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| Jeff Sonas writes on the Double Elimination Format: Some of you may recall an article I wrote a couple of years ago, as a follow-up to Yasser Seirawan's "Fresh Start" proposal for unifying the world chess championship. In that article, I evaluated thousands of different formats for determining the world champion, including various combinations of knockout or Swiss or round-robin qualifying tournaments, followed by candidates matches of various lengths. At the time, my conclusion was that FIDE's 128-player knockout tournament was an extremely poor way to determine a world champion, whereas Yasser's suggestion (a Swiss qualifier leading to a series of long candidate matches) was in fact a fantastic way to determine a world champion. In fact, it was almost the ideal format, mathematically speaking. However, Yasser told me later that he was surprised by the negative reaction from top players regarding his suggestion of a Swiss qualifier. But when you think about it from a top player's perspective, it really makes sense. In a Swiss tournament, or even a round-robin tournament, it is very difficult to "force" your way into first place on your own. Almost invariably, you need indirect help from the other players (who can either defeat your top challengers or at least hold them to a draw). Because of this interdependence, in such an important and lucrative event, it is inevitable that there will be accusations of collusion: either an out-of-contention player not trying their hardest, or two players agreeing to a mutually beneficial "grandmaster draw". According to Yasser, the top players much preferred the idea of a knockout, where neither of those collusion scenarios is relevant. In a knockout, all players are equally "in contention" until the moment they are eliminated, so nobody would choose to intentionally lose a game, and even if they did, it doesn't really hurt anyone else's chances very much. And two players in a knockout might agree to a brief draw for short-term tactical reasons, but that will only make their own match last even longer, to their own detriment in the long term. So, from a sporting perspective, the knockout tournament is very appealing to the top players, who feel more in control of their own destiny. Plus, knockouts are simply more fun to follow. Every game matters. Well, what's wrong with the knockout format? Easy: with so many participants, and so little time, there is just not enough room to identify the single strongest player in the field. It is very easy for the strongest player to falter in one game and suddenly become eliminated. We expect that an effective championship cycle will allow the strongest player (whoever that might be) a real chance to demonstrate their superiority by winning the cycle, and this clearly isn't the case when a minus-one score over a stretch of two games can eliminate you from the whole cycle, however much success you had in the previous games during the tournament. Thus a knockout tournament should not be the final championship event, merely a preliminary qualifying event. And there needs to be a way for a truly strong player to lose a match and nevertheless ultimately qualify for the championship, either through the use of a double-elimination format, or by there being additional knockout tournament(s) where players eliminated from the first tournament can have at least one more chance to qualify. My vote is for the double-elimination knockout format, which was originally suggested by Alexander Khalifman. In this scenario, losing a match does not eliminate you from the tournament; you simply drop down to the losers' bracket, where you keep playing elimination matches against other players who have also lost once. You aren't eliminated until you lose one of those matches. This is an ideal way to allow multiple players to qualify, and it lends itself to all kinds of variations if a specific number of qualifiers is desired. Unless you've thought a little bit about it, you may not be aware that there are many ways to structure a double-elimination tournament. It's not as simple as a single-elimination tournament would be, and there can be pitfalls. However, it turns out that there are very clean ways to design a 128-player double-elimination knockout