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Topic: World Championship format for 2006 (Read 3074 times) |
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MrBrain
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Re: World Championship format for 2006
« Reply #15 on: Nov 3rd, 2005, 3:03pm » |
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Perhaps an e-mail should be sent to those registered on the site. I didn't realize registrations were going on until I happened to pop in right now.
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Fritzlein
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Re: World Championship format for 2006
« Reply #16 on: Nov 3rd, 2005, 3:57pm » |
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on Nov 3rd, 2005, 1:28am, Ryan_Cable wrote:I just registered for the tournament.  |
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Awesome! That makes 11 now, so we'll almost certainly beat last year in terms of the number of people who actually play a game. And we still have another week of registration, so it's conceivable we could even beat the participation of the inaugural World Championship.
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I will be on a cruise with my family from December 21 to December 28, which, if I did the math right, means I will not be available any of Week 6. Looking at the competition, I am confident this will be a moot point,  but I still think it is rather strange to have a tournament over Christmas vacation. Am I the only person who will have trouble playing around Christmas time? Has this not been a problem in the past?
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Last year the championship was decided on December 18th, and everyone except me and Belbo was finished the week before. We did play a showcase game on the 23rd, but it didn't matter to the outcome. The new format ensures there will be no irrelevant games, though, so holiday conflicts are more likely to be a problem this year.
Also there will be more rounds. By my rough calculation, an eleven-player FDE tournament takes six or seven rounds, and that number edges up for every additional participant. On the other hand, after five rounds it should be down to the last two players, so not everyone will be inconvenienced.
I find that the holidays make it easier for me to schedule a game. This partly because my family knows they come in second to Arimaa, and I would interrupt whatever I was doing with them to play in the WC. But even apart from that, my family activities aren't usually like work, with an uninterrupted 8-hour chunk that nixes any games. When I'm on vacation it actually seems easier to find 30 time slots that would work out, like on the 23rd last year when I was free the whole day. Then again, I wasn't on a cruise ship!
Anyway, you can still be World Champion. Just win your first five games, forfeit the sixth to let one player catch up, and come back for a dramatic seventh-round triumph!
Quote:It looks like my goal of 2 wins is going to be very challenging.  |
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No kidding. This is a killer tournament. I'm just hoping the number of participants is odd (and I can avoid losing all my rating points to 99of9 until it starts) so that I get a first-round bye: that's the only easy game anyone is going to get.
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Fritzlein
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Re: World Championship format for 2006
« Reply #17 on: Nov 3rd, 2005, 4:05pm » |
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on Nov 3rd, 2005, 3:03pm, MrBrain wrote:| Perhaps an e-mail should be sent to those registered on the site. I didn't realize registrations were going on until I happened to pop in right now. |
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Ahh, but you mean to say you still aren't registered, even though you do realize now?  Seriously, although your deflated rating means you would get terrible pairings, it still would be your best shot at some slow games. Plus it is free.
Anyway, I think Omar did send out an e-mail to everyone when the registration opened, but that was long enough ago that a second mailing wouldn't be out of order. (Omar, are you philosophically opposed to mailing more than once per event?) In a current e-mail we could mention that eleven people have already signed up: It might inspire a few more folks to jump on the bandwagon if they knew it wasn't just a tiny club of guys playing.
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RonWeasley
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Harry's friend (Arimaa player #441)
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Re: World Championship format for 2006
« Reply #18 on: Nov 4th, 2005, 8:05am » |
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One unspoken subtext here is that everybody hopes Arimanator and blue_22 can play. Their experience and diversity of style make them icons in this community. Yes, there are good reasons for other players to enter, but from a spectator's point of view, these two belong with the other top players.
Unfortunately I can't schedule time to play this one. For the usual lame reasons. What I really need is a supply of Felix Felicis potion. Then I'd be lucky enough to get time to play. See you all in the postals!
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Fritzlein
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Arimaa player #706
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Re: World Championship format for 2006
« Reply #19 on: Nov 4th, 2005, 12:19pm » |
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on Nov 3rd, 2005, 4:05pm, Fritzlein wrote:
Ahh, but you mean to say you still aren't registered, even though you do realize now? |
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Mr. Brain is in! We're up to twelve! This tournament just keeps getting better...
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Fritzlein
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Re: World Championship format for 2006
« Reply #20 on: Nov 10th, 2005, 9:55am » |
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There are a couple of days left to register, so I am still hopeful more people will sign up, but if we end up playing with exactly twelve participants, the byes will be somewhat predictable.
| Round | No losses | One loss | Two losses | | 1 | 6 | 6 | 0 | | 2 | 3 | 6 | 3 | | 3 | 2 | 4 | 6 | | 4 | 1 | 3 | 8 | | 5A | 0 | 3 | 9 | | 5B | 1 | 1 | 10 |
There will be no byes the first two rounds. Going into the third round, there will be three players with two wins and no losses; the highest rated of these will get a bye. There will be no byes the fourth and fifth rounds.
