


Analysis of 3digit Lotery Games
The analysis of 3digit games involves the analysis of individual digits, pairs, sums, the numbers
themselves in exact order (straight), numbers in any order (boxes), and so on. The purpose of 3digit
game analysis is to determine the most and least frequently drawn numbers, digits, pairs, etc., and to
identify late entities in order to predict the winning numbers. Such analysis calls for
the actual statistics of the drawn number which are available at different web sites. On this web site we shall see only
the prominent features that lead to a more detailed analysis. Here is what's available on this page:
All 3digit numbers
Groupping and probabilities of 3Digit Games
Sum of Digits of 3Digit Games
All 3digit numbers
There are 1000 possible 3digit numbers, and they are: 000, 001, 002, 003, 004, ... , 999. That is, just start from 0 and count
upto 999. You can generate the full list of all 3digit numbers by cliking here.
Grouping and probabilities of 3Digit Games
Each one of the 1000 numbers in 3digit lottery games have equal chance of being drawn at any given time, therefore, the chance
of winning with one selected number in exact order (straight) is 1 in 1000.
In mathamatical terms, we say the probability of winning is 0.001 or 0.1%. On the other hand, when playing boxes and combos (any order) of a 3digit game,
the order in which the number is drawn doesn't matter, therefore instead of 1000 possibilities we have only 220. In this later case, the numbers
123,123, 132, 213, 231, 312, 321, for example, are represented by only one number 123. For this reason, the chance of winning with a box or a combo play is obviously higher than the
chance of winning with a straight play.
Since there are 220 possible outcomes, one may be tempted to conclude that the chance winning in a box is 1 in 220.
This is not exactly true since not all boxes have equal chances of winning; numbers with nonrepeating digits have a
better chance of winning than numbers with one digit repeated. For example, the number 123 has a better chance of winning than
the number 122, since 123 covers six possible permutations shown above, while 122 covers only three (122, 212, 221).
Consequently, we shall classify all the 3digit numbers into three groups, namely, nonrepeating numbers,
onerepeating (doubles) numbers, and triples. Very often, nonrepeating and onerepeating boxes are referred to
as 6way and 3way boxes (or combos), respectively.
Of the 1000 3digit numbers 720 are nonrepeating, 270 onerepeating, and 10 triples. Since a nonrepeating number has 5 more siblings, we
can divide 720 by 6 to obtain 120 distinct nonreapeating numbers. Similarly, there are 270/3=90 distinct onerepeating numbers.
The following table and figures summarize the foregoing facts and the probability of winning.
Group name and aliases  How many 3dig Numbers fall into this group  How many distinct members of the group  odds of winning with a number in the group  Probability of a number drawn to be in the goup 
Nonrepeat (6way)  720  120  1:167  72% 
Onerepeat (3way) (Doubles)  270  90  1:333  27% 
Triples  10  10  1:1000  1% 
For instance, if you play 123, 112, and 000, the chance of winning with these numbers in any arrangement are 1 in 167, 1 in 333, and 1 in 1000, respectively.
On the other hand, the probabilities listed above indicate that out of 100 draws, we should theoretically expect 72 nonrepeat numbers (72%),
27 onerepeats (27%), and 1 triple (1%). Analysis of actual winning numbers of all the 3digit games in the United States continuously conducted
by USLotteries.com reveal that the above figures very closely match the actual data.
Sum of Digits of 3Digit Games
The sum of the 3 digits of the lottery games ranges from 0 to 27. The digits of the number 000 sum up to 0, and that of 999 sum
up to 27, the rest lie in between. Well over 50% of 3digit numbers have a sum between 10 and 17, it is therefore not surprizing
to see winning numbers with sums 1017 drawn every other day.
You might be tempted to play all the numbers with sums that range from 10 to 17 everyday in order to win every other day. This
is quite naive since you are covering about 50% of the numbers and since the house edge
of a lottery game is about 50%, you will only be breaking even every other day and losing in rest. However, it is not a bad idea
to analise the trend of the sums in the past several days and play those that are overdue for a few days.
Click here to open a new window of the sums, odds and probabilities of all the 28 possible 3digits and the corresponding distinct 3digit numbers.


