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Kevin CummingsThe Old Judge cards most likely portray the players in their natural positions. Since, I think, there is a card of righty-hitting King Kelly batting lefty, I suppose the possibility does exist that the players could have been posed by the photographer in an unnatural position for some reason.
Not unlike some well-known modern-day situations, the possibility also exists that the players posed unnaturally on their own to play a trick on the photographer.
I find some of the poses in the Old Judge set to be so awkward or odd that they can certainly be ambiguous. The card I own of John Weyhing could certainly make you believe that the supposed lefty pitcher was a right-hander.