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# Koobix

## Introduction

Koobix is an Italian gambling game. It is based on the throw of six colored dice. There are a host of ways to bet on the outcome, as listed below.

## Rules

- The game uses 25 colored dice, colored as follows:
- 6 Blue
- 6 Red
- 6 Green
- 6 Yellow
- 1 White

- Six of the 25 dice will be chosen randomly, without replacement.
- For purposes of bets involving color, the white die is wild and can substitute for any color that will help the player. The white die is NOT wild for purposes of the side it lands on.
- The player may make only one bet at a time, so there will be no conflicts about which color the white die might substitute for.
- There are a host of ways of betting. Following is an overview:
- Total of first three dice rolled
- Total of first four dice rolled
- Total of first five dice rolled
- Total of all six dice
- Total of all six dice in groups (small, medium, or large total)
- Parity of all six dice (odd/even)
- Poker value of all six dice
- Specified color will be rolled at least once
- Number of consecutive odd/even/low/high dice
- Number of consecutive dice of the same color
- Number of consecutive increasing/decreasing dice
- Exact number of dice of specified color
- Specified die will be lower/higher than other specified die

- All wins pay on a "for one" basis.

For purposes of the analysis of each bet, I'm using the pays from Tuko Productions.

## Total of Three Dice

The following table shows the bets on any given total of the first three dice rolled. Combinations are based out of a total of 6^{3} = 216.

### Total of Three Dice

Total | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Total of 3 | 210 | 1 | 0.004630 | 0.972222 |

Total of 4 | 70 | 3 | 0.013889 | 0.972222 |

Total of 5 | 35 | 6 | 0.027778 | 0.972222 |

Total of 6 | 21 | 10 | 0.046296 | 0.972222 |

Total of 7 | 14 | 15 | 0.069444 | 0.972222 |

Total of 8 | 10 | 21 | 0.097222 | 0.972222 |

Total of 9 | 8.4 | 25 | 0.115741 | 0.972222 |

Total of 10 | 7.8 | 27 | 0.125000 | 0.975000 |

Total of 11 | 7.8 | 27 | 0.125000 | 0.975000 |

Total of 12 | 8.4 | 25 | 0.115741 | 0.972222 |

Total of 13 | 10 | 21 | 0.097222 | 0.972222 |

Total of 14 | 14 | 15 | 0.069444 | 0.972222 |

Total of 15 | 21 | 10 | 0.046296 | 0.972222 |

Total of 16 | 35 | 6 | 0.027778 | 0.972222 |

Total of 17 | 70 | 3 | 0.013889 | 0.972222 |

Total of 18 | 210 | 1 | 0.004630 | 0.972222 |

Total | 216 | 1.000000 |

## Total of Four Dice

The following table shows the bets on any given total of the first three dice rolled. Combinations are based out of a total of 6^{4} = 1,296.

### Total of Four Dice

Total | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Total of 4 | 1260 | 1 | 0.000772 | 0.972222 |

Total of 5 | 315 | 4 | 0.003086 | 0.972222 |

Total of 6 | 126 | 10 | 0.007716 | 0.972222 |

Total of 7 | 63 | 20 | 0.015432 | 0.972222 |

Total of 8 | 36 | 35 | 0.027006 | 0.972222 |

Total of 9 | 22.5 | 56 | 0.043210 | 0.972222 |

Total of 10 | 15.8 | 80 | 0.061728 | 0.975309 |

Total of 11 | 12.1 | 104 | 0.080247 | 0.970988 |

Total of 12 | 10.1 | 125 | 0.096451 | 0.974151 |

Total of 13 | 9 | 140 | 0.108025 | 0.972222 |

Total of 14 | 8.6 | 146 | 0.112654 | 0.968827 |

Total of 15 | 9 | 140 | 0.108025 | 0.972222 |

Total of 16 | 10.1 | 125 | 0.096451 | 0.974151 |

Total of 17 | 12.1 | 104 | 0.080247 | 0.970988 |

Total of 18 | 15.8 | 80 | 0.061728 | 0.975309 |

Total of 19 | 22.5 | 56 | 0.043210 | 0.972222 |

Total of 20 | 36 | 35 | 0.027006 | 0.972222 |

Total of 21 | 63 | 20 | 0.015432 | 0.972222 |

Total of 22 | 126 | 10 | 0.007716 | 0.972222 |

Total of 23 | 315 | 4 | 0.003086 | 0.972222 |

Total of 24 | 1260 | 1 | 0.000772 | 0.972222 |

Total | 1296 | 1.000000 |

## Total of Five Dice

The following table shows the bets on any given total of the first five dice rolled. Combinations are based out of a total of 6^{5} = 7,776.

