The Official Rules of Chess discus only two tournament types: the round robin, and the Swiss system. Why is it that the round robin is so popular, and why is it used so rarely for other kinds of tourney?

The Swiss is sort of an elimination tourney in which no one ever gets eliminated. For the second round, first-round winners play other first-round winners and losers play losers. In subsequent rounds, players are grouped by won/loss record, with, for example, players with two wins and two losses facing each other in the fifth round.

The Swiss system makes sense whenever the limiting factor is the number of rounds to be played. With a bit enough room and lots of chess sets, there’s no reason why some players should have to drop out of the tourney early, or to wait around for a match to become available. It would seem a natural choice not just for chess, but for other games like backgammon. Why shouldn’t backgammon players enjoy the same maximum participation that chess players do?

[apologies to Jonathan Steinberg, author of Why Switzerland?, which is the best book I know for understanding Switzerland, the country.]

Continue reading “Why Switzerland?”

The United States Chess Federation’s Official Rules of Chess (7th Edition, 2019) contains unusually detailed and precise rules governing how chess tourneys are to be run. And there is tournament software available that implements these rules.

I’ve been experimenting with one of these software packages to see if it can be adapted to run a backgammon tourney that I’m going to be directing early next year. In doing this, I’ve run across a rule about the distribution of prize funds that I find, frankly, bizarre. Continue reading “Playing Tournament Chess for Money”

The previous post discussed a way in which the game of tennis is broken. The advantage accruing to the server has become so great that it is no longer sensible to play and score tennis in the traditional way.

The response of the tennis establishment has been the invention of a new type of game, the tiebreak, in which the advantages of serving are shared more equally because in a tiebreak both players get a chance to serve. And this solution is probably, now, a permanent part of tennis – it’s hard to imagine going back to the days before the tiebreaker.

There is still a need, however, to address the underlying problem lest the imbalance between serve and return grow so large that all games except the tiebreaks become meaningless. And this should probably be done in a way that requires the smallest possible alteration of the existing rules of tennis.

I have a modest proposal.

Continue reading “A Modest Proposal”

Tourneygeek is enjoying its annual pilgrimage to Mason, Ohio, for the Western and Southern Open, one of the leading tennis tournaments leading up to the U.S. Open.

In past years, I’ve used the opportunity to explore such things as the effect of the draw on the expectations of individual players, and the effect that tennis’s distinctive tiered seeding system has on the way a tournament plays out.

This year, I’ve mostly just sat in my implausibly comfortable seats and enjoyed the tennis. But on the second day of the tourney I watched a match between John Isner and Dusan Lajovic, and this put me in mind, again, of the fact that one element of tennis, the serve, is broken.

Continue reading “The Broken Serve”

The last post discussed the two alternatives for the Consolation bracket needed for an upcoming tournament.  But in addition to a Consolation, my friend also needs a Last Chance bracket. Third brackets are almost always rather difficult brackets to build, and they depend on the second brackets they’re attached to in the same way that second brackets relate to first brackets.

Continue reading “The Last Chance Salon”

In the last post, I started showing how to build a bracket for the consolation in my friend’s tourney, which he expects to draw up to 48 entrants. In showing the method, I digressed to show how it generated the more familiar 64 brackets. Now let’s return to the problem of building the 48.

Along the way, I’ll introduce a new half maxim of tourney design: be squirrelly early.

Continue reading “Be Squirrelly Early”

A friend asked me for a 48 bracket for a tournament he’ll be running next month. The tourney will have a main flight, a consolation, and a last chance. He wants to pay two places in the main, and two more in the consolation.

Rather than just giving you the bracket I came up with, let me show you the process by which the bracket was built. The will take a few posts. For the first one, I’ll begin the process, and then digress to show how second brackets are built for a 64 main.

Continue reading “Building Lower Brackets”

One of my favorite web sites, FiveThirtyEight.com, runs a weekly feature by Oliver Roeder called the Riddler, which each week poses a couple of interesting (and usually difficult) questions in math, logic, and probability.

This week’s “Riddler Classic” question concerns tournament design. Given a competition in which the better player wins two-thirds of the time, and that you only care about maximizing the probability that that best player wins, how should your construct a blind-draw tournament with these rather severe constraints: four entrants and four total games; and five entrants and five total games.

(Note that this success criterion is the same as tourneygeek’s earliest measure of fairness (C). So we can relate this challenge to the frequent discussions of fairness (C) elsewhere on this site.)

Now, I’m unable to imagine any competition in which the better player wins two-thirds of the time regardless of the size of the skill differential between the two players. The best player ought to beat the worst player rather more often than they beat the next best. I can see why the Riddler doesn’t want to put its readers to the trouble of using a more realistic match model. But since I have one ready to use, I’m going to seek a solution using my simulator, in which skill levels are handled rather better. In deference to the question as posed, however, I’ll use a skill parameter of 2.4, which is about what’s required to give the better of any two randomly-chosen players a two-thirds chance to prevail.

My solution is below the fold – before looking at it, you might want to give it a shot yourself.

I was dead wrong! For the correct answer (or at least a better one), scroll down to the comment of Donald the Potholer. His “Page Ladder” brackets improve on the ones I found. For the 4/4 case he succeeds 49% of the time, and his 5/5 bracket succeeds 44.8%.

I’ll rewrite this post with new analysis after the official results have been announced.

Continue reading “Designing Tourneys for the Riddler, Corrected!”

A friend asked me for a specialized bracket for a backgammon tourney he’s running soon. He wants a 128 bracket that’s a full double elimination with a progressive consolation as a third bracket. There’s an unexpectedly nice one available.

Continue reading “128’s the Charm”

An interesting design problem from a reader.

The tourney is for “Cold War”, a two-handed version of the famous board game Diplomacy. As many as 64 players are expected. The chief limitation is time – apparently even in its two-handed form, the game takes a long time to play. So minimizing the number of rounds is crucial.

A single elimination 64 bracket takes six rounds to play. A full double elimination can take as many as 13 rounds, but since time is at a premium, that can be pared down to 10 rounds. One round is saved by not having a recharge, and two more by shifting the lower bracket.

But an unusual feature of this particular game offers a third possible bracket structure. Each player can easily play two games at the same time! So perhaps we can give players a second chance by simply playing two separate 64 brackets at the same time, with a playoff between the two bracket winners as a seventh round if the two brackets are not won by the same person.

This is marvelously efficient. Each player gets to play until they lose twice, but you save at least three rounds, and maybe four if you would otherwise insist on a recharge, because a recharge is never needed.

How should such a bracket be drawn, and how does it compare with conventional single and double elimination brackets in the item of fairness (C)?

Continue reading “Do Two Singles Make a Double?”