Initial Pairing Bug for McMahon Tournament?

Here is the tournament in question:

Here is the the pairing description in Sensei’s Library:

Per the description of first round pairing, players are paired “within the bands according to one of the methods outlined in Group Pairing (” The word within tells me that players with the same initial McMahon points should be paired against each other first.

The initial pairing for this tournament is Slide pairing, so I would have expected the following pairing between players whose initial score was 0:

gugamircea 2k vs Mudksip000 7k
RikoParis 2k vs Невероятный АЛК 7k
yegorister 2k vs Farnham 8k

Instead we see the slide applied irrespective of starting score:

gugamircea 2k vs huangyunict 9k
RikoParis 2k vs Comrade SeeRed 11k
yegorister 2k vs IBa 13k

The most unfortunate pairing is probably Невероятный АЛК 7k vs Cozy 25k. I can’t see how that will be a rewarding game for either player.

This seems to defeat the intention of McMahon tournaments, which “avoids the problem of severely unbalanced pairings in early rounds.”

In case evidence is needed that my proposed understanding of McMahon pairing is correct, consider the description of pairing in subsequent rounds:
"Pairing players with the same McMahon Score against each other using one of the methods outlined in Group Pairing (

So my question is, how do we get this fixed?



There’s certainly a possibility that the two issues are related. I’m new to the forum, but I don’t see a link to a github issue tracking that item, and the post is almost a year old…

@Eugene They are probably unrelated.

Ah well - McMahon is just one of those topics that I have on the radar as “tends to generate questions, doesn’t often get good answers”, so I went looking for other examples of that, in case we can maybe have a burst of tidying it up.

It did work exactly as it should, @DoubleSente.

Quoting SL:

Before the First Round

Order the field of players by strength. Divide the field into bands of players based upon number of rounds and the distribution of players strengths. […]

Dividing the field means setting up the McMahon bars. You chose 20k and 10k, respectively, as bottom and top bars, meaning that: a. every player ranked 10k or higher was placed in the top group; b. every player ranked 20k or lower was placed in the bottom group; and c. all players ranked from 19k to 11k were placed in bars corresponding to their ranks (19k players in the 19k bar, 18k players in the 18k bar and so on). This is the resulting division for your tournament:

List of Competitors

Top Group (Initial score: 0)

  • gugamircea [2k]
  • RikoParis [2k]
  • yegorister [2k]
  • havefun [3k]
  • VPshunt5 [3k]
  • tikka [4k]
  • DoubleSente [5k]
  • Kame Sen’nin [6k]
  • Невероятный АЛК [7k]
  • Mudksip000 [7k]
  • Farnham [8k]
  • He Who Walks in Shadows [8k]
  • Midboss [9k]
  • huangyunict [9k]
  • Maxis [10k]
  • Oppilas [10k]

11k Bar (Initial score: -1)

  • Comrade SeeRed [11k]
  • orangeagent [11k]
  • ysatcho [11k]

12k Bar (Initial score: -2)

  • pmurk [12k]
  • unicycleOLI [12k]
  • Dimago [12k]

13k Bar (Initial score: -3)

  • IBa [13k]
  • DerMannMitHut [13k]

15k Bar (Initial score: -5)

  • SebastianKenne [15k]

17k Bar (Initial score: -7)

  • Julko [17k]

Bottom Group (Initial score: -10)

  • Cozy [25k]
  • BlueFalcon [22k]

Then you set the number of rounds in a way that effectively asked the server to generate a tournament in which it would be possible for players in the bottom group, starting with a negative score of -10, to get enough points in only three rounds to overtake those starting with the default score of 0. So, it delivered just that.

I believe a way to make a McMahon tournament work the way you had envisioned, with a small number of players, would be setting the bottom/top bars to 10k/9k and increasing the number of rounds as much as you reasonably could.

Another false alarm. @anoek explained it here.


Cool, I hadn’t seen that one.

How so?

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My bad, late-night-writing inaccuracy. Already corrected the post. Anyway, each win amounts to a single point. Checking the tournament, the number of matches generated for the first round wouldn’t allow a player with a score of -10 to overtake, point by point, playing inside his own group, someone with a 0+ score. Then again, maybe I’m missing something. :ok_man:

There may be all sorts of different options how to define the initial bands, but in the end pairing should be by McMahon score.

