A round in which a player has no opponent and receives points without playing. It happens whenever the number of players available for pairing is odd.
Where the odd number comes from and how to avoid it in the first place - an odd field.
Not at random. The pairing rules define the order, and knowing it removes the suspicion that the organizer chose.
The requested bye is the one worth offering at amateur events: it lets somebody play five rounds of seven instead of not entering at all. State in the regulations how many are allowed and by when they must be requested - what belongs in the regulations.
A forfeit is not a bye, though both mean a game was not played. The distinction matters for the standings and for the report.
In tournament files these appear with specific codes rather than as ordinary results, which is how software knows to exclude them from ratings and to treat them differently in tie-breaks - when a forfeit is declared.
This is where byes become genuinely important, and where organizers get caught out.
The problem
Buchholz sums your opponents' scores. In a round where you had no opponent, there is no score to add - so a bye would otherwise depress your Buchholz and punish you for something you did not choose.
The solution used in the current rules is a virtual opponent: the unplayed round is treated as a game against a notional player whose score is derived from your own result and position. The details are set out in the tie-break regulations and were revised recently.
And whatever you do, announce the rule at the opening: «if the field is odd, somebody sits out a round and receives a point, chosen by the pairing rules». Thirty seconds, and no suspicion afterwards - the opening announcement.
A round in which a player has no opponent because the field is odd, and receives points without playing - normally a full point in a Swiss. It is not a game: there is no colour and it does not count for rating.
Not a random choice: it goes to the lowest-placed player who has not already had one, and nobody receives a second while anybody eligible has none. Pairing software applies the rule, which is what makes the answer defensible.
A bye requested in advance by a player who has to miss a round - arriving late or leaving early. It is usually worth half a point and must be requested before the round is paired. Worth offering at amateur events: it turns a non-entry into five rounds out of seven.
No. A bye means there was no opponent; a forfeit means there was one and somebody did not play. Both are recorded as unplayed and excluded from rating, but they are marked differently and treated differently in tie-breaks.
Buchholz sums your opponents' scores, and a bye has no opponent to add - which would otherwise punish you for something you did not choose. The current rules use a virtual opponent whose score is derived from your own result. Do not compute it by hand: use software implementing the current edition.
Keep a spare player willing to fill in, let the organizer play if somebody else runs the pairings, or use a round robin below twelve players. What you should never do is turn somebody away to keep the field even.
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Systems - an odd field, tie-breaks, how many rounds, forfeits.