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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 1234 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 412345, 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