Going into the sixth round there two possibilities
(A) There are three players left, each with one loss. The bye goes to the highest-rated player, unless he was the one who got the third-round bye, in which case the bye goes to the next highest-rated played who is left. The player with the bye plays the winner of the other two for the championship.
(B) There is one undefeated player left, and one player with one loss. There will be no more byes, because only two players remain. The undefeated player needs to win once for the championship, while the other player needs to win twice in a row.
To summarize, anyone who wins six games is the World Champion, no matter where they are seeded and no matter which round they lose in, as long as they don't lose twice. Either one or two players will get a bye and thus have a chance to win with only five victories. The byes are based partly on the tournament itself rather than purely on seeding: you have be winning to get a bye.
The whole tournament structure is more fair than traditional double-elimination with 12 players, where the top four seeds get a first-round bye and only need to win four times to become champion through the winners' bracket, but someone who isn't in the top four seeds and who loses the first round must win seven times to become champion through the loser's bracket.
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99of9
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Re: World Championship format for 2006
« Reply #21 on: Nov 10th, 2005, 9:56pm » |
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That seems a fairly good structure for 12 players. Now I just have to hope that someone can beat you in the first two rounds to give me a week off if I make it through myself. Go Mr Brain!
Omar I have a request for the prediction contest. I remember last time it was a little frustrating having 5% increments on the prediction choices. Especially near 0% and near 100%, 1% starts to matter a lot. I wonder if all integers between 90% and 100% could be included in the choices? (I'd be even happier with all integers between 50% and 100%, but I realise the way you set it up is not really compatible with this, because we didn't type a number in, we selected from a list.)
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| « Last Edit: Nov 10th, 2005, 9:57pm by 99of9 » |
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Fritzlein
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Re: World Championship format for 2006
« Reply #22 on: Nov 11th, 2005, 6:28pm » |
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I see grey_0x2A is in. Awesome! Not only do we have 13 registered, but I think this ensures us 14, since Paul said he would register if necessary to make it an even number. Either someone else will register, or Paul will step up to make sure there is no first-round bye. And if all 14 play, it will be the biggest World Championship ever as well as the best ever. Yay!
It is much harder to work out the byes with 14 players than it was with 12, because in the second round someone who is 1-0 will play someone who is 0-1. Thus we can't tell in advance whether there will be three or four eliminations in round two.
After three rounds, however, there will have been exactly seven eliminations, so a bye is certain in round four.
| Round | No losses | One loss | Two losses | | 1 | 7 | 7 | 0 | | 2A | 3 | 8 | 3 | | 2B | 4 | 6 | 4 | | 3 | 2 | 5 | 7 | | 4A | 1 | 4 | 9 | | 4B | 2 | 2 | 10 | | 5Aa | 0 | 4 | 10 | | 5Ab | 1 | 2 | 11 | | 5B | 1 | 2 | 11 |
By round 5 there are several possibilities, some involving a bye and some not. The tournament can no longer finish in 6 rounds, as was formerly possible; now it will take 7 or 8. By my best guesstimate, it seems possible for there to be only one bye awarded, but also possible for as many as five to be awarded, one each in rounds 3, 4, 5, 6, and 7.
I don't think five wins can win this tournament any more, even for a player who gets a bye; six wins now seem necessary. (But maybe it is possible that if many byes are awarded that one player will get two byes, so in that case five wins could be enough after all.) I don't think anyone could be required to win seven times for the trophy, because the tournament can't go eight rounds without the eventual champion getting a bye some time. If that calculation is correct, then one thing hasn't changed from the 12-player format: If you win six times you are Champion of the World!
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Ryan_Cable
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Re: World Championship format for 2006
« Reply #23 on: Nov 12th, 2005, 4:05am » |
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I think registration ends in less than 24 hours. Maybe someone should send Paul an email letting him know we have an odd number of players.
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PMertens
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Re: World Championship format for 2006
« Reply #24 on: Nov 12th, 2005, 4:58am » |
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did I call this "very small" ?? 
now thats going to be a lot of fun ...
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Fritzlein
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Re: World Championship format for 2006
« Reply #25 on: Nov 12th, 2005, 7:53am » |
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on Nov 12th, 2005, 4:58am, PMertens wrote:| now thats going to be a lot of fun ... |
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You can say that again. Acheron has signed up, so now we are 14. If we get #15 in the next few hours, we presumably get Paul to make 16!
