Texas Lottery Pick 4 Combinations Generator
This is a re-designed utility to generate all the combinations of a selected set of Texas Lottery Pick 4 numbers, with the option of fixing some
digits as well as pairs and triads. It also allows you to extract several Pick 4 patterns such as even-odds and high-low, in addition
to filtering out by sums or consecutivity. If this is the first time you are using this tool, we strongly recommend that you read the
Instructions on how to use the Texas Lottery Pick 4 Combinations Generator further down on this page.
Instructions for the Texas Lottery Pick 4 Combinations Generator
This tool generates Texas Pick 4 combinations of boxes (4-digit numbers without regard to their
arrangement). Basically, two steps are involved: 1, make your selections on the "Selection Panel" and, 2, click on the "List Results"
button. The generated numbers will be listed under the "Results Panel", which also contains the total numbers generated, the odds
(and probability) of winning with the generated Pick 4 set, frequency of the digits of the generated numbers, and the summary
of selection criteria.
There are eight selection criteria most with All and None buttons that will facilitate some selections. For example,
if you want to list all numbers with a sum of 18, you have to unselect all the other sums one by one. Alternatively, a faster way
would be to click on None and then click on 18. Note that you cannot leave all options of a criterion unselected.
The "Summary of Selection Criteria" displayed at the end of the "Results Pannel" will show in red whatever modifications you
have made on the default values.
Every selection you make is appended to your previous selection. So, the results listed will always incorporate all previous choices.
To start all over again, or to return to the initial default selections, click on the Reset All button at the bottom.
Initially, all the 715 possible Pick 4 combinations will be listed, with all checkboxes checked. Then, you can use one or
more of the following criteria to filter out your desired set of Texas Pick 4 list.
- Digit Selection
By default, combinations of all the Digits 0123456789 are considered. If you want not to include some Pick 4 digits, you
can do so by deleting them. To generate all combinations of the digits 135689, for example, just enter them and click on the "List Results"
button. If you want futher filtering such as non-repeating digits, go to the selection labeled 3. Repeating or not and
unselect Doubles, Dual-Doubles, Triples, and Quadruples. Alternatively, you may click on None
and then mark Non-Repeating. If you still want to impose more conditions, such as Pick 4 sums, go ahead do it; note
that at some point you may end up with no numbers generated if you specify a set of incompatible conditions.
- Key (fixed) Digit/Pair/Triad Selection
Sometimes, you may wish to generate numbers that must contain a digit, a pair, or a triad. For example, if you feel that 8 is
due in the Texas Pick 4, then enter 8 in the box to generate Pick 4 numbers that must contain 8. The
same goes for a pair and a tiad; just enter 234 to geneate all Pick 4 numbers that contain 234. There is still more hosepower
to this tool - you may impose "either or" condition by separating your entries by commas. If you enter "2,8", for instance, only
numbers that contain either 2 or 8 will be listed. In fact, you may enter more than two digits, pairs, and triads such as "2,8,07,234"
to list the numbers that contain at least one of 2, 8, 07, or 234.
- Repeating or not
Here, you may choose to list only Pick 4 non-repeating numbers, doubles, dual-doubles, triples, quadruples, or any combinations thereof.
If you want 1, 2, 3, or all 4 digits of Pick 4 to be even or odd, then use this selection criterion.
If you want 1, 2, 3, or all 4 digits of Pick 4 to be low (0,1,2,3,4) or high(5,6,7,8,9), then use this selection criterion.
Sums are simply the sum of the four Pick 4 digits. Some sums are more likely to be drawn than others simply because they
cover more numbers. If you want to filter out numbers with certain sums, then use this option.
- Root Sums
The Root Sum is the sum of the sum. For example, the number 3489 has a sum of 24, thus its Root Sum is 6 (i.e, 2+4). Root Sums
have the interesting characteristic of distributing all the Pick 4 numbers into nearly equal groups, that is, except Root Sums of
0, all the rest have nearly equal Root Sum (79 and 80). So, unlike Sums, Root Sum have about equal chances of
being drawn. This will allow the player to choose members of a hot or cold Pick 4 Root Sum.
The numbers with obvious consecutive digits are 0123, 1234, 2345, 3456, 4567, 5678, and 6789. If we analyze the frequency of
digits in this set, we will see that 0 and 9 appear only once, 1 and 8 appear twice, 2 and 7 appear 3 times, while the rest
appear four times. In order to have an equal frequency of all the digits, we have to view the arrangement of the digits as
circular, as shown in the figure, rather than linear as 0-1-2-3-4-5-6-7-8-9. As can be seen on the figure, 7890, 8901, and 9012
are also consecutive. So, our list of numbers with consecutive digits has to include 0789, 0189 and 0129.
What we refer to here as consecutivity is "within how many digits a number is spread". The numbers listed above are consecutive
within 4 digits therefore have a consecutivity of 4. Only quadruples have a consecutivity of 1, only dual-doubles and triples can
have a consecutivity of 2, and only doubles, dual-doubles and triples can have a consecutivity of 3. In many case, the consecutivity
of a number is the difference between the highest and the lowest digts plus 1. However, since we are using the circular arrangement
of the digits, the actual consecutivity is the shortest distance that includes all the four digits along the circular path.
To illustrate, consider 0234 and 0678. Both of these numbers are consecutive within 5 digits. It is obvious for 0234 since
(4-0)+1 = 5, but not for 0678. Here is how you determine the consecutivity of 0678 (or any other number in general). Start from
one of the digits and go clockwise until you have encountered all other digits on your way. If you start from 0 and go to 8 you'll
cover 9 digits; if you start from 6 and go to 0 you'll cover 5 digits; if you start from 7 and go to 6 you'll cover 10 digits;
if you start from 8 and go to 7 you'll cover 10 digits. So, 0678 is consecutive within 5 since the second one is the shotest path.
Note that the digits are equally distributed within a given consecutivity. For instance, for a consecutivity of 3, all the
digits of the generaed numbers appear 24 times.
Finally, if you still want to use the old tool, click here -> Old Texas Pick 4 Combinations Generator