### Total of Five Dice

Total | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Total of 5 | 7560 | 1 | 0.000129 | 0.972222 |

Total of 6 | 1512 | 5 | 0.000643 | 0.972222 |

Total of 7 | 504 | 15 | 0.001929 | 0.972222 |

Total of 8 | 216 | 35 | 0.004501 | 0.972222 |

Total of 9 | 108 | 70 | 0.009002 | 0.972222 |

Total of 10 | 60 | 126 | 0.016204 | 0.972222 |

Total of 11 | 36.9 | 205 | 0.026363 | 0.972801 |

Total of 12 | 24.8 | 305 | 0.039223 | 0.972737 |

Total of 13 | 18 | 420 | 0.054012 | 0.972222 |

Total of 14 | 14 | 540 | 0.069444 | 0.972222 |

Total of 15 | 11.6 | 651 | 0.083719 | 0.971142 |

Total of 16 | 10.3 | 735 | 0.094522 | 0.973573 |

Total of 17 | 9.7 | 780 | 0.100309 | 0.972994 |

Total of 18 | 9.7 | 780 | 0.100309 | 0.972994 |

Total of 19 | 10.3 | 735 | 0.094522 | 0.973573 |

Total of 20 | 11.6 | 651 | 0.083719 | 0.971142 |

Total of 21 | 14 | 540 | 0.069444 | 0.972222 |

Total of 22 | 18 | 420 | 0.054012 | 0.972222 |

Total of 23 | 24.8 | 305 | 0.039223 | 0.972737 |

Total of 24 | 36.9 | 205 | 0.026363 | 0.972801 |

Total of 25 | 60 | 126 | 0.016204 | 0.972222 |

Total of 26 | 108 | 70 | 0.009002 | 0.972222 |

Total of 27 | 216 | 35 | 0.004501 | 0.972222 |

Total of 28 | 504 | 15 | 0.001929 | 0.972222 |

Total of 29 | 1512 | 5 | 0.000643 | 0.972222 |

Total of 30 | 7560 | 1 | 0.000129 | 0.972222 |

Total | 7776 | 1.000000 |

## Total of All Six Dice

The following table shows the bets on any given total of the all six dice rolled. Combinations are based out of a total of 6^{6} = 46,656.

### Total of Six Dice

Total | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Total of 6 | 45357 | 1 | 0.000021 | 0.972158 |

