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# Fun with Pick 3 Pair Sums

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

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?

Entry #2