combinations Probability Return
Fewer even numbers 1.9 188,496 0.500000 0.950000
More even numbres 1.9 188,496 0.500000 0.950000

7bet img 3

Red/Black

This category features two bets only, on whether there will be more blue or black balls drawn. Since all blue balls are even and all blacks are odd, this category is mathematically equivalent to the odd/even category

Red/Black

Bet Pays Combinations Probability Return
Fewer even numbers 1.9 188,496 0.500000 0.950000
More even numbres 1.9 188,496 0.500000 0.950000

7bet img 4

Sum of Balls

This category features lots of bets on the sum of all seven balls drawn.

Sum of Balls

Bet Pays Combinations Probability Return
Under 50.5 5000 2,799 0.000104 0.518750
Under 75.5 200 122,028 0.004523 0.904637
Under 100.5 20 1,240,092 0.045966 0.919325
Under 125.5 4.66 5,491,278 0.203544 0.948515
Under 150.5 1.9 13,489,164 0.500000 0.950000
Under 175.5 1.192 21,487,050 0.796456 0.949375
Under 200.5 1.001 25,738,236 0.954034 0.954988
Over 100.5 1.001 25,738,236 0.954034 0.954988
Over 125.5 1.192 21,487,050 0.796456 0.949375
Over 150.5 1.9 13,489,164 0.500000 0.950000
Over 175.5 4.66 5,491,278 0.203544 0.948515
Over 200.5 20 1,240,092 0.045966 0.919325
Over 225.5 200 122,028 0.004523 0.904637
Over 250.5 2000 2,799 0.000104 0.207500

7bet img 5

Number of Balls by Color

This category features lots of bets on the number of all balls of a chosen color.

Number of Balls by Color

Bet Pays Combinations Probability Return
Over 1.5 chosen color 1.001 25,722,504 0.953451 0.954404
Under 1.5 chosen color 20 1,255,824 0.046549 0.930987
Over 2.5 chosen color 1.194 21,449,214 0.795053 0.949294
Under 2.5 chosen color 4.63 5,529,114 0.204947 0.948902
Over 3.5 chosen color 1.9 13,489,164 0.500000 0.950000
Under 3.5 chosen color 1.9 13,489,164 0.500000 0.950000
Exactly 0 chosen color 200 116,280 0.004310 0.862025
Exactly 1 chosen color 20 1,139,544 0.042239 0.844785
Exactly 2 chosen color 5.9 4,273,290 0.158397 0.934543
Exactly 3 chosen color 3.21 7,960,050 0.295053 0.947122
Exactly 4 chosen color 3.21 7,960,050 0.295053 0.947122
Exactly 5 chosen color 5.9 4,273,290 0.158397 0.934543
Exactly 6 chosen color 20 1,139,544 0.042239 0.844785
Exactly 7 chosen color 200 116,280 0.004310 0.862025

7bet img 6

Color of First Ball

This category is two simple bets on the color of the first ball.

Color of First Ball

Bet Pays Combinations Probability Return
First ball blue 1.9 21 0.500000 0.950000
First ball black 1.9 21 0.500000 0.950000

Sum of Balls by Color

This category is features bets on the sum of all balls of a chosen color.

Sum of Balls by Color

Bet Pays Combinations Probability Return
Sum blue balls over 73.5 1.795 14,271,691 0.529006 0.949565
Sum blue balls under 73.5 2.017 12,590,357 0.466684 0.941302
Sum black balls over 73.5 1.97 13,005,568 0.482075 0.949687
Sum black balls under 73.5 1.834 13,856,480 0.513615 0.941970
7bet img 7

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 seven balls.