I think the original poster described it very well.

This is the core of the McMahon system. And it’s not what we are doing in tournaments labelled McMahon. (It is exactly what we are doing in simultaneous McMahon tournaments though).


What I understood trying to dig this argument is that the only useful pairing with McMahon is “strenght”.

McMahon method sets an initial score and that should be aimed to what you said: avoiding “the problem of severely unbalanced pairings in early rounds.”
Players in each bar should play against other players in the same bar. That would make sense.

But, as you noticed, the pairing method on OGS is applied to the whole list. So, in the case of “slide”, the player in the middle of the list plays against the last one. “Massacre” will be even worse: fist and last in the list play together. This is completely counterintuitive for a McMahon method.

So, I don’t know if it’s a bug on OGS or it’s correct this way, but the only thing that makes sense to me is to use “strenght” pairing.

I don’t think it’s possible for this tournament.
Moderators will know it for sure.

Agreed that this makes most sense. It largely solves the problem for the first round. But not for subsequent rounds. (A 25k would always still play 25ks with strength pairing, even if she has won the first 12 rounds.)

I think that the “strenght” is referred to the points in the tournament, not the rank.

I don’t think so. (If it was, we’d indeed actually get McMahon tournaments.) Unfortunately I can’t find a suitable tournament at the moment to confirm or reject my (or your) thinking.

Thanks for clarifying what the system is doing @lucasfelix. What you’ve described makes sense, and I can understand if that is the logic the system currently employs. However, I still don’t believe it reflects the spirit of McMahon tournament pairing.

The purpose of a McMahon tournament is not to ensure that every player has a possibility of winning the tournament. Instead it explicitly embraces the fact that most players have no chance of winning. In fact the top bar is defined as the group of players who have a chance of winning per Sensei’s Library:

“This band contains the strongest players, who are said to be above the bar, and should contain all players that are thought to have a chance to win the tournament (for more details see BarTheory (”

Also, as mentioned in the original post, the description on SL explicitly says to pair players within the same band against each other.


I agree that pairing should be within bands, though it shouldn’t matter what pairing method you choose. If you choose slaughter pairing, it should apply the pairing within bands rather than to the whole list.

In other words, I believe this is an OGS bug and we shouldn’t have to work around it by using specific pairing types.


@anoek, thoughts on the conversation thus far?

Look, I do agree with what you and @richyfourtytwo are saying, but I believe the reason that particular tournament didn’t reflect what you called the spirit of McMahon pairing is the way it was configured.

By all means, ensuring that every player has the actual possibility of winning may not be the [main] purpose of the McMahon system, but I don’t think it follows that it’s reasonable to have a tournament in which it’s virtually impossible for someone to win.

“Order the field of players by strength, divide the field into bands of players based upon number of rounds and the distribution of players strengths.” Why would we care about the number of rounds if not for an underlying, implicit understanding that a tournament should be at least potentially winnable for each participant?

The server seems to agree that said principle comes first, McMahon pairing ot not, and uses the number of rounds/matches and the potential score as the main parameter when generating the tournament—to the point of ignoring the intended band division when it’s incompatible with that.

Think about what you would have ended up with if that weren’t the case. We’re talking about a single-rank-band McMahon tournament (I would get back to this later). Suppose the only consideration were to ensure the participants only played inside their respective bands. It’s two games per round, right? So:

To begin with, two participants wouldn’t play in the first two rounds. Julko 17k and SebastianKenne 15k are both alone in their respective bars, so both get a bye in every match in the first round, Julko moving to the 16k bar and SebastianKenne to the 14k one… where they’re alone again, so same thing happens in round two.

Then there’s the bottom group, Cozy 25k and BlueFalcon 22k. Say they play and BlueFalcon wins. He moves to the 19k bar, Cozy stays. Aaaand that’s it for them in the tournament. They don’t get to play again. They’re both alone in their bands. They get a bye in the second match, Cozy stays in the bottom group with -9.5 points, BlueFalcon remains in the 19k band with -8.5 points. Comes round two, Cozy gets a bye and moves to the 18k bar… but Bluefalcon gets his own bye to and moves to the 17k bar, so they don’t meet. They’re still alone in their groups. Next round? Same thing.

