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I just built a new deck, which turned out rather well. I am however having difficulty making up steps. My total rise from the ground to the top of the deck board is 20.5". I imagine I will need three risers of 6 27/32 inches. I will be using 5/4" x 6" deck boards for the treads and the backs will be open. The two boards for my tread will turn out to be 11". I guess they should overhang a bit. I would like my steps to be 48" across.
Remember that for 3 risers there are 2 treads. A carpenter never makes a set of stairs with the same number of treads as risers. If he did, the top tread would be flush with the upper floor or deck. Always place that first step down one riser from the floor or deck surface.
I would make the run 10 3/4" to give about a 1/2" overhang with about 1/4" gap between the boards. You've got the rise correctly figured as 6 27/32". I would recommend that you use pressure treated wood for the stringers, supports and pads. Also for 48" wide stairs, 3 stringers are required. Be sure to compact the dirt well under the pads. 
