Systematic, but not Sequential

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Chosen Numbers Heading - Systematic

Here at Chosen Numbers, we are assigning lottery numbers systematically.

Our quickpicks are NOT random selections, but selected programmatically.


What does that mean?


First off we have created a function to generate lottery numbers sequences based on the index.

For those who are computer or math savvy, this can be represented as a function:


f(x)={lottery number sequence}


So for a lottery which has 6 numbers from a pool of 49 numbers, or 13,938,816 possibilities, the first four and last four sequences from the function would be as follows:


f(1) = {1,2,3,4,5,6}

f(2) = {1,2,3,4,5,7}

f(3) = {1,2,3,4,5,8}

f(4) = {1,2,3,4,5,9}

...

(13,938,808 additional sequences)

...

f(13938813) = {43,44,45,47,48,49}

f(13938814) = {43,44,46,47,48,49}

f(13938815) = {43,45,46,47,48,49}

f(13938816) = {44,45,46,47,48,49}


How do We Choose?

So we have a function, now what?

We now need to find a logical way of presenting these numbers to the players.

This method must be programmatic.

It must span the entire pool of available numbers.

It must provide unique numbers until the pool resets when all sequences have been exhausted.

We have narrowed down the process to a couple of choices.

Sequentially or systematically.


Sequentially


Chosen Numbers - Sequential

The above image shows illustratively numbers being chosen sequentially.

Programmatically it would be easy. Just maintain a pointer and add one to it for the next sequence.

We could have chosen this approach, but that would not be too much fun for the players.

Lottery number sequences would be bunched together wherever the index is currently sitting, be it at the beginning, middle or end of the pool of numbers.

Players would also be able to predict the next sequence.

We believe players want to see numbers which do not look sequential.


Systematically


Chosen Numbers - Systematic

This is the approach we have adopted for our pools of numbers.


What we are storing is an offset and an increment.

We then add the increment and offset to the index and this provides the next sequence of lottery numbers.


We have some checks in place to see if the offset and increment exceeds the number of sequences in the pool.

If so, we start at the lower offset but increment it by 1.

This way we are providing lottery combinations throughout the entire range of the given lottery.

It also provides a bit of variety to the numbers generated.

The next sequences are not easy to predict.


Each lottery on our website has its own unique increment.

That way different sequences would be generated with lotteries with the same play format.

We decided the increment should be a number between 32000 and 34000.

We also decided to choose prime numbers for the increment as well (kind of following the methodology used by various crypto algorithms).

This logic is used for the main number sequences for a lottery.


For lotteries with a "Mega Ball" or "PowerBall", here we are adding a sequentially increased number.

Frankly, we chose this method for this additional "ball" because it was easier to implement.


Aside Note:

All of our lottery pools do start at the same index, and that index is f(1), so depending on the lottery, the first sequence is 1,2,3,4,5,6 for a lottery with six numbers drawn.


So that's how we do it.

Storing index pointers.

Remember, play with chosen numbers.



We Have Been Through This a Million Times

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Chosen Numbers - Why - A Million Times

We have a simulation setup to show the disadvantages of using random numbers at our Why Page.

The goal of that page - How many rolls of the dice will it take for each number to appear at least once?


We can give you the answer for systematically - it is always 6.

Random is a different story.

For each number to be hit at least once with random, the results can be anything from 6 to SOMETHING.


We asked ourselves, how high could this SOMETHING go?


We wrote another simulation to figure that out.


We did the side by side compare 1,000,000 times.

That is a million times running the "why" simulation.


Here is a snapshot of the results after running the "why" simulation a million times.


The number on the left is the number of rolls so each number was hit at least once.

The number on the right is how often it took for that many rolls (also known as frequency).


Results

  • 6 => 15,316
  • 7 => 38,606
  • 8 => 60,225
  • 9 => 74,701
  • 10 => 82,813
  • 11 => 84,367
  • 12 => 81,503
  • 13 => 75,622
  • 14 => 69,230
  • 15 => 61,554
  • 16 => 54,073
  • 17 => 46,635
  • 18 => 39,948
  • 19 => 34,248
  • 20 => 29,005
  • 21 => 24,673
  • 22 => 20,737
  • 23 => 17,489
  • 24 => 14,935
  • 25 => 12,179
  • 26 => 10,164
  • 27 => 8503
  • 28 => 7325
  • 29 => 5906
  • 30 => 5155
  • 31 => 4149
  • 32 => 3537
  • 33 => 2968
  • 34 => 2356
  • 35 => 1998
  • 36 => 1651
  • 37 => 1339
  • 38 => 1153
  • 39 => 1025
  • 40 => 761
  • 41 => 700
  • 42 => 576
  • 43 => 475
  • 44 => 427
  • 45 => 300
  • 46 => 287
  • 47 => 213
  • 48 => 174
  • 49 => 148
  • 50 => 151
  • 51 => 113
  • 52 => 100
  • 53 => 82
  • 54 => 64
  • 55 => 60
  • 56 => 37
  • 57 => 26
  • 58 => 27
  • 59 => 43
  • 60 => 23
  • 61 => 15
  • 62 => 14
  • 63 => 15
  • 64 => 15
  • 65 => 12
  • 66 => 7
  • 67 => 13
  • 68 => 6
  • 69 => 5
  • 70 => 2
  • 71 => 3
  • 72 => 5
  • 73 => 1
  • 75 => 2
  • 76 => 2
  • 80 => 3
  • 81 => 1
  • 83 => 1
  • 85 => 1
  • 89 => 1
  • 92 => 1
  • Total Rolls=14,702,658

Summary of the Results

With a six sided dice, the odds of any side of the dice to come up is 1 in 6.

In the sampling above, the worst case scenario was 92, with one occurrence.


92 rolls for each number to come up at least once.


That is a ridiculously high number.

But 1,000,000 times doing the why simulation is also a very high number.


With systematic, the number of rolls was always 6.

So with 1 million attempts, there would have been 6,000,000 rolls, ie. 6 x 1,000,000 of the systematic dice.


With random, as you can see above, there were 14,702,658 rolls.

Based on our efficiency calculation, systematic is 145% more efficient on average than random.

This is based on the calculation (14,702,658 / 6,000,000 * 100) - 100


Other interesting tidbits from the above data.

11 rolls had the highest frequency, with 84,367 times.


The higher the rolls, the less frequency (which one would expect).


There are some rolls between the lowest and highest which were never hit, for example 82, 84.


The image that we have included with this article could have been one of the 300 hits out of 1,000,000 where 45 was the number of rolls so every number was hit at least once - with 2 being the pesky rascal which was hindering the odds.

Conclusion

Random numbers are interesting, but they are no way to choose lottery numbers.

One would figure the odds of rolling a dice are 1 in 6.

The reality is the odds could be as low as 1 in 92, or even worse.

With 92 rolls, the efficiency of systematic over random is 1350%, but that is the worst case scenario in our sampling.


Systematic is the way to go.


Use chosen numbers when playing the lottery.