Basics
The odds of winning
Every lottery has a number of possible tickets, and your ticket is one of them. The odds of matching all main numbers is one divided by the number of combinations.
Counting combinations
To count the number of tickets, use the binomial coefficient: choosing k numbers from a pool of n, without replacement and ignoring order, gives n! / (k! × (n−k)!) combinations.
For a 6/49 game that is C(49,6) = 13,983,816 tickets. Buying one ticket gives you a 1-in-13.9-million chance of matching all six — the same chance as any other ticket.
Bonus numbers multiply the odds
Games with a separate bonus drum multiply the main-pool odds by the number of bonus combinations. A 5/69 main pool with a 1/26 bonus drum has C(69,5) × 26 = 292,201,338 tickets.
Why it matters
The pool size is the single biggest lever. A 6/49 game is about 20× easier to hit than a 5/69 + bonus game. That is arithmetic, not luck — and it is why comparing odds across games matters more than comparing jackpot headlines.