tournament so that it generates one, two, three, four, five, six, seven, or eight people who qualify into a championship cycle. My favorite approach is to have all winners' bracket matches last four games (starting with Round 3), while all losers' bracket matches last two games. This leaves room for two rounds of losers' bracket matches to be played simultaneously with each round of winners' bracket matches. In addition to the obvious benefit of having longer matches among the top players, I like this approach because it preserves the "power of two" numbers (128, 64, 16, etc.) that are so prevalent in typical knockout tournaments. Otherwise you can easily fall into a situation where one bracket reduces down to an odd number of players, and you have to give one of them a late-round bye, and it's very ugly. I know this is somewhat complicated, so I want to provide an illustrative example. As always, we would start with 128 players, and Round 1 consists of two-game-matches. Instead of going home, the 64 players who lose in Round 1 will drop down to the losers' bracket, where they get to face other players who have also lost one match. Thus, at the start of Round 2 we have 64 players in the winners' bracket, and 64 players in the losers' bracket. The Round 2 matches would again be two games long, and so at the end of Round 2 there would be 32 players still in the winners' bracket, and 32 players who just dropped down from the winners' bracket to the losers' bracket, and 32 players who just won their losers' bracket match. So now we have twice as many players in the losers' bracket as in the winners' bracket. The key is to preserve that 2:1 ratio until the end. To continue the example, and to show how we preserve that 2:1 ratio, let me go through one more round. We start Round 3 with 32 undefeated players (in the winners' bracket) and 64 players with one loss (in the losers' bracket). This round lasts four days, rather than two. In the winners' bracket, you have the usual 16 four-game matches involving undefeated players. Meanwhile, during the first two days of this round, down in the losers' bracket there are 32 normal two-game matches between players with one loss. That gets it down to 32 players left in the losers' bracket, and those 32 players immediately play another set of two-game matches (across days three and four of the round), getting us down to 16 players still in the losers' bracket. At the end of the four days, there are 16 undefeated players in the winners' bracket, 16 players who just dropped down to the losers' bracket, and 16 players who just won the last set of losers' bracket matches. That leaves us with 16 undefeated players in the winners' bracket, and 32 players with one loss in the losers' bracket. As you can see, the 2:1 ratio is preserved, and subsequent rounds work the same way. Ultimately, after Round 7, we are left with one player in the winners' bracket, and two players in the losers' bracket. If we had wanted only one player to qualify into the Candidates cycle, then the two players in the losers' bracket could play each other as the only Round 8 match, and the survivor faces the undefeated player, who gets draw odds in the Round 9 championship match. This has the wonderful benefit that the tournament championship can't be decided by tiebreak games (remember the FIDE Championship final between Anatoly Karpov and Viswanathan Anand which went to a rapid tiebreak?). If we had wanted two qualifiers, then we could simply take the undefeated player and the winner of that Round 8 match. And if we had wanted three qualifiers, then we would have just taken the original three players who were still around after Round 7, without bothering about the Round 8 or Round 9 matches, unless they were needed for prize money considerations or seeding into candidate matches. The really neat part is that if you want a few more people to qualify, you can control the number of qualifiers by deciding at what point you switch over to having only one set of losers' bracket matches per round (instead of two). By controlling which round this happens in, you can make the tournament generate four, five, six, seven, or even eight qualifiers. This makes the double-elimination knockout tournament perfectly suited to whatever type of championship cycle is proposed. Presumably