My advice: go on the first day. The first time the tour came to Boston, there were few people on the first day. I lost, as the tour went on, more and more people entered the lotto.
The second time it came to Boston, on the first day there were a small number of people there and me and a couple of friends won. So try to go as early in the run as you can.
"We like to snark around here. Sometimes we actually talk about theater...but we try not to let that get in our way." - dramamama611