Sum of all Seven Balls

Sum all Balls Combinations
28 1
29 1
30 2
31 3
32 5
33 7
34 11
35 15
36 21
37 28
38 38
39 49
40 65
41 82
42 105
43 131
44 164
45 201
46 248
47 300
48 364
49 436
50 522
51 618
52 733
53 860
54 1,009
55 1,175
56 1,367
57 1,579
58 1,824
59 2,093
60 2,400
61 2,738
62 3,120
63 3,539
64 4,010
65 4,524
66 5,098
67 5,724
68 6,418
69 7,171
70 8,003
71 8,902
72 9,889
73 10,954
74 12,116
75 13,365
76 14,723
77 16,177
78 17,750
79 19,430
80 21,239
81 23,164
82 25,230
83 27,421
84 29,762
85 32,238
86 34,873
87 37,651
88 40,598
89 43,694
90 46,966
91 50,395
92 54,005
93 57,776
94 61,734
95 65,855
96 70,165
97 74,640
98 79,304
99 84,130
100 89,144
101 94,316
102 99,670
103 105,177
104 110,857
105 116,680
106 122,667
107 128,784
108 135,051
109 141,434
110 147,950
111 154,564
112 161,293
113 168,099
114 174,997
115 181,951
116 188,972
117 196,023
118 203,116
119 210,211
120 217,318
121 224,400
122 231,463
123 238,470
124 245,427
125 252,296
126 259,082
127 265,749
128 272,299
129 278,697
130 284,946
131 291,011
132 296,893
133 302,562
134 308,015
135 313,225
136 318,191
137 322,886
138 327,309
139 331,437
140 335,268
141 338,782
142 341,978
143 344,839
144 347,363
145 349,538
146 351,362
147 352,826
148 353,929
149 354,665
150 355,034
151 355,034
152 354,665
153 353,929
154 352,826
155 351,362
156 349,538
157 347,363
158 344,839
159 341,978
160 338,782
161 335,268
162 331,437
163 327,309
164 322,886
165 318,191
166 313,225
167 308,015
168 302,562
169 296,893
170 291,011
171 284,946
172 278,697
173 272,299
174 265,749
175 259,082
176 252,296
177 245,427
178 238,470
179 231,463
180 224,400
181 217,318
182 210,211
183 203,116
184 196,023
185 188,972
186 181,951
187 174,997
188 168,099
189 161,293
190 154,564
191 147,950
192 141,434
193 135,051
194 128,784
195 122,667
196 116,680
197 110,857
198 105,177
199 99,670
200 94,316
201 89,144
202 84,130
203 79,304
204 74,640
205 70,165
206 65,855
207 61,734
208 57,776
209 54,005
210 50,395
211 46,966
212 43,694
213 40,598
214 37,651
215 34,873
216 32,238
217 29,762
218 27,421
219 25,230
220 23,164
221 21,239
222 19,430
223 17,750
224 16,177
225 14,723
226 13,365
227 12,116
228 10,954
229 9,889
230 8,902
231 8,003
232 7,171
233 6,418
234 5,724
235 5,098
236 4,524
237 4,010
238 3,539
239 3,120
240 2,738
241 2,400
242 2,093
243 1,824
244 1,579
245 1,367
246 1,175
247 1,009
248 860
249 733
250 618
251 522
252 436
253 364
254 300
255 248
256 201
257 164
258 131
259 105
260 82
261 65
262 49
263 38
264 28
265 21
266 15
267 11
268 7
269 5
270 3
271 2
272 1
273 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 54,264
4 54,264
6 74,613
8 74,613
10 94,962
12 100,947
14 121,296
16 127,281
18 153,615
20 160,930
22 187,264
24 200,564
26 228,228
28 242,858
30 276,717
32 292,677
34 327,866
36 351,351
38 388,080
40 413,105
42 457,380
44 431,011
46 456,687
48 471,989
50 494,781
52 507,199
54 531,993
56 540,408
58 561,219
60 571,867
62 587,597
64 592,954
66 609,630
68 609,928
70 620,236
72 619,983
74 623,735
76 616,927
78 618,842
80 603,962
82 597,616
84 580,482
86 564,547
88 557,754
90 543,824
92 532,780
94 514,389
96 504,681
98 482,720
100 469,401
102 449,646
104 432,235
106 409,696
108 395,507
110 370,121
112 352,833
