A chess rating is a number that predicts results. If two players meet, the higher rating is expected to score more often. After an event, the rating moves toward the results: up when you score more than expected, down when you score less.
The expectation is not a hunch
On the standard formula, the expected score for one game is 1 / (1 + 10^(-(your rating − opponent rating) / 400)). A 200-point favorite expects about 0.76. A 400-point favorite expects about 0.91. You do not get a full point of rating change for beating a much lower player, because that win was already likely.
K is how loud one event is
US Chess no longer uses a flat K of 32, 24, or 16. K is 800 divided by effective prior games plus the games in the event. Effective games are capped, and they shrink when the rating is lower, so scholastic ratings stay mobile. A player over 2200 in a dual-rated regular event uses a smaller K.
Bonus, floor, and the special formula
A bonus is added when the raw gain clears 10 times the square root of the games in the event (three-round events use 4 in that square root). The bonus is for an unusually hot event, and it turns off if you play the same opponent too often. A rating floor stops an established player from falling 200 points below their peak, on 100-point steps from 1200 to 2100. Players with 8 or fewer games, and players whose entire history is wins or entire history is losses, use the special formula instead of K.
Published ratings are rounded. The office stores the decimal. Two players can share a published 1600 and still be a fraction apart on the next event.
Questions
Does one game change a rating by itself?
US Chess rates the event as a whole. A round-by-round view is an estimate of the games so far, using the same pre-event rating. The posted number comes from the full event.