This Sunday, I tried my luck in the Book of Mormon rush tickets lottery. I managed to enter twice – once for the matinée and once more for the evening performance. I didn’t win tickets either times, but thought it would be fun to calculate my odds.
At each lottery, they have 22 seats, most of them in the first row, for $32 each. Each participant’s ballot is allowed to request either 1 or 2 tickets. Since it’s rare for people to attend the theater alone, we can safely assume that there will be only 11 winners at each drawing. From my observations, there were approximately 100 to 150 people at the lottery. My odd of winning at any single lottery is therefore 11/150, or 7.3%.
Since the Eugene O’Neil theater is conveniently located right by my office, I’m planning to enter the lottery as many times as possible. I was curious to find how many times I’d have to enter the lottery before a win is nearly guaranteed, statistically. Thus, (1-7.3%)^n would represent the probability of me not winning the lottery for n consecutive times.
I was surprised to discover that it only took a little over 9 times (fine, let’s say 10) for me to boost my chances of winning at least once to 50%. If I go just over 30 times, then my chances of winning at least once rises to 90%. And if I’m terribly unlucky, it will 60 lotteries to guarantee a 99% chance of winning at least once.
If I show up just five minutes before each drawing and stay for the announcement, it’ll only cost me about 25 minutes per participation. Assuming that my time is worth a shiny $20 per hour (pre-tax, of course), it would require a time-equivalent monetary investment of $75-$500 to have a pair of tickets safely in my hands. (Of course, that doesn’t include the actual $32 per ticket I’d have to pay.) Tickets for Book of Mormon cost anywhere from $70-$430 each, so I would say this is a pretty good gamble.
So I’ve already attended the lottery twice. With my schedule, I can participate at most 6 times per week (that once on Thursday and Friday, and twice on Saturday and Sunday). At this rate, I’ll surely be able to land myself two seats in 5-10 weeks!