114 331,682
116 312,749
118 289,930
120 275,333
122 252,109
124 237,273
126 220,044
128 205,132
130 189,342
132 176,139
134 160,851
136 148,357
138 135,188
140 123,838
142 111,830
144 101,722
146 91,122
148 82,672
150 73,812
152 65,750
154 58,628
156 52,618
158 46,197
160 40,931
162 36,459
164 32,002
166 28,362
168 24,634
170 21,683
172 18,689
174 16,308
176 13,865
178 12,039
180 10,217
182 8,763
184 7,316
186 6,262
188 5,196
190 4,505
192 3,636
194 3,081
196 2,560
198 2,166
200 1,764
202 1,470
204 1,189
206 974
208 772
210 637
212 492
214 393
216 304
218 239
220 183
222 151
224 105
226 82
228 65
230 49
232 38
234 28
236 21
238 15
240 11
242 7
244 5
246 3
248 2
250 1
252 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 54,264
2 -
3 54,264
4 20,349
5 54,264
6 20,349
7 54,264
8 40,698
9 60,249
10 40,698
11 60,249
12 61,047
13 66,234
14 61,047
15 72,219
16 82,726
17 78,204
18 82,726
19 84,189
20 104,405
21 96,159
22 105,735
23 102,144
24 128,744
25 114,324
26 130,074
27 126,294
28 154,413
29 138,474
30 157,073
31 150,654
32 182,742
33 169,029
34 186,732
35 181,419
36 213,752
37 200,004
38 219,072
39 218,589
40 248,752
41 237,594
42 255,423
43 202,335
44 266,105
45 227,745
46 255,108
47 241,185
48 268,492
49 261,241
50 258,846
51 275,311
52 273,602
53 290,012
54 265,349
55 298,938
56 281,498
57 314,480
58 273,308
59 318,052
60 289,562
61 328,451
62 281,456
63 332,865
64 297,815
65 338,121
66 288,526
67 337,183
68 303,681
69 343,073
70 293,188
71 336,784
72 307,202
73 337,325
74 294,196
75 331,462
76 305,718
77 326,235
78 290,241
79 314,605
80 299,271
81 309,597
82 279,972
83 291,782
84 285,222
85 280,591
86 282,429
87 268,353
88 283,836
89 256,545
90 277,221
91 243,481
92 274,764
93 236,623
94 265,573
95 222,524
96 260,582
97 214,423
98 248,752
99 204,855
100 241,101
101 195,300
102 227,962
103 184,278
104 218,918
105 179,254
106 204,344
107 166,566
108 193,886
109 159,876
110 179,123
111 151,715
112 168,455
113 143,565
114 153,503
115 133,942
116 142,562
117 130,313
118 128,625
119 119,433
120 118,741
121 114,755
122 105,777
123 108,807
124 96,845
125 103,283
126 86,226
127 96,696
128 79,555
129 90,740
130 69,867
131 83,927
132 64,211
133 77,743
134 56,805
135 71,118
136 52,122
137 65,119
138 45,773
139 58,677
140 42,105
141 53,069
142 36,813
143 47,226
144 34,286
145 42,216
146 30,114
147 36,970
148 27,398
149 32,556
150 24,472
151 28,116
152 22,981
153 24,509
154 19,992
155 20,877
156 18,522
157 17,869
158 16,863
159 15,048
160 15,414
161 12,853
162 13,881
163 10,637
164 12,516
165 9,050
166 11,109
167 7,446
168 9,912
169 6,263
170 8,652
171 5,067
172 7,602
173 4,295
174 6,552
175 3,513
176 5,670
177 2,948
178 4,788
179 2,377
180 4,095
181 2,025
182 3,381
183 1,670
184 2,835
185 1,536
186 2,310
187 1,191
188 1,890
189 1,069
190 1,491
191 948
192 1,218
193 840
194 924
195 735
196 735
197 643
198 546
199 554
200 420
201 478
202 294
203 406
204 231
205 345
206 147
207 288
208 105
209 241
210 63
211 197
212 42
213 162
214 21
215 130
216 21
217 105
218 -
219 82
220 -
221 65
222 -
223 49
224 -
225 38
226 -
227 28
228 -
229 21
230 -
231 15
232 -
233 11
234 -
235 7
236 -
237 5
238 -
239 3
240 -
241 2
242 -
243 1
244 -
245 1

Written by: Michael Shackleford