It's still a long odds, if you are talking about the jackpot. Considering the average odds of a lottery being 1:10,000,000, the probability of winning at least once during a 20 year period (1000 tickets) is about 1:10,000, which means the probability of NOT winning is 99.99%.
See the funny thing about number is how you presented it, a lot of people will think that an 1:10,000 odds is somewhat achievable while a 99.99% failure rate is considered to be almost impossible.
But there is a difference between 1/10,000 and 1/10,000,000. In each of our lifetimes we should expect to achieve at least one meaningful 1/10,000-probability event (because we likely play a 1/10,000 lottery of one type or another every day), whereas we should expect to achieve zero 1/10,00,000-probability events.
(At least that's how I rationalize asking the beautiful blonde at the bar for a date in whichever city I am in each Saturday night.)