I should have also added that a ticket on a reserved train usually, but does not absolutely guarantee you a seat. In rare instances, usually because of equipment shortages, a coach might be removed from a consist at the last minute, leaving the reserved train in an oversold situation. However, quite like the unreserved train, Amtrak will operate this train as standing-room only (their official policy, from their
web site, "Each passenger paying a fare will be entitled to a seat, to the extent coach seats are available.").
As you might imagine, in cases like this, Amtrak does not always end up with happy customers...