What's the fastest way, without using Python, to select every other vertex of an edge ring with an even number of verts?
2 Answers
In edit mode with entire edge ring selected:
Select> Checker Deselect
This should deselect every other vertex.
You can then use the 'offset' value in the toolshelf if you want the other vertices in the edge ring selected.
No Offset:

Offset by 1:

Note: This works in edge and face mode too, deselecting alternate edges or faces to get a checkerboard selection.
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7Oh boy, I'm humbled. It even takes the active vertex into account as a starting point. Thank you – Haunt_House Aug 24 '13 at 17:24
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I can't find the offset. – 00Ghz Aug 25 '13 at 05:33
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7The offset option as well as the nth option (so you can select every 3rd vertex or 6th vertex...) is available in the operator options - either F6 or at the bottom of the toolbar panel T – sambler Aug 25 '13 at 06:59
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2I would like to comment is that Blender is absolutely brilliant. – foobarbecue Mar 01 '18 at 02:12
If the topology is well-formed for it, which is surprisingly often, then CtrlShiftNumpad + 'Select Next Active' will select a sequence of vertices, edges, or faces, in a pattern established by the last 2 selections:
If you switch off 'Select' on AltH Reveal Hidden, and make use of 'Header > Select > Select Loops > Edge Loops' and/or 'Header > Select > Select Loops > Edge Rings', then by hiding and unhiding, you can find your way to a wide range of useful patterns that are not always available through 'Checker Deselect' :
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