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# Tialuvslotto's Blog

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## September 21, 2014, 4:32 pmFun with Pick 3 Pair Sums

Recently I read a post that referred to the sums of pairs, an idea that I had not previously considered. So I set up a spreadsheet so that I could play around with the concept, and I’m glad I did.

I summed each of the 55 pairs in the Pick 3 game and then grouped the pairs by the Last Digit of the Pair Sum. For example, pair ‘56’ sums to 11, so it went into group 1, Pair ‘77’ sums to 14 so I put it in group 4.  Root sums would also work, but I like LDS.

This gives 10 groups of pairs with LDS 0-9. Once I started playing around with these groups I noticed some really interesting characteristics.

 0 00 19 28 37 46 55 1 01 29 38 47 56 2 02 11 39 48 57 66 3 03 12 49 58 67 4 04 13 22 59 68 77 5 05 14 23 69 78 6 06 15 24 33 79 88 7 07 16 25 34 89 8 08 17 26 35 44 99 9 09 18 27 36 45

-the even sums of pair groups each have 6 pairs: 2 doubles, 2 odd pairs and 2 even pairs

-the odd sum of pair groups each have 5 pairs: 1 mirror pair, 2 consecutive pairs and 2 “ghost” pairs (one even digit, one odd digit)

Although the even numbered groups have more combinations, all groups hit at the same rate – since doubles hit less often.

-Looking at the Even/Odd combinations of these groups, there are only 2 possible configurations: EEE and OOE. 75% of the time you will get OOE,that is 2 Odd-numbered pair groups and 1 even-numbered pair group.  25% of the time you will get 3 Even-numbered pair groups.  No other configuration of E/O is possible – go ahead, give it a try!

-About half the time when a double is drawn it will be EEE (3 even or odd digits e.g. 266, 799), and the other half of the doubles will be OOE (a mixture of even and odd, e.g. 223, 558).

Unmatched numbers with the EEE configuration show up about 12% of the time, and are always all even or all odd combinations such as 157 or 246.

Doubles will have only 2 sum groups but unmatched will ALWAYS have 3 different sum groups.

The arrangements of High and Low sums are much more in line with what we expect:

HHH 11.5%

HHL 38.5%

LLH 38.5%

LLL 11.5%

About 60% of the time there will be at least one repeat group from one game to the next, with most of these (45%) being 1 repeat group.

The pair sum groups have a median skip of 2, so there are few long out streaks, with most streaks resolving after 7-15 outs.

Now, this is not a system, but it seems that with all these quirks it has potential as the basis of a system.

Any ideas?

Last Edited: September 21, 2014, 4:33 pm

Entry #2

## September 21, 2014, 4:29 pmThoth's "Distance" Indicator

While browsing through old posts I came across this gem of a post by Thoth.  The whole thread is well worth studying -- Thoth has done much in-depth analysis of the Pick 3 game and his posts are well worth some time.

I was particularly struck by his measure of the "distance" of a Pick 3 combination.

To find the distance, Thoth first arranges the combination from lowest to highest, so 327 becomes 237 and 996 becomes 699.  He then takes the delta of the first two numbers and the last two numbers.

For example, 327 ordered is 237.  We then subtract 3-2 to get 1 as our low-mid or front distance.  Similarly we subtract 7-3 to get 4 as our mid-high or back distance.   Thus the distance signature for this combination is 1-4.  For doubles, say 699, we subtract 9-6=3 for our front distance and 9-9=0 to get the back distance.  Thus, the distance signature of 699 is 3-0.

There are 55 of these signatures all together. 00 is the signature for all the triples.  There are 18 doubles signatures which all contain a zero.

A double signature will always be 01,02,03,04,05,06,07,08,09 or 10,20,30,40,50,60,70,80,90.  This neatly divides the doubles group exactly in half, based on whether the third digit is lower than the double digit (zero in back, eg.699 = 3-0) or the third digit is higher than the double digit (zero in front, e.g. 229 = 0-7).

The remaining signatures are assigned to the unmatched numbers and range from 1-1 to 8-1. The presence of a "1" in the signature always indicates a consecutive pair.  The unmatched numbers can also be evenly divided using the signatures with 60 combinations having a signature of 2-5 or less and the remaining 60 having a signature of 2-6 or higher.

100 of the 120 unmatched combination signatures will contain a '1' or a '2', so a combination with a distance signature such as 4-3 would be a rarity, only appearing about 16% of the time.  This is because there are few combinations that produce those signatures.

About a third of the doubles combinations will also contain a 1 or a 2 -- 17 from each group of 60 -- 01,02 or 10,20.

So far, the main way I have used this indicator is for doubles tracking.  Since the doubles are divided in half by the position of the zero in the signature, one can eliminate 50% of the doubles combinations for any game where you feel that the zero will fall in the front or back of the signature, and further elimination can be done if you want to include or exclude the '1' or '2' from the distance signature.

Entry #1