Total of 7 | 7560 | 6 | 0.000129 | 0.972222 |

Total of 8 | 2160 | 21 | 0.000450 | 0.972222 |

Total of 9 | 810 | 56 | 0.001200 | 0.972222 |

Total of 10 | 360 | 126 | 0.002701 | 0.972222 |

Total of 11 | 180 | 252 | 0.005401 | 0.972222 |

Total of 12 | 99.5 | 456 | 0.009774 | 0.972479 |

Total of 13 | 60 | 756 | 0.016204 | 0.972222 |

Total of 14 | 39.1 | 1161 | 0.024884 | 0.972975 |

Total of 15 | 27.2 | 1666 | 0.035708 | 0.971262 |

Total of 16 | 20.2 | 2247 | 0.048161 | 0.972852 |

Total of 17 | 15.9 | 2856 | 0.061214 | 0.973302 |

Total of 18 | 13.2 | 3431 | 0.073538 | 0.970705 |

Total of 19 | 11.6 | 3906 | 0.083719 | 0.971142 |

Total of 20 | 10.8 | 4221 | 0.090471 | 0.977083 |

Total of 21 | 10.5 | 4332 | 0.092850 | 0.974923 |

Total of 22 | 10.8 | 4221 | 0.090471 | 0.977083 |

Total of 23 | 11.6 | 3906 | 0.083719 | 0.971142 |

Total of 24 | 13.2 | 3431 | 0.073538 | 0.970705 |

Total of 25 | 15.9 | 2856 | 0.061214 | 0.973302 |

Total of 26 | 20.2 | 2247 | 0.048161 | 0.972852 |

Total of 27 | 27.2 | 1666 | 0.035708 | 0.971262 |

Total of 28 | 39.1 | 1161 | 0.024884 | 0.972975 |

Total of 29 | 60 | 756 | 0.016204 | 0.972222 |

Total of 30 | 99.5 | 456 | 0.009774 | 0.972479 |

Total of 31 | 180 | 252 | 0.005401 | 0.972222 |

Total of 32 | 360 | 126 | 0.002701 | 0.972222 |

Total of 33 | 810 | 56 | 0.001200 | 0.972222 |

Total of 34 | 2160 | 21 | 0.000450 | 0.972222 |

Total of 35 | 7560 | 6 | 0.000129 | 0.972222 |

Total of 36 | 45357 | 1 | 0.000021 | 0.972158 |

46656 | 1.000000 |

## Range Bets

Range bets can be based on the total of three, four, five, or six dice, as specified by the player. The player may be on the range of the total (low, medium, or high) or whether the total will be odd or even. The following table shows the range bets available for three to six dice respectively.

### Range Bets with Three Dice

Bet | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Odd | 1.9 | 108 | 0.500000 | 0.950000 |

Even | 1.9 | 108 | 0.500000 | 0.950000 |

3 to 9 | 2.6 | 81 | 0.375000 | 0.975000 |

10 or 11 | 3.9 | 54 | 0.250000 | 0.975000 |

12 to 18 | 2.6 | 81 | 0.375000 | 0.975000 |

### Range Bets with Four Dice

Bet | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Odd | 1.9 | 648 | 0.500000 | 0.950000 |

Even | 1.9 | 648 | 0.500000 | 0.950000 |

Total of 4 to 12 | 2.9 | 435 | 0.335648 | 0.973380 |

Total of 13 to 15 | 2.9 | 426 | 0.328704 | 0.953241 |

Total of 16 to 24 | 2.9 | 435 | 0.335648 | 0.973380 |

### Range Bets with Five Dice

Bet | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Odd | 1.9 | 3,888 | 0.500000 | 0.950000 |

Even | 1.9 | 3,888 | 0.500000 | 0.950000 |

Total of 5 to 16 | 2.4 | 3,108 | 0.399691 | 0.959259 |

Total of 17 or 18 | 4.8 | 1,560 | 0.200617 | 0.962963 |

Total of 19 to 30 | 2.4 | 3,108 | 0.399691 | 0.959259 |

### Range Bets with Six Dice

Bet | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Odd | 1.9 | 23,328 | 0.500000 | 0.950000 |

Even | 1.9 | 23,328 | 0.500000 | 0.950000 |

Total of 6 to 19 | 2.7 | 16,941 | 0.363104 | 0.980382 |

Total of 20 to 22 | 3.6 | 12,774 | 0.273791 | 0.985648 |

Total of 23 to 36 | 2.7 | 16,941 | 0.363104 | 0.980382 |

## Poker Bets

The following three bets are based on just the numbers rolled on the dice, as opposed to the color. The bet on a three of a kind wins on at least three of a kind or more. Combinations are based out of 6^{6} = 46,656 possible.

### Poker Bets without Color

Total | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Three of a kind | 2.6 | 17,136 | 0.367284 | 0.954938 |

Consecutive Three of a kind | 10 | 4,506 | 0.096579 | 0.965792 |

Straight | 62.4 | 720 | 0.015432 | 0.962963 |

Consecutive Straight | 22500 | 2 | 0.000043 | 0.964506 |

The following two bets are based on the numbers rolled on the dice as well the color. To be honest with you, I accepted the return quoted in the help file and calculated the probability based on that and what a win pays. The math would have been rather messy. The bet on a three of a kind wins on at least three of a kind or more. Remember that the white die is wild.

### Poker Bets with Color

Total | Pays | Probability | Return |
---|---|---|---|

Suited three of a kind | 30.7 | 0.031427 | 0.964797 |

Suited and consecutive three of a kind | 146 | 0.006606 | 0.964446 |

## Combo Bet

There are lots of ways to do a combo bet. First, the player must choose a particular die by it's order rolled, for example the third. Then the player may choose any combination of the following about that die:

- Exactly which side it will land on.
- It's color
- Whether it's low (1 to 3), high (4 to 6), odd, or even

The win is commensurate with the probability of winning. Remember that if choosing a color, then white is wild for purposes of color.

