I had originally posted this to the Pick 3 Forum, and someone requested that I also post it here as well.
For those of you who are not familiar with Vtracs, there is a good explanation at http://www.compulotto.com/concept.htm.
There are a total of 125 different Vtrac numbers, 5 of which are triples, 60 doubles and 60 which contain three unique numbers.
Odd / Even
27 are all odd digits, 54 contain two odd and one even digit, 36 contain one odd and two even digits, and 8 are all even digits.
Sum of Lines
Here are the sum ranges, and the number of combinations:
9 = 19 8-10 = 55 7-11 = 85 6-12 = 105 5-13 = 117 4-14 = 123 3-15 = 125
Roots
In the traditional Pick 3, every root (with the exception of 0) has an equal probability of appearing. Not so with Vtracs. Here are the roots, and the number of combinations:
1 = 18 2 = 15 3 = 11 4 = 9 5 = 9 6 = 11 7 = 15 8 = 18 9 = 19
Repeating numbers
Given any Vtac number where all three digits are different, the probability that at least one of the digits will repeat in the next drawing is 93.6%. If the number contains a double, the probability is 78.4%. If the number is a triple, the probability is 46.8%. Overall, the probability is 77.0% [0.48*0.936] + [0.48*0.784] + [0.04*0.488].
Of the 125 Vtrac combinations, there are 35 that I call "boxed combinations". They are 111-112-113-114-115-122-123-124-125-133-134-135-144-145-155-222-223-224-225-233-234-235-244-245-255-333-334-335-344-345-355-444-445-455 and 555.
As you can see, there are 5 triples, 20 doubles and 10 with three unique numbers.
There are 10 that contain all odd digits, 12 that have two odd and one even digit, 9 that have one odd and two even digits, and 4 that contain all even digits.
The range of the sum of the numbers with the number of combinations:
9 = 5 8-10 = 13 7-11 = 21 6-12 = 27 5-13 = 31 4-14 = 33 3-15 = 35
The roots are more evenly distributed, either having 3, 4 or 5 combinations each.
Given any Vtrac number that has three unique digits, the probability that at least one number will repeat in the next drawing is 88.6%. If the number was a double, the probability is 71.4%. If the number was a triple, the probability is 42.9%. Overall, the probability is 72.2% [ 0.286*0.886] + [0.571*0.714] + [0.143*0.429].
Hope this is of some small help.
Rick