The Blackstone Group has paid $1.9 billion for the Tussauds Group, which owns the Madame Tussaud's Wax Museums in London, New York and, of course, Las Vegas, reports the New York Times. The deal will allow the company to combine the group with its existing amusement park and attractions operator, Merlin Entertainments Group.

The combination will create the second-largest amusement park operator in the world as measured by attendance. Only the Magic Kingdon is bigger.

The rationale for this deal is not too different from the other deals on the Strip. The business has a strong cash flow. One American consultant tells Bloomberg: "It's an industry that during times of wars, recessions and depressions and other economic turndowns doesn't see the depth of the decline that other industries feel. Properly operated, spread geographically, it's a very good business to be in."

One aspect is different. Big companies are fewer and farther between in Europe and often much harder for private equity companies to buy. So, the deals in Europe tend to be smaller and focused on creating larger companies that will be more valuable than the sum of their parts.

In other words, by combining two or more amusement operators, Blackstone can float the bigger company at a premium. At least, that's the theory. The analysts like the look of the two companies together and there is plenty of room to expand in the U.S., which is where Merlin CEO Nick Varney told a conference call they plan to go.

Amusement parks are not a foolproof business, though: Disney has struggled in its parks outside the U.S. and the London Eye was fraught with some initial problems. (And then there's the farcical history of the Voyager orbiter.) On the other hand, despite movies, TV and many other media, overexposure to starts has not dimmed the allure of seeing how lifelike the wax statues can be.

So, Madame Tussaud's will continue to make money and especially if the new owners boost ticket prices to maintain profitability.