[TStoneMBD]

when schneids checkcalls the turn the only hands he could really have at this point are

Ax
JJ/TT
and maybe KJs.

the opponent certainly cant expect schneids to fold Ax on this river and its extremely unlikely that the opponent cant beat JJ or TT on this board after making it all the way to the river so theres no reason to bluff against those hands. The only hand he'd be value betting against is KJs when he has a weak ace.

basically what im saying is that i think R! should be checking this river with Ax and isn't likely to be holding a hand that loses to TT or JJ so he should be checking down hands that lose to AT.