Tool to generate covering design / reduced lotto wheel systems for the random picking games of chance such as Lottery, Lotto or Euromillions, the principle being to guarantee a minimum winning.
Covering Design for Lottery - dCode
Tag(s) : Combinatorics
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Covering Design for Lottery
Covering Design Generator
Answers to Questions (FAQ)
What is a convering design? (Definition)
A covering design is a mathematical method for generating grids to be played in a random draw game (Lotto, EuroMillions, etc.) that guarantee a win.
In other words, instead of playing all possible combinations, the covering system selects an optimized subset of grids that ensures, for a given win level (e.g., at least two correct numbers), that all possible draws meeting this criterion are covered.
Example: In a draw of 5 numbers out of 50, a reducing system can guarantee that the player will have at least 2 correct numbers in at least one of his grids.
Why use a reduced covering design?
Players use a covering system to increase the probability of matching a certain number of correct numbers, while reducing the total cost of betting.
Example: Instead of playing all 1,225 possible combinations of two numbers out of 50, an optimized covering system allows only 130 grids to be played while guaranteeing that at least one grid will have two correct numbers in each draw.
This guarantees a win, but not necessarily a profit: covering designs improve coverage, but do not change the fundamental probabilities of the draw.
How to generate a reduced system/covering design?
Generating a covering system relies on complex combinatorial calculations. The goal is to find a minimal subset of combinations that meets a given coverage criterion. These calculations are extremely time-consuming: no fast algorithm is known, and some solutions require several days of computation.
dCode offers pre-computed covering systems, sometimes optimal (smallest possible sets), sometimes non-optimal (slightly larger but already valid sets).
A list of known systems is available at here
How to guarantee a draw with all the correct numbers?
For a draw with N numbers, the only way to guarantee playing all the correct numbers is to play all possible combinations.
No covering design can guarantee a maximum win, because as soon as a combination is not played, there is a draw in which it would be the only winning one.
Reduction systems therefore only guarantee partial coverage (at least N correct numbers), not the full jackpot.
Are covering systems legal?
Yes, they are perfectly legal. They do not change the way the game works, but are limited to a mathematical optimization of the grids played.
Be careful, however, as some lotteries limit the number of grids a single player can play in a single drawing.
Source code
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