This guide explains the mathematical terms used by the Lotto Plus combination and wheel tools. Coverage results are conditional calculations about main-number pools; they are not forecasts or guarantees of a future draw.
Main-number pools
A pool is a user-selected working set of Lotto Plus main numbers. It is used to investigate combinations or build tickets. A pool is not inherently predictive and does not establish that its numbers will be drawn.
Unordered combinations
A combination is an unordered selection of main numbers. The tools can work with pairs, triplets, quads and five-number combinations. For example, 3, 12 and 27 represent the same triplet regardless of the order in which they are written.
Combination Explorer counts selected combinations in recorded main-number draws. Combination Wheel generates combinations from the selected pool. Powerball is not part of the main-number combination.
Full wheels
The Combination Wheel accepts a main-number pool of 5–12 values and generates every possible five-number main combination from that pool. For a pool of n numbers, the number of combinations is written as C(n,5): the number of ways to choose five values without regard to order.
For example, a pool of 12 numbers produces C(12,5) = 792 main combinations. A full wheel becomes larger as the pool grows.
Powerball and the Combination Wheel
Users may select zero, one or multiple Powerball values after selecting the main pool. Each selected Powerball is paired with every generated main combination to create final play lines.
Powerball remains separate throughout this process. It does not become part of C(n,5), and it is not included in the main-number wheel’s combination count.
Coverage Explorer
The Coverage Explorer uses current main numbers 1–35, selected pool sizes 6–12 and five-number tickets. Powerball is excluded. The construction follows the positional idea represented by LD(n,5,5,4): positions in a selected pool are covered by five-number tickets so that every possible five-position winning set has at least four positions represented in one ticket.
Positions are mapped back to the user’s selected main-number pool. Position 1 means the first selected pool value, not necessarily Lotto Plus number 1.
Coverage ticket counts
The current verified constructions contain:
- Pool 6 → 1 ticket
- Pool 7 → 3 tickets
- Pool 8 → 5 tickets
- Pool 9 → 9 tickets
- Pool 10 → 14 tickets
- Pool 11 → 22 tickets
- Pool 12 → 35 tickets
Exact/optimal versus verified construction
For pool sizes 6–9, the current research data describes the constructions as exact/optimal for those pool sizes.
For pool sizes 10–12, the implementation describes them as verified valid constructions and does not claim that they use the mathematically smallest possible number of tickets.
Exhaustive verification
The Coverage Explorer enumerates every possible five-position winning subset within the selected pool and tests the best overlap provided by the generated tickets. It reports the number of subsets tested, the best overlap distribution, the minimum best overlap and whether the selected target is passed.
The Wheel Verifier applies the same positional principle to a user-submitted wheel. The Wheel Comparator compares two submitted wheels using their exhaustive coverage results and overlap distributions.
Conditional 4-of-5 coverage
This is conditional on pool inclusion. It does not guarantee that the winning main numbers are inside the pool, a winning ticket, a prize, a jackpot or any future result. Powerball is outside this coverage guarantee.
Pool inclusion probability
Pool inclusion asks whether all five winning main numbers are inside the selected pool. For a pool of n values, the tool calculates:
The numerator counts the five-number outcomes contained in the selected pool. The denominator counts every five-number main outcome in the current 1–35 model.
Pool inclusion probability and conditional internal coverage are different questions. Inclusion asks whether the pool contains the complete winning main set. Coverage asks how the tickets perform after that condition is already true.