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Might be PhotoPills: https://play.google.com/store/apps/details?id=com.photopills.android.photopills&hl=en
At least is very similiar to one of its tools.
Photopills calculates DoF among many other things and should be able to answer your questions. It is a paid app but it's been worth every penny.
You said on the fly - that can have different interpretations. If on the fly, in your case, means you have a bit of time (which it looks like, as a posed picture) but not a ton (they're not statues or still photos), then you could use the DoF calculator from photopills. It costs, but has tons of helpful features, including a calculator to tell you how much depth of field you have based on distance, focal length, and camera (sensor really, but the options list asks your camera body).
If you pull the app and section up before you start shooting (and bring a measuring tool! Easy cheap option is a couple of sewing ruler tapes), it shouldn't take more than... 30 seconds? A minute tops, I think, to measure your focus distance and find an aperture setting.
Not actually a game (sorry about that), but this app called PhotoPills has a ton of really helpful tools for photographers, and it's exactly $10, so the gift card is the perfect amount! Thanks for doing this giveaway! :)
The app photo pills works great for this type of thing as well!
I saw photopills is half price today. Might be worth a look.
Ah that's PhotoPills, a fantastic app for planning your shots.