there would be some kind of plan where there is a series of final matches, including the defending champion and maybe others, plus a specific number of qualifiers from the knockout tournament. Everyone would love to have the knockout tournament include matches of four games, instead of two. Everyone, that is, except the sponsor, who has to support a much longer event, and that eats up a lot of money. So, although it pains me, I feel compelled to point out that we could do that whole format I just described, except in half the time, by having the winners' bracket matches last two days each, and the losers' bracket matches last ONE day each. In fact, it really wouldn't look too different from the current Tripoli tournament. The main difference is that the first time you lose a match, you aren't eliminated yet. Instead, you come back tomorrow and play a single-day match against someone else in the losers' bracket, maybe following the same time controls as a typical tiebreak. If you win, you come back the next day and do the same thing again, while the undefeated players are conducting their own tiebreak matches. If you survive long enough, to the round where once again there is only one losers' bracket match per round, then you're back to one game per day at regular time controls, with tiebreaks every other day. It's grueling for the players, but I'm sure they would prefer it to the current alternative of a single-elimination tournament, where they just go home if they lose one match. It is very easy to criticize the current knockout format and call it a lottery, without suggesting a truly practical alternative. It needs to have the support of the top players, and it needs to be perceived as a more effective structure that will be won by a more deserving player. I hope you agree that my suggested changes to the current format would be both superior and quite feasible. Please feel free to send me email at jeff@chessmetrics.com if you have any questions, comments, or suggestions. Description of the the Sonas-style double-elimination tournament structure Here is a more specific description of the Sonas-style double-elimination tournament structure, and how it could be adapted to produce a particular number of qualifying players. 1. Summary of Sonas-style double-elimination tournament format The first round of the double-elimination tournament is identical to the current format, with 128 players facing each other in a single round of two-game matches. The first difference is that Round 1 losers don't go home; they get to play against each other in a separate set of elimination matches which include all the players who have exactly one loss. As players lose in this bracket, they are eliminated. At the same time, undefeated players who lose a "winners' bracket" match would drop down into the elimination bracket for the next round. As a brief illustration from the 2004 Tripoli tournament, #31 seed Giovanni Vescovi, who lost his first-round match in an upset, would not be eliminated, but instead would play #95 Magnus Carlsen (who also lost his first-round match) in a Round 2 two-game elimination match. The loser of that match, who would then have two match defeats, would at last be eliminated, but as long as a player avoided a second match defeat, they could still continue on through the elimination bracket and win the tournament (or at least finish in second or third place) to qualify for the final "long match" part of the championship cycle. The way the numbers work out, in Round 2 there would be 32 "winners' bracket" matches which include the 64 remaining unbeaten players, and 32 elimination matches that include the 64 players with one match loss. Clearly, then, at the end of the two-game matches in Round 2, there would be 32 unbeaten players, 64 players with one loss, and 32 players who had lost both their first two matches and would therefore be eliminated. Notice that there are twice as many players in the elimination bracket as in the winners' bracket, and that the numbers are exact "powers of two". It is very important to maintain these two features as long as possible, so that there is never an odd number of players left in the elimination bracket (which would be disastrous and lead to somebody arbitrarily receiving a bye). That is the reason why we can't