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I ran Continental X-Kings 29 x 2.4"
Fast rolling tread and wide profile really helped for me. They were quick on asphalt and fine, hard packed gravel, and the extra cushioning really helped on the washboard, which really hammers you, especially in the Gila in NM.
That's what worked for me, but I also rode with, and finished an hour behind Will who rode a cross bike with 38c tyres I think.
Nothing will make the "Rail Trail" in Idaho not shit. 30+ miles of wheel sized undulations in dark volcanic gravel.
https://www.youtube.com/watch?v=UtCboD4tQ8I
29, 2.2