## Package Optimizer

This filter removes surplus tickets from the Package while maintaining the selected win guarantee. The filter opens from menu Package - Reduce - Optimize Coverage. You can use the filter either to create optimized wheels or to filter the result of your lottery strategy to reduce the cost of your bet.

### Wheels

Wheels with a win guarantee are usually described as "x if y (n)". Where "x" is the lowest guaranteed match when "y" winning numbers are drawn from "n" numbers the wheel is created from. For example wheel "3 if 6 (20)" guarantees at least one match 3 prize when any 6 numbers out of pool's 20 numbers hit in the next draw. The smallest possible wheel with such win guarantee contains ten tickets. It means you must bet at least 10 tickets if you want to win at least one match 3 prize. All six winning numbers must come from the twenty numbers the wheel is combined from.

#### Example

Use the following steps to create an optimized wheel from 20 numbers with 3 if 6 win guarantee in Expert Lotto 6/49 Demo lottery:

1. Use menu Package - Insert - Full Wheel.
2. In Full Wheel window select Create all combinations of 6 numbers from a pool of 20 numbers. Interval: 1
3. Click button Insert to insert the full wheel into the Package. The Package will contain 38,760 tickets.
4. Use menu Package - Reduce - Optimize Coverage to open this filter window.
5. Select I want to have 100% guarantee of matching at least 3 winning numbers when I hit any 6 numbers. Algorithm preference: smaller resulting wheel
6. Click button OK to start the filter. The filter window will close and you can track the filter progress at the lower right corner of the main window.
7. The filtering may take several minutes to finish, depending on how fast your computer is and how many execution cores your CPU has.
8. When the filter is finished, you will see the filtered tickets in the Package. There will be approximately 14 tickets left.
9. Use menu Package - Coverage to calculate the win guarantee of the optimized wheel.
10. Select Show my winnings when I hit 6 numbers and click button Show.
11. You will see that the lowest possible win is one Match 3 prize.

Note that the resulting optimized wheel consists of 14 tickets while the smallest possible wheel for the same win guarantee needs just 10 tickets. The algorithm this filter implements will never produce wheels that match highly optimized and tightly woven wheels you can find on internet. The main purpose of this filter is the coverage optimization of tickets resulting from your lottery strategy, not creation of optimized wheels from scratch.

If you are on a tight budget, you can create even smaller optimized wheels:

1. Repeat steps 1 to 4 above.
2. Select I want to have 95% guarantee of matching at least 3 winning numbers when I hit any 6 numbers. Algorithm preference: smaller resulting wheel
3. Click button OK to start the filter. The filter window will close and you can track the filter progress at the lower right corner of the main window.
4. The filtering may take several minutes to finish, depending on how fast your computer is and how many execution cores your CPU has.
5. When the filter is finished, you will see the filtered tickets in the Package. There will be approximately 8 tickets left.
6. Use menu Package - Coverage to calculate the win guarantee of the optimized wheel.
7. Select Show my winnings when I hit 6 numbers and click button Show.
8. You will see that there is about 4% chance of winning nothing. That means the wheel guarantees win with a chance of 96%.

In the steps above we lowered the required win guarantee from 100% to 95% and the resulting wheel consists of 8 tickets only. That is reduction by 42%. So while still having very high chance (95%) of winning at least one match 3 prize we managed to lower the wheel size significantly and thus saved a lot of money.

Keep in mind that lowering the required win guarantee by a few percent or just a fraction of percent can decrease the size of optimized wheel by tens or hundreds of tickets.

### Optimize Coverage

If you have just finished applying all the filters according to your lottery strategy and the resulting set of tickets is too large for your betting budget, then there are two options. Either continue filtering with the risk of making an error in your estimates and filtering out the winning tickets. Or use Package Optimizer or Best Tickets filters to reduce the count of tickets and aim for lower tier prizes.

