Worked through by hand, "Why lottery odds are bad?" 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.
A lottery odds calculator does the counting for any pool: enter how many numbers are drawn and from how many, and it returns the odds for each tier. For multiple tickets the calculator simply adds the chances, since each ticket covers a different combination. Ten tickets in a draw of fourteen million combinations give ten chances in fourteen million; the odds improve in step with the money spent, no faster.
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 permits.
How do lottery odds work for the smaller prizes? Each prize tier asks for a partial match, and its odds come from counting the ways to match some drawn numbers and miss the rest. A draw with many tiers can offer odds of winning anything near one in ten, while the jackpot stays remote. Written as a percentage, a chance of one in fourteen million is about seven millionths of one percent, a figure most people read as zero.
Enter how many numbers are drawn and from how large a pool, and the calculator returns the odds for every prize tier of that game.
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.
The pattern of drawing numbers from a pool without putting any back; it gives the exact probability of matching three, four or five numbers, and the tier table writes it out.
One over the full count of combinations: about one in fourteen million for six from forty nine, and near three hundred million for five from seventy plus one of twenty five.
No. Every draw starts fresh, so loyalty, a lucky shop or years of play never add to a player's chances.
Each tier needs a partial match, and its odds come from counting the ways to hit some drawn numbers while missing the rest.