Still doesn't help. Horse back riding is in principle very closely related to ancient warfare, so if anything it supports my point, but new york race tracks with betting and especially cheating being the very topic of your poorly sourced folk etymology is effable.
Dead Ringer (disambiguation) : https://en.wikipedia.org/wiki/Dead_Ringer_(disambiguation)
Wringer (disambiguation) : https://en.wikipedia.org/wiki/Wringer_(disambiguation)