I just noticed a potential problem: Acheron and MrBrain have the same rating. In that case, which one gets seeded higher? Who is the tournament director for resolving such issues? If it were up to me, I would clarify the pairing rules to say, after the "further ties broken by pre-tournament rating" to say "still further ties broken randomly".
Also, I have another regret about the pairing rules. In the second round there will be seven 1-0 players. Six of them will play each other in three pairs. The seventh will have to play someone who is 0-1. The way the rules are now, the 1-0 player is paired with the lowest rated 0-1 player. I feel this is not in keeping with the spirit of the pairing. If you can't play someone whose record is as good as yours, you should have to play the highest-rated player with a worse record.
Oh, well, the format is obviously experimental, and this year's experience can be used to make things run more smoothly next year.
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Ryan_Cable
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Re: World Championship format for 2006
« Reply #26 on: Nov 12th, 2005, 7:14pm » |
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The situation where both the undefeated and single loss groups are odd does seem to be in need of a fix for next year. If I understand it correctly, for the 14 player case, in the second round, the fourth ranked winner would play the last ranked looser. This is very harsh for the looser, but the part that is most out of touch with the spirit of the tournament is that the fourth ranked winner gets a weaker opponent than the top three winners. For the 15 player case it is the fifth ranked player who gets this lucky pairing.
I only see two ways to avoid this: To pair highest ranked undefeated player that does not have a bye with lowest ranked single looser, which almost certainly dooms the last ranked player to a crushing defeat, or to give byes to the undefeated player that does not already have a bye and to the top ranked single looser, making it possible for a single round to have 3 byes.
I think solution 1, though harsh, is probably best. I believe the two goals of this format are to give the best chance of picking the player with the top true rating within a limited number of rounds and to never penalize a player for having a higher rating. Solution 1 meets both of these goals, but solution 2 is likely to add rounds to the tournament. Letting one of the undefeated players play the top ranked looser is clearly wrong, because the top ranked looser is heavily penalized over the second ranked looser who would get to play the lowest ranked looser.
Another problem for the 15 player case is that the top ranked player gets the least useful bye. In round one, seed 1 gets a bye and seed 2 gets to play seed 15. In round two, seed 2 gets a bye (assuming there is not an amazing upset) and seed 1 has to play the lowest ranked winner (roughly seed 8). In the third round, if seed 3 has managed to defeat seed 14 and the second lowest ranked winner (roughly seed 7) and if four players were eliminated after round two as is most likely, seed 3 would get a powerful bye.
One way to solve both of these problems is if we added fictional players to the end of the rankings to pad the seeding up to 2^n. These fictional players would always loose to higher ranked players whether real or fictional. If we have 2^n- x players (where x<2^(n-1)), in round one the top x players would get effective byes, and all of the fictional players would get 0-1 records. After round one, only players with a single defeat will have the opportunity to play a fictional player. The number of undefeated players would always be a power of 2 so the only time it might be necessary to give a true bye is when there is one or fewer undefeated players left. This solution is likely to add at least one round to the tournament.
A simpler (and I think better) way to solve the problem is to assign byes to the player with the most defeats that is still in the tournament, with ties broken in favor of the person who lost in the latest round, with ties broken in favor of highest pre-tournament ranking. This top ranked looser is still in worse shape than anyone in the undefeated bracket, since they can choose to take a week off by forfeiting and still end up in the same place as the looser who received a bye, or if they (wisely) play their game, they have the chance to stay in the undefeated bracket. Since there is almost always someone falling down into the single looser group, the people getting the later byes (which are likely to be more useful), will almost always have better performances and/or higher ratings than those getting the earlier byes. It would still be necessary to find a fix for the case where there is an odd number of undefeated players, but I think solution 1 from above would still work.
After we see how the tournament works out, we will have a year to consider all sorts of changes.
PS Paul and BlackKnight have registered, giving us 16 players and making much of this moot unless someone else signs up.
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Fritzlein
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Re: World Championship format for 2006
« Reply #27 on: Nov 12th, 2005, 7:52pm » |
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Sixteen! Fantastic!
| Round | No losses | One loss | Two losses | | 1 | 8 | 8 | 0 | | 2 | 4 | 8 | 4 | | 3 | 2 | 6 | 8 | | 4 | 1 | 4 | 11 | | 5 | 1 | 2 | 13 | | 6A | 0 | 3 | 13 | | 6B | 1 | 1 | 13 |
If noboby signs up to make it seventeen participants or more, then the bye picture is much clearer: Noboby gets a bye until round 5, and the person who gets it then will have entirely earned it by being the only undefeated player left. Anyone can get the bye by winning the first four games.
