Depth of field, focal lengths and sensor sizes

I like photographing people. I also like to carry a small camera around.

Photos of people generally look better when you separate the subject from the background using a narrow depth of field.

So do I lose a narrow depth of field when I use my Ricoh GR compared to my 1DS? Or more interestingly, a crop sensor DSLR compared to my 1DS?

None of the explanations on depth of field and sensor size I have read on the web quite made sense to me, and some seemed plain wrong, so I thought I’d do some comparisons…

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