Well, one could argue that that should still be possible, that everyone having the virtual possibility of winning the tournament not only isn’t the main focus of a McMahon, but that such a consideration can and should be disregarded if incompatible with an intended group division/number of rounds combo and ask @anoek to make the system reflect that…

But I believe OGS already has the system in place for tournaments that, borrowing again from your words, would respect the spirit of the McMahon pairing system, even, like in this particular case, with a small roster of players and an imbalance of ranks (16 SDKs / 3 11k / 3 12k / 2 13k / 1 15k / 1 17k / 1 25k / 1 22k).

The issue is a lack of information (at least this is something I could’t find in the FAQ, for example): it’s not made clear that McMahon uses the single-rank-band assigning method whereas Simultaneous McMahon generates multiple-rank bands.

For the same roster and the same number of rounds, I believe that choosing Simultaneous McMahon and a minimum group size of, say, 5 would lead to to the tournament you had envisioned. Three bars: SDKs (top group), a 11k-13k group and a 13k-25k bottom group, with respective initial scores of 0, -1 and -2, everyone would get to play, within the band, according to the group pairing method, and have the possibility of winning.

As for the single-rank-band McMahon, it would work better with more players sharing the same rank—and, yes, I believe it would take a number of rounds/matches consistent with the resulting number of bands.

Hi @lucasfelix,

I appreciate the clarification on how Simultaneous McMahon works, and you’re right, that does sound a lot closer to what I was expecting from standard McMahon. It would have been helpful if that were more clear in the FAQ. However, I’m assuming that in the case of Simultaneous McMahon, players from the different groups would never play each other regardless of outcome. Is that correct? In that case, it still does not fit quite the same niche as what I’m arguing for.

I also acknowledge that the single rank bands of the tournament in question are poorly suited to pairing exclusively within bands. Maybe there is room for the idea of pairing first within bands, and expanding the pairings into adjacent bands if necessary?

As to the question of how McMahon is meant to be structured, you quoted the line on SL:
“Order the field of players by strength, divide the field into bands of players based upon number of rounds and the distribution of players strengths.”
However, you left out the very next sentence, which I feel makes my point:
"Players in the same band will be paired against each other in the first round."

The SL page also covers the question of future rounds:
"Pairing players with the same McMahon Score against each other using one of the methods outlined in Group Pairing."

This is significantly different from the description of Simultaneous McMahon because it would allow successful players from the lower groups to play unsuccessful players from higher groups.

Consider a tournament with initial bands:

8 players : 0 points
8 players : -1 points
8 players -2 points

After the first round, the second round distribution would be:

4 players: 1 point
8 players: 0 points
8 players: -1 points
4 players: -2 points

Third round:

2 players: 2 points
6 players: 1 point
8 players: 0 points
6 players: -1 points
2 players: -2 points

Final points distribution after the third round:

1 player: 3 points
4 players: 2 points
7 players: 1 point
7 players: 0 points
4 players: -1 points
1 player: -2 points

That was long winded, but I hope it clarifies my understanding of the McMahon system. It should have enough rounds to identify a single winner (in the above case 3), but it is mathematically impossible that a player in the bottom group would have won, since their best possible final score is 1, and the winner would necessarily score 3 by going undefeated. This is supported again by SL:
"The process is repeated until all rounds have been played (Note: Some tournaments stop when exactly one player from the top group is left with a perfect undefeated record)."

Does that make sense?

No, the difference is that the initial bands will be comprised of multiple ranks, but changes in the score will still move the player to the next group.

I think that’s exactly what we can use the Simultaneous McMahon for. Setting a minimal number of players for each band as to ensure everyone will have an opponent of similar strength and adapt the number of rounds to the number of bands.

A point we’re in agreement about. I was trying to cover why that didn’t happen and how we can make sure it will.

Exactly. That’s my point: you’d need more rounds. And as we’ve seen, OGS’s tournament system gets all creative when asked to generate a competition in which it’s mathematically impossible for someone to win.