just pick any double-elimination scheme. It will also be important to rotate the matchups within the elimination bracket slightly, to minimize the chance of specific players facing each other more than once during the tournament. Once the "powers of two" pattern ends, this adjustment will no longer be necessary, because the matchups will already be rotated. Starting in Round 3, the matches would be four games long in the winners' bracket, which always includes all the undefeated players. Using four-game matches keeps the tournament progressing reasonably rapidly, while still giving the strongest players a chance to recover from one unlucky loss and maintain their spot in the series of four-game matches. Meanwhile, during those four days, down in the "elimination bracket", one set of two-game matches will eliminate 50% of the players in the bracket, and then another set of two-game matches will eliminate a further 50% of the survivors. For instance, out of those 64 players with one match loss entering Round 3, 32 would be eliminated in the first two days, and then an additional 16 would be eliminated in the next two days. Only 16 players would survive to the end of Round 3. They would be joined by the 16 players who had lost their four-game match in Round 3, leaving 16 undefeated players and 32 once-defeated players at the end of the round. It is not immediately clear how many qualifiers out of the tournament would be required. Somewhere between one and eight. It would depend on the overall characteristic of the world championship cycle. It might just be one single winner of the double-elimination tournament, who would play against the defending champion, or perhaps the defending champion would join three qualifiers in a four-player final, with two rounds of long matches. Maybe the loser of the previous cycle's championship match would automatically qualify into the round of matches, there are many possibilities. It would even be possible for the winner of important tournaments like Linares, Wijk aan Zee, or Dortmund, to automatically qualify into the final series of matches, and maybe the number of qualifiers needed out of the double-elimination tournament could be dynamically decided at the start of the tournament, based on whether any players won more than one of the supertournaments. The details of that overall decision are clearly going to have ramifications both political and financial, and are not for me to decide! The point is that this "Sonas-style" double-elimination tournament lends itself extremely well to any number of required qualifiers, from one all the way up to eight. Interestingly enough, despite the four-game matches after Round 2, this tournament would not last significantly longer than the current single-elimination format (with its four-game semifinal matches and six-game final match). Currently there are 20 playing days (5 rounds of two days each, plus 1 round of four days, plus 1 round of six days), and most of the variations of this double-elimination format require only 24 playing days. In traditional double-elimination tournaments that involve just one winner, in sports like baseball, croquet, or billiards, the final stages inevitably produce an undefeated finalist who is then matched up against an opponent that has already lost once. If this happens in baseball, the team from the elimination bracket has to beat the undefeated team in two straight games in order to win. That would be weird in chess, to say that the player with one match loss has to win two straight short matches against the undefeated player. Far better would be to provide the undefeated player with a small advantage and have them play only one (longer) match. The obvious solution would be to give the unbeaten player "draw odds" in the final, which means they win the tournament if the final match finishes in a tied score. The big benefit of this approach is that there would be no need for rapid time control tiebreaks in the tournament final. 