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Topic: Byes in tournaments
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Registered: Dec 16, 2001
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Byes in tournaments
Posted: Dec 2, 2017, 8:16 PM

The current system in tournament rounds with unevenly divisible numbers of players seems unfavorable to the top seeded player - the earliest round in which there are an uneven number of players is when the top seeded player is currently given a bye. By unevenly divisible, I mean a number of participants which is not only a multiple of two + at most one three - 12 is a fine number of entrants which isn't unfavorable to the top seed. In the Winter's Coming tournaments we are facing several unfavorable tournament situations for the top seeds. Often, the first bye round can happen at a point in the tournament in which the top seeded player would otherwise be facing a relatively low seeded opponent and would likely cruise to a quick win. The next time a bye is given, it goes to the second seeded player (and then to the third seeded player after that). This can frequently lead to a situation in which the second or third seeded player in the tournament gets a bye while the top seeded player dukes it out with the other player (third or second) for the privilege of playing the player with a bye in the final round. With a nicely divisible by two number like 16 entrants, the top seeded player would likely play the fourth seed in the semifinal and then play the winner of 2nd vs. 3rd in the final. There are a couple of ways that this could be changed so that the deck isn't as stacked against the top seed if there aren't a nice round number of tourney entrants. One is to have a few of the lowest seeded players play a preliminary round. Another is to allow the top seeded player a first refusal on a potential bye in a round, so that if s/he did not take an initial bye in the first odd number of players round, a bye would again be offered to her/him the next time there were an odd number of players - which could well be when the top three seeds were the only participants left in the tournament.

Retired from TB Pente, but still playing live games & exploring variants like D, poof and boat


Posts: 375
Registered: Dec 16, 2001
Age: 40
Re: Byes in tournaments
Posted: Dec 3, 2017, 12:49 AM

Watsu is correct.

Assuming all higher ranked seeds win all matches, The current system helps the #1 seed only when the tournament starts with 3 players (obviously) (And by extension, 6 or 12 players), or when the tournament starts with 17 players. In those situations, the tournament would reduce to the top 3 seeds, with the #1 seed getting the bye while the 2 and 3 seeds battle for the chance to advance and play the #1. This is how it should be, generally speaking, as Watsu alluded to: 1 versus 4; 2 versus 3. Or, if then umber of starting players is such that the top 4 wno't be in the semi-final round, then it should be 2 versus 3 while 1 has a bye.

Under the current system, The 1 seed is very much disadvantaged if there are 5, 10, or 20 players at the start, or if there are 11 or 22 or 19 or 21. Or 9 or 18. Those situations reduces to the top 3, but one of the other two players gets the bye 9sometimes it's the 2 seed, sometimes the 3 seed, but either way it doesn't make sense for the 1 seed to have to beat both the 2 and the 3 in succession.

The #1 is relatively unaffected if the tournament starts with 7, 13, 14, or 15 players.

Examining the two possible suggestions to remedy this:

1) First refusal - This would be possibly the more "logical" solution, granting the bye when it is most useful and desired instead of automatically granting it when it might not be useful. But it makes more work for the administrator of the tournament.

2) Restructuring the first round to avoid such problems:

Tournaments with a starting number of players that is a power of 2 need no adjustment (2,4,8,16,32, etc.) Likewise for tournaments with 3,6,12,24,48, etc.

With 5 players, there are two possibilities:
A) 1 versus (4 or 5), and 2 versus 3. In other words, the 1 seed DOES play in the first round so that he can use his bye in the second round when there are 3 players and it's more valuable. In this situation, if the 2 or 3 seed wishes to have a first round bye, he can. Regardless of who gets the bye in the first round, as long as it isn't the the 1 seed, things will work out favorably for the 1 seed but won't have much effect on the 2 or 3 seed.
B) Have the 4 and 5 seed play a "play-in" match to create a bracket of 4. (This method could be used anytime the number of entrants is 2^n + 1 (so, when there are 5,9,17,33 entrants, etc.).

Whichever of those methods is used for a 5 person tournament, that same method could be used for 10, 20, 40, etc, once it reduces down to 5 people.

The current system works fairly well if the number of players is 2^n - 1 (so, 7, 15, 31, etc) because the 1 seed sits out the first round, after which point the number of players remaining will be a power of 2 and there won't be any more byes the rest of the way. The same is true if the number of starting players is something that quickly reduces to 2^n - 1 (such as 14,30, etc.).

If there are 13 players (or 26,52, etc.), the current system seems to work okay, because 13 reduces to 7 which reduces to 4, at which point the top 2 seeds have gotten a bye and we're left with a nice 4-person bracket. The same is true when the number of starting players is such that it reduces to a power of 2 after 2 rounds of play.

If the tournament starts with a number of entrants that I didn't discuss above, it means the tournament would reduce to one of the above examples, and the appropriate method could be applied.

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