Reducing the number of Pick 3 combos

[Icewynd]

So, you've looked at the Pick 3 numbers, done your rundown and made your combinations. But, if you play too many combos a win might not be profitable. So the task is to filter down your combinations to eliminate those that aren't likely to win. Easy, no? OK, not easy, but there are some things we can do...

Filter out Sums
The sum of the combination (e.g. 123 = 1+2+3=6) only repeats 5% of the time from one draw to the next. So, if you filter out all combinations with the same sum as the last draw you will be right 95% of the time.

Filter out Roots
The Root or Root Sum is the reduction of the combination sum to a single digit (e.g. 563, sum is 5+6+3=14, Root is 1+4 =5). This method eliminates more combos that the Sum, but is less acuraate. The Root will be different from the last root about 90% of the time.

Filter by Line Length
Length of line is the difference between the highest digit in the combo and the lowest digit (e.g. 931 - line length is 9-1=8). The line length is most often different than the line length from the last winner. This filter will be accurate about 87% of the time.

Good luck with these!

 

[PAB]

Hi Icewynd,

Interesting that you have mentioned Root.

Filter out Roots
The Root or Root Sum is the reduction of the combination sum to a single digit (e.g. 563, sum is 5+6+3=14, Root is 1+4 =5). This method eliminates more combos that the Sum, but is less acuraate. The Root will be different from the last root about 90% of the time.

I keep two types of Root, one which I class as just Root which is the total of the digits but just the once, and the other which I class as Digital Root, which is what you are using, and involves continually adding the digits together until there is only one digit left.
I don't actually do the Lotto you are talking about because I live in the UK, but I just thought I would mention the fact that you could extend the Root analysis an extra step.

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Icewynd]

Thanks, PAB!

I will check it out.

 

[PAB]

You are welcome Icewynd,

Thanks, PAB!

I will check it out.

Every little helps, good luck!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Icewynd]

I've been doing some reading and I've also discovered refrences to another Root concept "Last Digit of Sum" or LDS. This idea goes by various other names, but I picked the one I found to be most descriptive. Basically this measure takes the last digit of the sum of the combination. E.g. 356, 3+5+6=14, so we would take 4 as the Last Digit of Sum. If the sum is only 1 digit then that is also the Last Digit of Sum.

This measure has an advantage over the Root concept (add sum digits until you are left with one) as each LDS number is associated with 22 boxed combinations while the root is associated with 24 or 25 boxed combinations for the Roots 1-9 and 1 boxed combination for the Root 0.

Pick whichever measure works best for you!

 

[PAB]

Nice work as usual Icewynd ,

Living in the UK we don't have a Pick 3 or Pick 4 Lotto as such, only what we call HotPicks where you can pick anything from 1 number to 5 numbers from 1-49, BUT they all have to be different. Basically, it is just an extension of the Main 649 Lotto and takes place at the same time as the Main 649 draw.

I just did a quick Google search and it appears that your Lotto Pick 3 numbers are from 0-9, and that the drawn numbers can either be all be the same, or 2 the same and 1 different, or all different, is that correct?
I just wondered if you had done an analysis for the LDS on the total combinations available?

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[PAB]

Hi Icewynd,

I just did some calculations and came up with the following for your LDS scenario.

I am not a 100% sure of the facts of the Pick 3 Lotto but this is how I understand it, please correct me if I am wrong!

There are 1,000 PERMUTATIONS, not COMBINATIONS of 0-9 numbers with 3 numbers being drawn. This is represented by using the Excel formula:-

=PERMUT(10,1)*PERMUT(10,1)*PERMUT(10,1)

Here is the Sum Total and corresponding Total Combinations for ALL possible 1,000 combinations:-

0 = 1 Combination
1 = 3 Combinations
2 = 6 Combinations
3 = 10 Combinations
4 = 15 Combinations
5 = 21 Combinations
6 = 28 Combinations
7 = 36 Combinations
8 = 45 Combinations
9 = 55 Combinations
10 = 63 Combinations
11 = 69 Combinations
12 = 73 Combinations
13 = 75 Combinations
14 = 75 Combinations
15 = 73 Combinations
16 = 69 Combinations
17 = 63 Combinations
18 = 55 Combinations
19 = 45 Combinations
20 = 36 Combinations
21 = 28 Combinations
22 = 21 Combinations
23 = 15 Combinations
24 = 10 Combinations
25 = 6 Combinations
26 = 3 Combinations
27 = 1 Combinations

Total Combinations = 1,000

Here is the Last Digit Sum of the combination LDS summary table:-

0 = 100 Combinations
1 = 100 Combinations
2 = 100 Combinations
3 = 100 Combinations
4 = 100 Combinations
5 = 100 Combinations
6 = 100 Combinations
7 = 100 Combinations
8 = 100 Combinations
9 = 100 Combinations

I hope this helps!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[Icewynd]

Thanks, PAB!

Yes the Pick 3 game, as played across North America, has participants pick 3 digits out of 10 (0-9) which can form 1,000 unique combinations. This is known as 'straight' play and you win if you have the correct 3 digits in the correct order.

However, you can also play 'boxed' combinations, of which there are 220. These are the any-way combinations of 3 digits (6-way for 3 different digits, 3 way for 2 different digits). So, the digits 1,2 and 3 can be combined as 123, 132, 231, 213, 321 and 312, but 123 will win the 'boxed' prize if any of these six combinations come up.

No surprise, the Last Digit of Sum filter is equally as effective as the Root filter in that it does not match the last draw 90% of the time.