As a lottery buff who attends the live lottery draws in Ontario, I have learned that when you say "YES" to the Encore number (the tag game) a lot more happens than you think.
The 7 digit number you get is from the pool of 10 million, that is selected from the central computer system. But for those who say "NO", then your encore number is from a pool of about 25,000 combinations the central computer uses for unentered tickets. Its rotates the combinations and prints the same number often on Non-Entered selections.
Every now and then, I hear lottery players say that their Encore came up and they never played it. Unfortunately, the number on their Non-Played ticket is not a true number from the pool. In the case of that number there could be hundreds across Ontario with it because its given from the 25,000 batch. One time when Encore was 6 digits, I didn't play the Encore, I got two identical Encore numbers and thought that strange -- because it would be one in a million for that to happen.
I was wrong, it was one in roughly 25,000.
On a sidenote, the lottery terminal itself in the convenience stores/malls/smoke shops/retailers chooses the quick pick selection on your ticket, not the central computer. The central computer issues the Encore number and records the ticket selections in its database.
Sources OLG, and my findings with lottery officials.
Derek