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I broke a Shimano track one many years ago... and have still not bothered to fix it because I have two other chainwhips for some reason. But I saw these somewhere and thought, hmm, that could save some time.
Do they save time though? They must, right? You just squeeze and go, rather than drape the chain around and wait for it to slip off again.
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I guess it would have to be quicker, if you have it set for a particular size cog and always grab that one. My style (which I don't think I've ever seen elsewhere) is pretty easy to use though, and would be right up there with a bit of practice.
A bit of a shake to throw the loop around the teeth, take up the slack, and bam.
My home made chain whip has a closed loop; I just hold it against the doubled up slack in the chain. It's as secure as anything.