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Combine all ingredients except venison in a large bowl. Submerge venison in the marinade, cover with plastic wrap and refrigerate at least 8 hours and up to 12 hours.
Heat broiler, stovetop grill pan or grill. Remove venison from marinade and season with salt and pepper. Working in batches if necessary, place steaks under the broiler or on the grilling surface and cook, flipping once, until medium-rare, 4 to 5 minutes per side. Allow venison to rest for 5 minutes before serving.