 Last Updated: May 11, 2020

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

1. The game uses 25 colored dice, colored as follows:
• 6 Blue
• 6 Red
• 6 Green
• 6 Yellow
• 1 White
2. Six of the 25 dice will be chosen randomly, without replacement.
3. 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.
4. 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.
5. 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
6. 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 63 = 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 64 = 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 65 = 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 66 = 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 66 = 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 66 = 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 66 = 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%.