We just had another Purim Meshulash 3 years ago, but there won't be another one for another 13 years! Because you see, we're on the cusp of a major transition in the Hebrew calendar.
Some background information: (Licensed calendar geeks can skip right to the data.)
There are three variables that make one Hebrew year different from another:
1) Cheshvan can have 29 or 30 days.
2) Kislev can have 29 or 30 days.
3) There can be one or two months of Adar.
This means that the 9-month period from Adar to Cheshvan (which just happens to include all the biblical holidays plus Purim; forget about Chanukah though) is completely fixed. If you know the day of the week of any holiday in that period, you know them all.
Therefore, since Rosh Hashanah can only fall on four days of the week (Monday, Tuesday, Thursday, Saturday), there are only four types of years if we're just looking at the period from Adar to Cheshvan. (Since this period spans two Hebrew years, I'm using Gregorian year numbers below for clarity.)
The four types, in order of frequency, with their distinctive features:
- Rosh Hashanah on Thursday, 31.9% of years. This means there is a "three-day yom tov" for Rosh Hashanah, and for those who observe 2 days of yom tov, there are two more "three-day yom tovs" for Sukkot and Shemini Atzeret. Yom Kippur is on Shabbat. Purim begins on Saturday night. We just had this in 2007.
- Rosh Hashanah on Shabbat, 28.6% of years. Most of the fall holidays are on weekends. Pesach starts on a Wednesday night, leading to a "three-day yom tov" for those who observe 2 days of yom tov. Shavuot is on Friday, leading into (or including) Shabbat. This causes a disparity between 1-day-yom-tov and 2-day-yom-tov communities regarding Torah reading for several Shabbatot.
- Rosh Hashanah on Monday, 28.0% of years. Pesach begins on Shabbat. This also causes a disparity regarding Torah reading, because the 8th day of Pesach (if one exists) is also on Shabbat. Shavuot begins on Saturday night, yet another "three-day yom tov" for people who swing that way. Tisha B'Av falls on Shabbat and is delayed to Sunday.
- Rosh Hashanah on Tuesday, the least common by far with only 11.5% of years. This is what we have in 2008. Pesach begins on Saturday night, leading to all manner of hijinks. Tisha B'Av also begins on Saturday night. Purim is on Friday, leading to Purim Meshulash in walled cities.
Let's look at the days of the week of Rosh Hashanah in recent years (and next year):
So what do we have here? A lot of Saturdays (50% of the years in this sample, including 4 years out of 5 for one 5-year span there), more Tuesdays than would be statistically expected (you'd expect about one a decade), and no Mondays at all for over a decade.
But that's about to change drastically:
Yes, that's right -- the entire decade of the 2010s will be nothing but Thursdays and Mondays! The convenience to working people of having the fall holidays on weekends, which we have grown accustomed to, will be wholly alien for the new generation. Mechon Hadar's new page about Purim on Friday will be a purely academic exercise, as will all the guides to Shabbat Erev Pesach that will see a lot of use this year.
After that, things will start to stabilize:
So that's the long-term forecast!