What kind of tournament system would allow dropping rounds?

[Celebrir]

A tiebreak tournament does not necessarily equal only one additional game. E.g., it could be a mini-round-robin. It is only one game only if the number of mutually tied players is two and they must play only one tiebreak game against each other.

True, but if it is a mini-round-robin There is a relatively high chance that it ends in another tie. And it still might be a single match which are two worst-case-scenario (depending on the players tied) I would like to prevent.

Style is a non-issue. A player who cannot cope with a particular opponent's style must improve his skill.

That sounds weird. I didn't mean that it would be a auto-loss, but that the player is not playing as strong against some styles as he does against others and I believe that this is true for nearly every player (To show a prominent example look at the games between Yamashita Keigo and Iyama Yuta. There is a clear tendency but it is not like the result is known before)

Usually, an opponent-dependent tiebreaker does not take into account the whole tournament; it is not a tiebreaker measuring the tournament results of all participants (other than the player himself) of the tournament.

Okay "whole" was a to strong word, but "quite a lot" should be the right word. It is for sure far more than if the tied players are only compared between themselves.

A first-order opponent-dependent tiebreaker (such as SOS) does not take into account a lot of opponents. In many tournaments with relatively few rounds and an intermediate to big sized top group, a first-order opponent-dependent tiebreaker often takes into account an only small percentage of those opponents involved in the tie. Those players shall be distinguished but such a tiebreaker often depends much on other opponents.

In my opinion "2*number of rounds - number of same opponents" is still a good number. I think it is good that the tiebraker takes other players into account as well, because there are often different possibilities to achieve a score and one might have been easier and the other might have been harder. The opponent-depending tiebrakers show that.

Your opinion reformulated can be made a bit more meaningful to being worried about tiebreak games measuring performance AGAINST usually fewer opponents than some first-order opponent-dependent tiebreaker measures performance BY usually more opponents. Such an objection is more concerned with the number of measured opponents than with the number of the player's measured own results. IMO, measuring the player's own results is always more meaningful than measuring his opponents' results. This is so because a tournament is a competition about which player achieves his best own results. For this reason, Wins or MMS is the tournament's first placement criterion (and SOS never is the first placement criterion). A tiebreak tournament measures the same kind of thing as the first placement criterion because this is the most meaningful for the player's own performance.

I agree that a players own performance is the most important. However, for me the opponents performance/strength is also a part of the players performance. E.g. someones performance is stronger if he beats you than if he beats me and the player who beats you should always be higher in the rankings than the player who beats me even if they both have 1 win.

There is, however, an alternative: a tiebreak tournament with games played against new opponents, in which only the tied' players results are interpreted for the prize distribution but the opponents are motivated by, say, rating effects of the tiebreak games so that every opponent takes the tiebreak games seriously. Unfortunately, I doubt that any such motivation is good enough to overcome psychologic preferences by such opponents for wishing that certain of the tied players may get better final places. So the alternative is, IMO, only good as a thought experiment.

I don't like this solution because we really open the door for all kinds of bribery here (not saying the general go-community would do that but better safe than sorry. Neither would the general go community discuss this topic so there are always people who aren't normal)

[RobertJasiek]

it is good that the tiebraker takes other players into account as well, because there are often different possibilities to achieve a score and one might have been easier and the other might have been harder. The opponent-depending tiebrakers show that.

On average over an infinite number of tournaments played under idealised same conditions (i.e. simultaneous tournaments), opponent-depending tiebrakers show it. Otherwise, there is only an expectation that they might show part of it. In practice, they show a mixture of earlier rounds wins, opponents tournament-strengths, pairing luck due to too little information and other factors influencing them.

the opponents performance/strength is also a part of the players performance.

It is, but it cannot be measured well enough to meaningfully order places. Opponent-depending tiebrakers can, with suitably sizes groups and a suitable pairing strategy, be much more meaningful (from round 3 on only) for pairing players so that same start group players end, after the last round, with opponent-scores as close to each other as possible. The better (because fairer because closer to same opponent-scores) the pairing is the less meaningful opponent-depending tiebrakers are for splitting final places.

[Matti]

To summarize:

If the prizes are divisible, the tournament which allow players to drop rounds at will can work.

If there are indivisible prizes, allowing players to drop rounds at will can introduce problems. One would need extra rules to sort this out. One could for example require that a player who hasn't lost any game may not drop a round. However, if there are more than one big indivisible prize, then additional rules are needed.