And this is why I have a gas dryer.
But your gas dryer takes 120 VAC.
480 Delta systems in a building are very rare these days. But it is still 277 to ground.
And the risk of fibrillation also depends on the frequency, for AC. As it happens, the highest risk is somewhere in the vicinity of 50 or 60 Hz… which is just what we use for our electrical distribution. A significantly higher or lower frequency would be much safer, though of course those run into other practical difficulties (lower frequencies need bigger transformers, and higher frequencies are harder to synch up and have greater radiative losses, IIRC).
Edison was right!
If the drier is working fine, you either did it right or you are about to be electrocuted in the near future.
I’m not an electrician but I’ve replaced breakers and some electrical fixtures around the house. I’ve always checked, even after turning off the breaker to the circuit, each wire with respect to ground and each other with a multimeter. Is that not standard practice working with electricity?
Yes, just like it is the standard practice that interstate truck drivers always drive below the speed limit. But in both cases, there are economic incentives for the workers to take shortcuts to get the job done faster, even if they might be a bit risky.
Familiarity breeds contempt…
You, as an amateur, are naturally cautious. You also have no time constraints. Many professional electricians work with live circuits as a matter of course. If they expect the current to be off, they should really check it, but it’s easy to skip that, assuming that turning the breaker off has cut the power. If some amateur has wired it up badly and he didn’t notice… Pow!!
Thanks engineer_comp_geek!
FYI - Appliances come with “Installation Instructions” or you can get them from the manufacturer for older appliances. Those instructions cover 3 wire/4 wire installation.
FURTHERMORE specific appliances will require specific amperage rated circuit breakers. For example various model kitchen ranges may need a 20, 30, 40, or 50 amp breaker depending on the specific model.
Not following the recommendations and instructions of the manufacturer can result in electrocution or fire.
I got it mostly right, and thanks to the vast reservoir of human knowledge that is the SDMB, my electrocution will not be forthcoming. 
…unless you’re colorblind. 
I’m not color blind. My mother had me tested.