### Combo Bets

Number | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Number | 5.8 | 25 | 0.166667 | 0.966667 |

Color | 3.4 | 42 | 0.280000 | 0.952000 |

White | 23.8 | 6 | 0.040000 | 0.952000 |

Even,odd,low,high | 1.9 | 75 | 0.500000 | 0.950000 |

Number & color | 20.4 | 7 | 0.046667 | 0.952000 |

Number & white | 142.8 | 1 | 0.006667 | 0.952000 |

Even,odd,low,high & color | 6.8 | 21 | 0.140000 | 0.952000 |

Even,odd,low,high & white | 47.6 | 3 | 0.020000 | 0.952000 |

## Odd,Even,Low,High

In the following bets, the player will choose a number from three to six and a type of bet (low, high, odd, or even). The player will win if the total of dice rolled that match the condition is equal or greater to the number chosen. For example, if the player chooses five odd dice, which pays 20.6, then the player will win if at least five of the six dice rolled are odd. Probabilities are based on 6^{6} = 46,656 possible combinations.

### Odd,Even,Low,High

Number | Pays | Combinations | Probability | Return |
---|---|---|---|---|

3 | 3.1 | 14,580 | 0.312500 | 0.968750 |

4 | 7.7 | 5,832 | 0.125000 | 0.962500 |

5 | 20.6 | 2,187 | 0.046875 | 0.965625 |

6 | 62 | 729 | 0.015625 | 0.968750 |

## Consecutive Same Color

The following bets are based on the number of consecutive dice of the same color. The player must choose a color and at least how many will be consecutive. Remember that the white die is wild and will substitute for whatever color that will benefit the player. The player will win if the total dice rolled matching the color chosen is equal or greater than the number selected. For example, if the player bets on four yellows, the player will win if at least four of the dice are yellow and consecutive (with the wild white counting as yellow). Probabilities are based on a total of permut(25,6) = 25!/19! = 25*24*23*22*21*20 = 127,512,000 possible permutations.

### Consecutive Same Color

Number | Pays | Combinations | Probability | Return |
---|---|---|---|---|

3 | 18.3 | 6,703,200 | 0.052569 | 0.962016 |

4 | 128.1 | 957,600 | 0.007510 | 0.962016 |

5 | 1281 | 95,760 | 0.000751 | 0.962016 |

6 | 24338 | 5,040 | 0.000040 | 0.961976 |

## Consecutive Increasing/Decreasing

The following bets are based on the total consecutive increasing or decreasing dice. The bettor must choose increasing or decreasing and a number from 3 to 6. If the player bets increasing, then he wins if there is a run of dice starting with 1 and increasing one at a time, in order, at least as long as the length chosen. For example, if the player bets on four increasing, then the sequence 1-2-3-4 must be in the roll somewhere. The player wins if a sequence exists longer than the number chosen. In the case of four increasing, the player would win if the roll were 4-1-2-3-4-5, for example. Bets on decreasing work the same way, but starting with a 6 and decreasing one at a time, in order. Probabilities are based on 6^{6} = 46,656 possible combinations.

### Consecutive Increasing/Decreasing

Number | Pays | Combinations | Probability | Return |
---|---|---|---|---|

3 | 14.4 | 3,117 | 0.066808 | 0.962037 |

4 | 149.6 | 300 | 0.006430 | 0.961934 |

5 | 1952 | 23 | 0.000493 | 0.962277 |

6 | 44900 | 1 | 0.000021 | 0.962363 |

## Rainbow

Rainbow bets require the player to choose a color and a number from 0 to 6. The player wins if the total number of dice matching the color chosen is equal exactly to the number chosen. For example, if the player chooses 5 green, then the player will win if five of the dice are green. Remember that the white die is wild for purposes of color; it will count as a color that favors the player.

### Rainbow

Number | Pays | Combinations | Probability | Return |
---|---|---|---|---|

0 | 6.3 | 27132 | 0.153202 | 0.965170 |

1 | 2.1 | 78336 | 0.442326 | 0.928885 |

2 | 2.2 | 76500 | 0.431959 | 0.950311 |

3 | 5.3 | 31620 | 0.178543 | 0.946279 |

4 | 30.3 | 5625 | 0.031762 | 0.962380 |

5 | 444 | 384 | 0.002168 | 0.962710 |

6 | 24300 | 7 | 0.000040 | 0.960474 |

## Match

Finally, there is a match bet that pits one die against another. The player chooses two positions and bets whether the first in the first position will be greater or less than the second position. Ties lose. Wins pay 2.3. The probability of winning is 15/36 = 41.67%, for a return of 95.83%.

## External Links

- Tuko Productions — A supplier of games of Internet casinos, where you can play Koobix for free.
- Wizard of Vegas — Discussion about Koobix in my forum.

Written by:Michael Shackleford