2. Round-by-round tournament structure In case you're still a little confused about how the tournament would work, here is a more systematic summary of what each round would look like. This is for the case where the tournament needs to be won by just one player, who perhaps would advance to face the defending champion in a "long" match. Further down are exact details about what would change if more than one qualifier is needed. Round 1 (Days 1-2) Days 1-2: 128 players, 64 two-game matches; 64 players in winners' bracket, 64 in elimination bracket, 0 eliminated Round 2 (Days 3-4) Winners' bracket: Days 3-4: 64 players, 32 two-game matches; 32 players stay in winners' bracket for Round 3, 32 players drop down to elimination bracket for Round 3 Elimination bracket: Days 3-4: 64 players, 32 two-game matches; 32 players stay in elimination bracket for Round 3, 32 players eliminated Overall results from Round 2: 32 players in winners' bracket, 64 in elimination bracket, 32 eliminated Round 3 (Days 5-8) Winners' bracket: Days 5-8: 32 players, 16 four-game matches; 16 players stay in winners' bracket for Round 4, 16 players drop down to elimination bracket for Round 4 Elimination bracket: Days 5-6: 64 players, 32 two-game matches; 32 players stay in elimination bracket for Days 7-8, 32 players eliminated Days 7-8: 32 players, 16 two-game matches; 16 players stay in elimination bracket for Round 4, 16 players eliminated Overall results from Round 3: 16 players in winners' bracket, 32 in elimination bracket, 48 eliminated Round 4 (Days 9-12) Winners' bracket: Days 9-12: 16 players, 8 four-game matches; 8 players stay in winners' bracket for Round 5, 8 players drop down to elimination bracket for Round 5 Elimination bracket: Days 9-10: 32 players, 16 two-game matches; 16 players stay in elimination bracket for Days 11-12, 16 players eliminated Days 11-12: 16 players, 8 two-game matches; 8 players stay in elimination bracket for Round 5, 8 players eliminated Overall results from Round 4: 8 players in winners' bracket, 16 in elimination bracket, 24 eliminated Round 5 (Days 13-16) Winners' bracket: Days 13-16: 8 players, 4 four-game matches; 4 players stay in winners' bracket for Round 6, 4 players drop down to elimination bracket for Round 6 Elimination bracket: Days 13-14: 16 players, 8 two-game matches; 8 players stay in elimination bracket for Days 15-16, 8 players eliminated Days 15-16: 8 players, 4 two-game matches; 4 players stay in elimination bracket for Round 6, 4 players eliminated Overall results from Round 5: 4 players in winners' bracket, 8 in elimination bracket, 12 eliminated Round 6 (Days 17-20) Winners' bracket: Days 17-20: 4 players, 2 four-game matches; 2 players stay in winners' bracket for Round 7, 2 players drop down to elimination bracket for Round 7 Elimination bracket: Days 17-18: 8 players, 4 two-game matches; 4 players stay in elimination bracket for Days 19-20, 4 players eliminated Days 19-20: 4 players, 2 two-game matches; 2 players stay in elimination bracket for Round 7, 2 players eliminated Overall results from Round 6: 2 players in winners' bracket, 4 in elimination bracket, 6 eliminated Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player advances to championship round (Round 9), 1 player drops down to elimination bracket for Round 8 Elimination bracket: Days 21-22: 4 players, 2 two-game matches; 2 players stay in elimination bracket for Days 23-24, 2 players eliminated Days 23-24: 2 players, 1 two-game match; 1 player stays in elimination bracket for Round 8, 1 player eliminated Overall results from Round 7: 1 player in winners' bracket, 2 in elimination bracket, 3 eliminated Round 8 (Days 25-26) Elimination bracket: Days 25-26: 2 players, 1 two-game match; 1 player advances to championship round (Round 9), 1 player eliminated Round 9 (Days 27-30) Championship round: Days 27-30: 2 players, 1 four-game match; 1 player wins tournament championship 3. Adapting the tournament structure to produce a specific number of qualifiers Using that overall structure as a starting point, I would now like to describe how the structure would change, depending on how many qualifiers are needed. IF ONE QUALIFIER IS NEEDED: The players who wins the championship match (Round 9) is the only qualifier. IF TWO QUALIFIERS ARE NEEDED: There is no championship round. The last unbeaten player is the tournament winner, and the loser of that match drops down to the elimination bracket to play one more match (in Round 8) to determine the second qualifier. Rounds 1-6 unchanged, still providing 2 players in winners' bracket and 4 in elimination bracket, for Round 7 Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player drops to elimination bracket for Round 8 Elimination bracket: Days 21-22: 4 players, 2 two-game matches; 2 players stay in elimination bracket for Days 23-24, 2 players eliminated Days 23-24: 2 players, 1 two-game match; 1 player stays in elimination bracket for Round 8, 1 player eliminated Overall results from Round 7: 1 player qualifies, 2 in elimination bracket, 3 eliminated Round 8 (Days 25-28) Elimination bracket: Days 25-28: 2 players, 1 four-game match; 1 player finishes in second place, 1 player eliminated IF THREE QUALIFIERS ARE NEEDED: There is no Round 8. The last unbeaten player is the winner, and the loser of that match finishes in second place. Even though both players qualify, we would still play the match between them, to determine a tournament winner and possibly to determine placement in the final set of world championship matches. In addition to those two qualifiers, all additional qualifiers will come from the final round of elimination bracket In Round 7, the two-game elimination bracket matches will resolve four players down to one, who is the final qualifier. Rounds 1-6 unchanged, still providing 2 players in winners' bracket and 4 in elimination bracket, for Round 7 Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-22: 4 players, 2 two-game matches; 2 players stay in elimination bracket for Days 23-24, 2 players eliminated Days 23-24: 2 players, 1 two-game match; 1 player finishes in third place, 1 player eliminated Overall results from Round 7: 3 players qualify, 3 eliminated IF FOUR QUALIFIERS ARE NEEDED: The elimination bracket matches in Round 7 will change from two-game matches to four-game matches. Because this rounds will only include one set of elimination matches, rather than two, this leads to an elimination bracket with one extra player at the end of Round 7, so there would be two qualifiers from the elimination bracket, in addition to the first and second place finishers. Rounds 1-6 unchanged, still providing 2 players in winners' bracket and 4 in elimination bracket, for Round 7 Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-24: 4 players, 2 four-game matches; 2 players qualify, 2 players eliminated Overall results from Round 7: 4 players qualify, 2 eliminated IF FIVE QUALIFIERS ARE NEEDED: The elimination bracket matches in Rounds 6-7 will change from two-game matches to four-game matches. Because those rounds will only include one set of elimination matches, rather than two, this leads to an elimination bracket with slightly more players. By the time it gets to the Round 7 elimination bracket, there would be six players (and three matches) instead of four players (and two players). The winners of those three matches are the final three qualifiers. Rounds 1-5 unchanged, still providing 4 players in winners' bracket and 8 in elimination bracket, for Round 6 Round 6 (Days 17-20) Winners' bracket: Days 17-20: 4 players, 2 four-game matches; 2 players stay in winners' bracket for Round 7, 2 players drop down to elimination bracket for Round 7 Elimination bracket: Days 17-20: 8 players, 4 four-game matches; 4 players stay in elimination bracket for Round 7, 4 players eliminated Overall results from Round 6: 2 players in winners' bracket, 6 in elimination bracket, 4 eliminated Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-24: 6 players, 3 four-game matches; 3 players qualify, 3 players eliminated Overall results from Round 7: 5 players qualify, 3 eliminated IF SIX QUALIFIERS ARE NEEDED: The elimination bracket matches in Rounds 5-7 will change from two-game matches to four-game matches. Because those rounds will only include one set of elimination matches, rather than two, this leads to an elimination bracket with slightly more players. By the time it gets to the Round 7 elimination bracket, there would be eight players (and four matches). The winners of those four matches are the final four qualifiers. Rounds 1-4 unchanged, still providing 8 players in winners' bracket and 16 in elimination bracket, for Round 5 Round 5 (Days 13-16) Winners' bracket: Days 13-16: 8 players, 4 four-game matches; 4 players stay in winners' bracket for Round 6, 4 players drop down to elimination bracket for Round 6 Elimination bracket: Days 13-16: 16 players, 8 four-game matches; 8 players