F.A.Q.

• Are LT's numbers optimal?
• How do you calculate average coverage?

Generally no, except for very small number sets. However, unlike other systems, we can measure how good our numbers are; so we can genuinely say, our numbers are amongst the most performant available online.

Imagine a very large grid where each cell is a possible outcome for a given game. Let's call the number of cells P. Each ticket row will win a certain number of game outcomes depending on the division. Let's call the number of outcomes each row wins N and the number of rows on your ticket R. If you were to shade the game cells that each row wins, you might find that some cells are coloured twice or more depending on the division and number of rows. For our calculation it's easier to calculate the portion of cells that are never shaded (U). This is because as more rows are added, the unshaded area gets smaller and smaller, but at an ever decreasing rate.

For one row: U = 1-N/P, for two rows: U = (1-N/P) * (1-N/P) or (1-N/P)².
For R rows: U = (1-N/P)^R.

Using the proportion of unshaded cells (U), we can find the expected number of wins (W):
W = P*(1-U) or W = P*(1-(1-N/P)^R).