Worked through by hand, "How lottery odds are calculated?" begins with the pool. The odds of winning the lottery follow from counting. A draw picks a set of numbers from a larger pool, and every possible set is equally likely, so the chance of one ticket matching the whole set is one divided by the number of sets. What those odds look like depends on the size of the pool and on how many numbers are drawn, and the counting is the same for every game of this kind.
What is lottery odds for one person holding one ticket? The same number as for everyone else. Your chances of winning the lottery do not grow with loyalty, with a lucky shop or with years of play, because each draw starts fresh. The honest answer to what my odds are is printed in the game rules: one chance for every combination bought, against the full count of combinations the draw allows.
Lottery odds are calculated with one formula from school math: the number of ways to choose some numbers from a pool. Six numbers from forty nine give nearly fourteen million combinations, so the odds of the top prize are about one in fourteen million. A game drawing five from seventy, with one extra ball from a second pool of twenty five, multiplies two such counts and lands near three hundred million. Every number added to the pool raises the count steeply.
Other questions
Do extra tickets improve lottery odds?
Chances grow in proportion: ten different tickets in a draw of fourteen million give ten chances in fourteen million, never faster than the money spent.
How are odds for smaller prize tiers worked out?
Each tier needs a partial match, and its odds come from counting the ways to hit some drawn numbers while missing the rest.
What is one in fourteen million as a percentage?
About seven millionths of one percent, a figure so small that most people take it for zero.
Do past draws affect the next lottery draw?
No. Every draw starts fresh, so loyalty, a lucky shop or years of play never add to a player's chances.
Where are a game's official odds published?
In the game rules, which state one chance for each combination bought against the full count of combinations the draw allows.