stay in elimination bracket for Round 6, 8 players eliminated Overall results from Round 5: 4 players in winners' bracket, 12 in elimination bracket, 8 eliminated Round 6 (Days 17-20) Winners' bracket: Days 17-20: 4 players, 2 four-game matches; 2 players stay in winners' bracket for Round 7, 2 players drop down to elimination bracket for Round 7 Elimination bracket: Days 17-20: 12 players, 6 four-game matches; 6 players stay in elimination bracket for Round 7, 6 players eliminated Overall results from Round 6: 2 players in winners' bracket, 8 in elimination bracket, 6 eliminated Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-24: 8 players, 4 four-game matches; 4 players qualify, 4 players eliminated Overall results from Round 7: 6 players qualify, 4 eliminated IF SEVEN QUALIFIERS ARE NEEDED: The elimination bracket matches in Rounds 4-7 will change from two-game matches to four-game matches. Because those rounds will only include one set of elimination matches, rather than two, this leads to an elimination bracket with slightly more players. By the time it gets to the Round 7 elimination bracket, there would be ten players (and five matches). The winners of those five matches are the final five qualifiers. Rounds 1-3 unchanged, still providing 16 players in winners' bracket and 32 in elimination bracket, for Round 4 Round 4 (Days 9-12) Winners' bracket: Days 9-12: 16 players, 8 four-game matches; 8 players stay in winners' bracket for Round 5, 8 players drop down to elimination bracket for Round 5 Elimination bracket: Days 9-12: 32 players, 16 four-game matches; 16 players stay in elimination bracket for Round 5, 16 players eliminated Overall results from Round 4: 8 players in winners' bracket, 24 in elimination bracket, 16 eliminated Round 5 (Days 13-16) Winners' bracket: Days 13-16: 8 players, 4 four-game matches; 4 players stay in winners' bracket for Round 6, 4 players drop down to elimination bracket for Round 6 Elimination bracket: Days 13-16: 24 players, 12 four-game matches; 12 players stay in elimination bracket for Round 6, 12 players eliminated Overall results from Round 5: 4 players in winners' bracket, 16 in elimination bracket, 12 eliminated Round 6 (Days 17-20) Winners' bracket: Days 17-20: 4 players, 2 four-game matches; 2 players stay in winners' bracket for Round 7, 2 players drop down to elimination bracket for Round 7 Elimination bracket: Days 17-20: 16 players, 8 four-game matches; 8 players stay in elimination bracket for Round 7, 8 players eliminated Overall results from Round 6: 2 players in winners' bracket, 10 in elimination bracket, 8 eliminated Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-24: 10 players, 5 four-game matches; 5 players qualify, 5 players eliminated Overall results from Round 7: 7 players qualify, 5 eliminated IF EIGHT QUALIFIERS ARE NEEDED: The elimination bracket matches in Rounds 3-7 will change from two-game matches to four-game matches. Because those rounds will only include one set of elimination matches, rather than two, This leads to an elimination bracket with slightly more players. By the time it gets to the Round 7 elimination bracket, there would be twelve players (and six matches). The winners of those six matches are the final six qualifiers. Rounds 1-2 unchanged, still providing 32 players in winners' bracket and 64 in elimination bracket, for Round 3 Round 3 (Days 5-8) Winners' bracket: Days 5-8: 32 players, 16 four-game matches; 16 players stay in winners' bracket for Round 4, 16 players drop down to elimination bracket for Round 4 Elimination bracket: Days 5-8: 64 players, 32 four-game matches; 32 players stay in elimination bracket for Round 4, 32 players eliminated Overall results from Round 3: 8 players in winners' bracket, 48 in elimination bracket, 32 eliminated Round 4 (Days 9-12) Winners' bracket: Days 9-12: 16 players, 8 four-game matches; 8 players stay in winners' bracket for Round 5, 8 players drop down to elimination bracket for Round 5 Elimination bracket: Days 9-12: 48 players, 24 four-game matches; 24 players stay in elimination bracket for Round 5, 24 players eliminated Overall results from Round 4: 8 players in winners' bracket, 32 in elimination bracket, 24 eliminated Round 5 (Days 13-16) Winners' bracket: Days 13-16: 8 players, 4 four-game matches; 4 players stay in