# 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

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

## 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