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, never 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.
Statisticians call the pattern behind these counts the hypergeometric distribution: numbers taken from a pool without putting any back. It gives the probability of hitting exactly three, four or five of the drawn numbers, and the lottery winning probability table in the game rules is that distribution written out. The probability of winning a prize of any size is the sum of those rows, and the math is exact, with nothing left to estimate.