winners' bracket for Round 6, 4 players drop down to elimination bracket for Round 6 Elimination bracket: Days 13-16: 32 players, 16 four-game matches; 16 players stay in elimination bracket for Round 6, 16 players eliminated Overall results from Round 5: 4 players in winners' bracket, 20 in elimination bracket, 16 eliminated Round 6 (Days 17-20) Winners' bracket: Days 17-20: 4 players, 2 four-game matches; 2 players stay in winners' bracket for Round 7, 2 players drop down to elimination bracket for Round 7 Elimination bracket: Days 17-20: 20 players, 10 four-game matches; 10 players stay in elimination bracket for Round 7, 10 players eliminated Overall results from Round 6: 2 players in winners' bracket, 12 in elimination bracket, 10 eliminated Round 7 (Days 21-24) Winners' bracket: Days 21-24: 2 players, 1 four-game match; 1 player wins the tournament, 1 player finishes in second place Elimination bracket: Days 21-24: 12 players, 6 four-game matches; 6 players qualify, 6 players eliminated Overall results from Round 7: 8 players qualify, 6 eliminated 4. Example round-by-round pairings in a double-elimination tournament As a further illustration, in the case where only one qualifier is desired, here is what the matchups might look like, assuming no upsets. Round 1 matchups #1:#128, #2:#127, #3:#126, #4:#125, #5:#124, #6:#123, #7:#122, #8:#121, #9:#120, #10:#119, #11:#118, #12:#117, #13:#116, #14:#115, #15:#114, #16:#113, #17:#112, #18:#111, #19:#110, #20:#109, #21:#108, #22:#107, #23:#106, #24:#105, #25:#104, #26:#103, #27:#102, #28:#101, #29:#100, #30:#99, #31:#98, #32:#97, #33:#96, #34:#95, #35:#94, #36:#93, #37:#92, #38:#91, #39:#90, #40:#89, #41:#88, #42:#87, #43:#86, #44:#85, #45:#84, #46:#83, #47:#82, #48:#81, #49:#80, #50:#79, #51:#78, #52:#77, #53:#76, #54:#75, #55:#74, #56:#73, #57:#72, #58:#71, #59:#70, #60:#69, #61:#68, #62:#67, #63:#66, #64:#65 Round 2 matchups (winners' bracket) #1:#64, #2:#63, #3:#62, #4:#61, #5:#60, #6:#59, #7:#58, #8:#57, #9:#56, #10:#55, #11:#54, #12:#53, #13:#52, #14:#51, #15:#50, #16:#49, #17:#48, #18:#47, #19:#46, #20:#45, #21:#44, #22:#43, #23:#42, #24:#41, #25:#40, #26:#39, #27:#38, #28:#37, #29:#36, #30:#35, #31:#34, #32:#33 Round 2 matchups (elimination bracket) #65:#128, #66:#127, #67:#126, #68:#125, #69:#124, #70:#123, #71:#122, #72:#121, #73:#120, #74:#119, #75:#118, #76:#117, #77:#116, #78:#115, #79:#114, #80:#113, #81:#112, #82:#111, #83:#110, #84:#109, #85:#108, #86:#107, #87:#106, #88:#105, #89:#104, #90:#103, #91:#102, #92:#101, #93:#100, #94:#99, #95:#98, #96:#97 Round 3 matchups (winners' bracket) #1:#32, #2:#31, #3:#30, #4:#29, #5:#28, #6:#27, #7:#26, #8:#25, #9:#24, #10:#23, #11:#22, #12:#21, #13:#20, #14:#19, #15:#18, #16:#17 Round 3A matchups (elimination bracket) #33:#95, #34:#96, #35:#93, #36:#94, #37:#91, #38:#92, #39:#89, #40:#90, #41:#87, #42:#88, #43:#85, #44:#86, #45:#83, #46:#84, #47:#81, #48:#82, #49:#79, #50:#80, #51:#77, #52:#78, #53:#75, #54:#76, #55:#73, #56:#74, #57:#71, #58:#72, #59:#69, #60:#70, #61:#67, #62:#68, #63:#65, #64:#66 Round 3B matchups (elimination bracket) #33:#64, #34:#63, #35:#62, #36:#61, #37:#60, #38:#59, #39:#58, #40:#57, #41:#56, #42:#55, #43:#54, #44:#53, #45:#52, #46:#51, #47:#50, #48:#49 Round 4 matchups (winners' brackets) #1:#16, #2:#15, #3:#14, #4:#13, #5:#12, #6:#11, #7:#10, #8:#9 Round 4A matchups (elimination bracket) #17:#45, #18:#46, #19:#47, #20:#48, #21:#41, #22:#42, #23:#43, #24:#44, #25:#37, #26:#38, #27:#39, #28:#40, #29:#33, #30:#34, #31:#35, #32:#36 Round 4B matchups (elimination bracket) #17:#32, #18:#31, #19:#30, #20:#29, #21:#28, #22:#27, #23:#26, #24:#25 Round 5 matchups (winners' bracket) #1:#8, #2:#7, #3:#6, #4:#5 Round 5A matchups (elimination bracket) #9:#17, #10:#18, #11:#19, #12:#20, #13:#21, #14:#22, #15:#23, #16:#24 Round 5B matchups (elimination bracket) #9:#16, #10:#15, #11:#14, #12:#13 Round 6 matchups (winners' bracket) #1:#4, #2:#3 Round 6A matchups (elimination bracket) #5:#9, #6:#10, #7:#11, #8:#12 Round 6B matchups (elimination bracket) #5:#8, #6:#7 Round 7 matchups (winners' bracket) #1:#2 Round 7A matchups (elimination bracket) #3:#5, #4:#6 Round 7B matchups (elimination bracket) #3:#4 Round 8 matchups (elimination bracket) #2:#3 Round #9 matchups (championship round) #1:#2 |
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