Ninety-seven players enter. Ninety-six of them get a board, an opponent and a clock. One of them gets a bye, which is a point and an empty afternoon.
The pairing bye: one point, no game
Every round of a Swiss needs an even number of players. When the number is odd, somebody has to be left out, and the FIDE Swiss rules say who: the lowest rated player in the lowest score group who has not already had one. So it lands near the bottom of the wall chart, it rotates, and the leaders never see it. It is worth a full point.
You find out when the pairings go up. Your name is on the list with the word bye next to it instead of a board number, and there is nothing to claim and nobody to shake hands with.
The half point bye you ask for
The other kind you request. Most weekend opens let you take a bye for a round you cannot play, because your train gets in at eight, or there is a wedding on the Saturday, or you work Friday evenings. That one is normally worth half a point.
Three things to get right. Ask before the deadline printed in the entry conditions, which is usually before round one. Expect a limit, commonly one or two per event. And expect the final round to be excluded, because organisers do not want prizes decided by people who went home.
Ask late and some organisers will give you a zero point bye instead, which is a round marked as played and lost.
What a bye does to your tiebreaks
Nothing to your rating. There was no game, so there is no rated result, and the Elo arithmetic never runs.
Tiebreaks are where it costs you. The usual first tiebreak in a Swiss is Buchholz, which adds up the final scores of all your opponents, and an unplayed round gets counted as a draw against a notional opponent rather than against a real player who went on to score points. Two players finish on four out of five, and the one who played five real games tends to take the trophy on Buchholz while the one who took a bye takes the smaller envelope.
A bye is also not a forfeit win. If your opponent is paired and simply does not turn up, the arbiter waits out the default time set in the regulations and then awards you the point, marked with a plus on the chart. Also unrated, but a different entry in the arbiter’s book.
Knockouts use the word for the opposite reason. A knockout needs the field to halve cleanly, so if 206 players enter an event built for 256 places, fifty of them have to skip round one. Those go to the top seeds. Same word, opposite meaning: there the bye is a reward for being good.
The first bye I was ever given, I went back to the hotel, fell asleep, and lost the next round in twenty-two moves. So if you do get one, do not go home. Eat something, walk outside for twenty minutes, and put in a short set of puzzles before the next round rather than watching the top boards for three hours. Your next opponent will have been playing chess all afternoon, and you want to arrive at the board already warm.