#### Example

Let's use the following simple (and not very effective) lottery strategy in Expert Lotto 6/49 Demo lottery:

1. Start with the full wheel of all possible combinations: menu Package - Insert - Full Wheel, select Create all combinations of 6 numbers from a pool of 49.
2. Use Odd/Even filter to keep only tickets with the most frequent ratio of 3:3. There will be 4,655,200 tickets left.
3. Use Low/High filter to keep only tickets with the most frequent ratio of 3:3. There will be 1,532,168 tickets left.
4. Use Sum Range filter to keep only tickets with the most frequent sum values 153 to 173. There will be 543,748 tickets left.

From statistical point of view these tickets have very high chance of winning. However so many tickets are way over any betting budget. So we will use Package Optimizer filter to go after lower tier prizes. The Package contains over half a million tickets that the filter must iterate over many times so we need to increase the filtering speed by optimizing the coverage for selected numbers only.

1. Use menu Tools - Options - Number Coloring to display number coloring settings.
2. Switch to Hot/Cold tab and select Scan for hot/cold numbers in 30 latest draws, Maximum frequency of cold numbers: 2, Minimum frequency of hot numbers: 5
3. Toggle button in the main toolbar and select Hot/Cold in the combo box listing all available number colorings.
4. Use menu Package - Reduce - Optimize Coverage and adjust filter settings as on the screenshot below
5. Click button OK to start filtering.

When the filtering is finished (it will take a while), there will be about 29 tickets left. Those tickets meet all the conditions of our lottery strategy above (odd/even, low/high, sum range) and have 95% chance of winning at least one Match 3 prize if the next winning numbers consist entirely from hot or cold numbers.

To verify the win guarantee, open Package Optimizer filter window again. Select the same set of numbers on the ticket panel (see the picture above) and click button Show Coverage. Then choose Show my winnings when I hit 6 numbers and click button Show.

Package Optimizer filter is capable of reducing the ticket count by several orders of magnitude while maintaining the required win guarantee.

### Filter Settings

Use the edit fields to define the required win guarantee. For example win guarantee 4 if 5 is expressed as I want to have 100% guarantee of matching at least 4 numbers when I hit any 5 numbers. It means you are guaranteed to win at least one Match 4 prize if the winning numbers include at least 5 numbers of your wheel.

It is possible to significantly reduce the count of filtered tickets (and increase filtering speed) by reducing the probability of winning the required price. For example reducing the chance from 100% to e.g. 98% or 95% still gives very high chance of winning but it will also reduce the size of resulting wheel.

Option Algorithm preference affects filter performance. When smaller resulting wheel is selected, the filter will take more time to finish however the resulting optimized wheel will be smaller and more compact. With option shorter filtering time the filter will perform faster but the resulting wheel will need more tickets to meet the required win guarantee.

The ticket panel on the right of the filter window shows all the numbers in the Package. If a number is not present than its box has gray background and cannot be ticket using mouse.

It is possible to optimize coverage for a smaller set of numbers only. Simply use your mouse to tick/untick numbers on the ticket panel. For example you can tick only numbers that the most/least frequent in several past draws, numbers that did (not) hit for a long time etc. Number coloring highlights numbers selected in statistical tables.

Show Current Coverage button calculates and shows the win coverage of tickets in the Package. Menu Package - Coverage also shows the win coverage of the tickets in the Package. However the coverage is calculated for the whole number pool, i.e. all 49 numbers in a x/49 lottery. The coverage calculator started from Package Optimizer window shows the coverage only for numbers selected on the ticket panel in the filter window. So you can see the win guarantee when you expect that the winning numbers will be drawn from a smaller set of numbers.

The filtering time increases exponentially with the size of the number pool - optimizing the coverage of only 15 numbers will be fast, however optimizing the coverage of the whole 49 number pool will take hours. If possible, untick some numbers on the ticket panel in the filter window.

The filter runs much faster on modern multi-core CPUs. Check the number of execution cores your CPU has, then click menu Tools - Options - Miscellaneous - Execution and enter the number of cores into Number of threads for long running tasks field.

You can watch the filter progress at the lower right corner of the main window. Click the progress bar to see additional info about the current size of the wheel and the current coverage percentage. You can stop the filter if the coverage is high enough (e.g. 90% or 95%).

Always check the current coverage before applying this filter. If the win guarantee of the tickets in the Package is e.g. 92% before using this filter then it doesn't make sense to require 100% win guarantee.