Is it "steak house" or "steakhouse"?

Is the correct term for a restaurant that specializes in steaks "steak house" or "steakhouse"? And why do I care?

Well, I care because when dealing with search engines like Google or Yahoo!, small changes in spelling can mean a lot. A search on Google for "steak house Prague" and "steakhouse Prague" yields different results, and the same is often true even when speaking just of plural vs. singular forms of the same word (e.g. a search for "mexican restaurant prague" doesn't show any results for Nelso, while a search for "mexican restaurants prague" puts Nelso on the first page of results, at #8). This is a limitation of using computer algorithms to parse the meaning of natural language queries - no human being would think of "Do you know any good steak houses in Prague?" and "Do you know any good steakhouses in Prague?" as being different questions. These would be taken as two forms of exactly the same question.

What do the American restaurants call themselves? There seems to be no agreement on the correct wording. The legendary Ruth's Chris Steak House uses the two word form, while the equally well-known Morton's Steakhouse spells it as one word. Black Angus Steakhouse splits the difference, calling the place a "steakhouse", but using the title "Black Angus Steakhouse - Black Angus Restaurant, Steak House" on the home page in an attempt to reach more searchers.

In the end, I'll probably change our current usage of "Steak House" to "Steakhouse" just to satisfy Google. A search for "steakhouse" on Google yields 17,700,000 results, while a search for "steak house" yields 9,230,000 results. In fact, a search for "steak house" on Google offers up the suggestion "Did you mean: steakhouse?". That's all the convincing I need.