


Analysis of 4digit Lotery Games
The analysis of 4digit 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 4digit
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:
Groupping and probabilities of 4Digit Games
Sum of Digits of 4Digit Games
Groupping and probabilities of 4Digit Games
Each one of the 10000 numbers in 4digit 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 10,000.
In mathamatical terms, we say the probability of winning is 0.0001 or 0.01%. On the other hand, when playing boxes and combos (any order) of a 4digit game,
the order in which the number is drawn doesn't matter, therefore instead of 10,000 possibilities we have only 715. In this later case, the numbers
1122,2211, 1221, 2112, 1212, 2121, for example, can be represented by only one number  1122. 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 715 possible outcomes, one may be tempted to conclude that the chance winning in a box is 1 in 715.
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, two digits repeated, and one digit tripled. For example, the number 1234
has a better chance of winning than the number 1122, since 1234 covers 24 possible permutations (thus the name 24way box), while 1122 covers
only the six shown above.
Consequently, we shall classify all the 4digit numbers into five groups, namely, nonrepeating numbers,
doubles (onerepeating) numbers, dualdoubles (tworepeating), triples (onetripled) and quadruplets
(all four identical). Very often, the first four groups are referred to as 24way, 12way, 6way, and 4way boxes (or combos), respectively.
Of the 10,000 4digit numbers 5040 are nonrepeating, 4320 onerepeating (doubles), 270 tworepeating (dualdoubles), 360 onetripled, and 10 quadruples. Since a nonrepeating number has 23 more siblings, we
can divide 5040 by 24 to obtain 210 distinct nonreapeating numbers. Similarly, there are 4320/12=360 distinct onerepeating numbers, 270/6=45 distinct dualdoubles, 360/4=90 distinct triples.
The following table and figures summarize the foregoing facts and the probability of winning.
Group name and aliases  How many 4dig 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 
Nonrepeating (24way)  5040  210  1:417  50.40% 
Onerepeating (12way) (Doubles)  4320  360  1:833  43.20% 
Tworepeating (6way) (DualDoubles)  270  45  1:1667  2.70% 
Onetripled (4way) (triples)  360  90  1:2500  3.60% 
Quadruples  10  10  1:10,000  0.1% 
For instance, if you play 1234, 1122, and 0000, the chance of winning with these numbers in any arrangement are 1 in 417, 1 in 1,667, and 1 in 10,000, respectively.
On the other hand, the probabilities listed above indicate that out of 1000 draws, we should theoretically expect 504 nonrepeat numbers (50.40%),
432 doubles (43.20%), 27 dualdoubles (2.70%), 36 triples (3.6%), and 1 quadruple (0.1%). 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.
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Sum of Digits of 4Digit Games
The sum of the 4 digits of the lottery games ranges from 0 to 36. The digits of the number 0000 sum up to 0, and that of 9999 sum
up to 36, the rest lie in between. Well over 50% of 4digit numbers have a sum between 14 and 22, it is therefore not surprizing
to see winning numbers with sums 1422 drawn every other day.
You might be tempted to play all the numbers with sums that range from 14 to 22 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 state lottery game is 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 37 possible 4digits and the corresponding distinct 4digit numbers.
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