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I'am learning German (any other language will do).

I choose randomly a countable noun - for example the noun "Hotel".

I write the noun into google together with German numeral for "two" in double quotes: "zwei Hotels" and write down the number of matches (229000).

I repeat the experiment with 3 - "drei Hotels" (14100 matches), 4 (8490), 5 (3670), 6 (3160), 7 (3700) ...

What probability distribution should I expect to obtain?

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This sounds like a Benford's Law kind of situation.'s_law – Suresh Venkat May 9 '10 at 6:06
Is this inspired by (possibly NSFW) the xkcd strips X Girls Y Cups and Numbers? – Zsbán Ambrus May 9 '10 at 9:24
Not at all, but thank you for the pointer. – danatel May 9 '10 at 11:30
up vote 3 down vote accepted

The distribution probably depends on the kind of noun, although Benford's law might cover a lot of cases.

There's some related empirical data from, of all places, the art world! Artist Golan Levin created a project based on the volume of search results for the numbers one through a million. There are a lot of interesting outliers, of course: 1040, 90210, recent years. But one thing that leaps out is that there are spikes at round numbers (multiples of 100, 10, 5, and so on). I'd be interested to know if there are models of these "round number" peaks.

You can see the project here, which charts all million data points:

And here are two graphs from the piece, of the frequencies of the first few hundreds of numbers:

alt text

and thousands (the vertical scale is a bit cut off):

alt text

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