Custom discount lotto schemes

Discount schemes are a good way to save money when playing a larger number of variants. By playing a reduced scheme one tries to catch fewer signs than the total possible number.
Thus, for a scheme reduced to minus 1, one tries to catch with one less number. (eg: if there are 6 numbers drawn, try to catch only 5 of them)
A reduced scheme is formed by selecting certain variants from all the simple variants (unfolded variants) resulting from the combination of all the numbers that we want to play. The choice of variants must be made so that all possible variants played are found in the scheme with at most one wrong sign.
The idea can be continued to further reduce the number of variants played by choosing to play schemes reduced to -2 or -3, etc.

This method of playing is beneficial if we understand the following things:

  • We cannot beat luck (chance). That's why there is no method to improve the chances of catching all the drawn numbers (eg: we can't know for sure what the next 6 drawn numbers will be)
  • We can mathematically improve the chance of catching as many variants as possible with 1 or 2 wrong numbers, but in this way we recover part of the money.
20 numbers
6 of 49
20 numbers at -2

It can be seen that the highest chance (74%) of getting variants is in the category of 4 correct numbers.
Thus, this game scheme favors variants with 2 wrong results

20 numbers
6 of 49
20 numbers at -1

There is a higher chance (33%) of catching variants in the category of 5 correct numbers.

20 numbers
5 out of 40
20 numbers at -2

It can be seen that the highest chance (66%) of getting variants is in the category of 3 correct numbers.
Thus, this game scheme favors variants with 2 wrong results

20 numbers
5 out of 40
20 numbers at -1

There is a higher chance (33%) of catching variants in the category of 4 correct numbers.