As an app, Shotgun Free doesn’t do much. Give it a shake and it makes the sound of a shell being chambered. Tilt it up sharply and the gun fires with a bang as loud as an Apple (AAPL) iPhone can make — which isn’t terribly loud.

But the app is popular. It’s been downloaded nearly 4 million times since it was launched in early March. An average of 60,000 to 70,000 people have been using it daily ever since.

More to the point, the small ads that run across the bottom of screen are displayed 200,000 to 300,000 times a day, which is how Shotgun Free ended up as case study No. 1 in a white paper issued this week by MobClix, the Palo Alto start-up that acts as a middleman between Shotgun’s developer — Inedible Software — and the advertisers who pay them $3 per 1,000 ad impressions. That works out to $600 to $900 a day.

There are eight case studies in the MobClix report, and a lesson for mobile developers in each of them.

In the case of Shotgun Free, the lesson is that when the ads were rotated twice as frequently — every 15 seconds, rather than every 30 seconds — the click-through-rate doubled and revenues increased 20%.

The lesson of BlackJack Free, which generates 1.5 million ad impressions a day at $0.40 to $2 per thousand (depending on the size of the ad), is that users rebel when you replace small ads with big ones.

The publishers of Duck Shoot (150,000 to 250,000 daily ad impressions for $1.00-$2.50 per thousand) managed to breathe new life into a paid app that had run out of steam by offering a new, ad-supported free version.

Shotgun’s developers went the other route. They started out free — “it’s a simple shotgun, it deserves to be free,” says Inedible co-founder James Anthony — and then introduced a $0.99 “pro” version with more guns and no ads. They make a lot more money giving it away.

Of course, with more than 85,000 iPhone apps competing fiercely for attention, most developers lose money. That’s why Mobclix — which makes a market in mobile ads — showcased only winners.

The white paper is available as a pdf here. To see a video of Shotgun’s developers talking about their business model, click here.

See also:

• Trouble in the (99-cent) App Store

[Follow Philip Elmer-DeWitt on Twitter @ philiped]