In round 6 the higher-ranked of the two in the loser's bracket gets the bye, while the lower-ranked has the sad task of playing the lone remaining undefeated. However, if the lower-ranked fellow does manage to win, he is rewarded with a bye in round 7, and will play the winner of the round 7 game for all the marbles in round 8.
If one player goes undefeated, he will win in seven rounds with the two byes in the tournament going to him and the second-place finisher. If nobody goes undefeated, the tournament will last eight rounds, and will end with byes awarded to either the top two or the top three finishers.
Ryan, I did consider that early-round byes are less useful than late-round byes. However, I still believe the first bye should go to the highest eligible person for several reasons:
(1) Often, there is no guarantee that anyone else will get a bye. It would be slightly strange if a few lower-ranked players got a bye and the top player never did, forcing him to work harder to win in spite of having the higher seed.
(2) Sometimes it will work out so that all remaining players have received a bye, and a second bye must be awarded to someone. The best performer should have the first shot at the second bye.
(3) Although a late-round bye is more useful, it's a handicap to have to win an extra game to become eligible for it. For example in the sixteen-player tournament, the top performer gets the "least useful" bye in round 5, while two other players are getting knocked out without having had a chance at a bye. It's true that the bye which goes to the second-best performer in round 6 is nicer, but the player who got it presumably had about a 50% chance of getting knocked out in round 5. And the third bye in round seven is clearly the "most useful" bye, since one of the top two players will be eliminating the other in the meantime, but presumably the player who got the round 7 bye had about a 75% chance of being eliminated in round 5 or 6 without ever having had a bye.
Well, I would need to see how it works out in practice in a lot of different situations, but in general a bye in the hand seems more valuable than a potential bye later on.
As far as the pairings within the rounds, I agree that there are issues when the number of players is each bracket odd. I wanted something algorithmic and simple, but sometimes there will exist alternate pairings more in the spirit of the tourney than the ones produced by the algorithm. Therefore, while I'm not sure there is a better way of assigning byes, I wouldn't be at all surprised to find a better pairing algorithm.
P.S. Unless I am mistaken, the sixteen-player tournament is precisely egalitarian in the sense that for every player six wins are necessary to become champion, and for every player six wins are sufficient to become chapmion. The assignment of byes no longer affects the requirements: Win six games before losing two.
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| « Last Edit: Nov 12th, 2005, 7:54pm by Fritzlein » |
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Ryan_Cable
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Re: World Championship format for 2006
« Reply #28 on: Nov 12th, 2005, 11:37pm » |
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on Nov 12th, 2005, 7:52pm, Fritzlein wrote:
Well, I would need to see how it works out in practice in a lot of different situations, but in general a bye in the hand seems more valuable than a potential bye later on. |
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I think it depends on the situation. A fourth or fifth round bye in the hand is probably worth more than a later bye in the bush, but a first round bye is clearly worth less than a second or third round bye in the bush with a rating distribution like the one in this tournament. One possibility is to give byes under the current system and allow players to decline a bye to maintain their bye eligibility for later rounds. This might give too much of an advantage to the top seed though.
on Nov 12th, 2005, 7:52pm, Fritzlein wrote:
As far as the pairings within the rounds, I agree that there are issues when the number of players is each bracket odd. I wanted something algorithmic and simple, but sometimes there will exist alternate pairings more in the spirit of the tourney than the ones produced by the algorithm. Therefore, while I'm not sure there is a better way of assigning byes, I wouldn't be at all surprised to find a better pairing algorithm. |
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I agree; the pairing is the more important thing to fix.
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omar
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Re: World Championship format for 2006
« Reply #29 on: Nov 15th, 2005, 5:05pm » |
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on Nov 10th, 2005, 9:56pm, 99of9 wrote:That seems a fairly good structure for 12 players. Now I just have to hope that someone can beat you in the first two rounds to give me a week off if I make it through myself. Go Mr Brain!
Omar I have a request for the prediction contest. I remember last time it was a little frustrating having 5% increments on the prediction choices. Especially near 0% and near 100%, 1% starts to matter a lot. I wonder if all integers between 90% and 100% could be included in the choices? (I'd be even happier with all integers between 50% and 100%, but I realise the way you set it up is not really compatible with this, because we didn't type a number in, we selected from a list.) |
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Sorry Toby, I didn't see your request in time. I'll see if it seems easy enough I'll change it, otherwise I don't want to risk breaking the system now that it's being used.
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