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Topic: 2007 World Championship Format (Read 5485 times) |
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Fritzlein
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2007 World Championship Format
« on: Aug 18th, 2006, 3:43pm » |
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If the World Championship begins in mid-November like last year, that's only three months away. If registration is going to open one month in advance, we have only two months for discussing the rules. 
Actually, I don't think much discussion is needed, because things worked quite well last year. Here are some features of Omar's format which I think worked very well:
* Participation open to everyone
* Registration fee refunded if all games played
* Floating double elimination
* One game per player per week, scheduled by ranking time slots
* 90 seconds per move, with 120 seconds per move when only 4 players remain
* Capturing all opposing rabbits is a win
I woud rather it were triple-elimination, but I can understand not wanting to lengthen the tournament.
In a different conversation Omar had raised the possibility of limiting the tournament to 16 participants on the basis of rating. I am deeply opposed to this idea, because ratings are greatly subject to manipulation. I am of the opinion that any adult of normal intelligence and no prior Arimaa knowledge could, between now and the World Championship, learn methods by rote for winning against certain bots, and achieve a 2500 rating. If this happens, fine, but nobody who hasn't studied bot-bashing in the same way should lose a seat in the World Championships because of it.
I also have two quibbles with the floating double-elimination algorithm of last year. First, repeat pairings need to be avoided with a higher priority than assigning a bye to the most deserving player. (The issue didn't arise in last year's World Championship, but did arise in the Computer Championship.) [EDIT]I'm wrong; it did arise in round six of the World Championship too.[/EDIT]
Second, the assignment of second and third place should not be by order of elimination. Rather it should be by number of wins. If people tie for number of wins, then they should keep playing elimination games to break the tie. For example, if the records of the players end up being
6-0
4-2
4-2
3-2
etc.
then the two 4-2 players should play an additional game to determine second and third place. If the records of the players end up
7-0
6-2
5-2
5-2
5-2
4-2
etc.
then the three 5-2 players should play elimination for third place. In general, playing additional elimination games seems preferable to me in comparision to a tiebreaking scheme based on things other than wins and losses.
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| « Last Edit: Sep 22nd, 2006, 5:37pm by Fritzlein » |
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Fritzlein
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Re: 2007 World Championship Format
« Reply #1 on: Aug 19th, 2006, 10:51am » |
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on Aug 18th, 2006, 3:43pm, Fritzlein wrote:| In a different conversation Omar had raised the possibility of limiting the tournament to 16 participants on the basis of rating. I am deeply opposed to this idea... |
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Oh, and I forgot to mention that adding new players doesn't lengthen the tournament much. Last year with 16 players it took eight rounds, and for up to 32 players it takes a maximum of nine rounds. One extra round seems a small price to pay for keeping the tournament open. (Actually, in my opinion, the more rounds the better. I'd like a 15-round World Championship. I know Omar feels otherwise. How does everyone else feel about the World Championship covering many weeks?)
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| « Last Edit: Aug 19th, 2006, 11:01am by Fritzlein » |
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PMertens
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Re: 2007 World Championship Format
« Reply #2 on: Aug 19th, 2006, 11:32am » |
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if 15 rounds means 2048 players than I think you are slightly optimistic about arimaa-popularity ...
(but I would like it)
Making rating a cutoff is not a wise idea since a certain number of top 16 players will not necessarily play.
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| « Last Edit: Aug 19th, 2006, 11:33am by PMertens » |
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Fritzlein
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Re: 2007 World Championship Format
« Reply #3 on: Aug 19th, 2006, 12:29pm » |
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on Aug 19th, 2006, 11:32am, PMertens wrote:if 15 rounds means 2048 players than I think you are slightly optimistic about arimaa-popularity ...
(but I would like it) |
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Hehe. If I'm not mistaken, 2048 players in floating double-elimination could theoretically go 16 rounds, although 15 rounds is more typical. But when I mentioned a longer tournament, I was thinking floating triple elimination.
If we have 24 players sign up for an open World Championship this year (and I don't think that's unrealistically optimistic), then I believe floating triple elimination will be done in thirteen rounds for sure, but with an average under twelve rounds. Yes, triple elimination would mean a larger probability that you would have an irreconcilble conflict on some week, but it also means you could more easily survive that forced loss that one week and go on to win the tournament, becuase you would still have two lives left rather than one. It's not like any of us can clear our schedules for nine weeks anyway, so a possible twelve-week commitment isn't going to force anyone out who would otherwise play, would it?
Who all is with me in wanting a twelve-round triple-elimination World Championship?
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seanick
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Re: 2007 World Championship Format
« Reply #4 on: Aug 19th, 2006, 12:29pm » |
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maybe I am dense but can you explain how the round system ends up taking x number of weeks? I don't think the actual number of people that can play will double with only one additional week, for instance.
obviously between 2 people it would take up to 3 weeks. 4 people would take.. at least 4 weeks but possibly up to 5?... etc.
-for triple elimination that might be worth thinking about. has it only been discussed (but never tried) thus far? or has it been used in the past?
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| « Last Edit: Aug 19th, 2006, 12:34pm by seanick » |
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Fritzlein
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Re: 2007 World Championship Format
« Reply #5 on: Aug 20th, 2006, 12:48am » |
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on Aug 19th, 2006, 12:29pm, seanick wrote:| maybe I am dense but can you explain how the round system ends up taking x number of weeks? |
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I don't have any formula; I just work it out by hand. The number of rounds for a given number of players varies depending on when and if the last undefeated player gets a loss. With floating double elimination and 2^N players I can work out all the cases, but I can't with weird numbers of players or triple elimination. Here are the floating double elimination rounds for 16 and 32 players:
| Rounds | No loss players | One loss players | | 0 | 16 | 0 | | 1 | 8 | 8 | | 2 | 4 | 8 | | 3 | 2 | 6 | | 4 | 1 | 4 | | 5 | 1 | 2 | | 6a | 1 | 1 | | 6b | 0 | 3 | | 7aa | 1 | 0 | | 7ab | 0 | 2 | | 7b | 0 | 2 | | 8ab | 0 | 1 | | 8b | 0 | 1 |
So with 16 players, it takes 7 or 8 rounds, depending only on whether the eventual champion is undefeated or not.
| Rounds | No loss players | One loss players | | 0 | 32 | 0 | | 1 | 16 | 16 | | 2 | 8 | 16 | | 3 | 4 | 12 | | 4 | 2 | 8 | | 5 | 1 | 5 | | 6a | 1 | 2 | | 6b | 0 | 4 | | 7a | 1 | 1 | | 7b | 0 | 2 | | 8aa | 1 | 0 | | 8ab | 0 | 2 | | 8b | 0 | 1 | | 9ab | 0 | 1 |
So with 32 players, it takes 8 or 9 rounds, but it no longer depends only on whether the eventual champion is undefeated or not, because now it can end in eight rounds with a one-loss champion.
Since 32 players takes exactly one more round than 16, one might suppose that each doubling of players adds one more round, but in fact it seems to add slightly more than one round per doubling in general. Perhaps the general formula includes a lg(N) term and a lg(lg(N)) term.
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| « Last Edit: Aug 20th, 2006, 1:20am by Fritzlein » |
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Fritzlein
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Re: 2007 World Championship Format
« Reply #6 on: Aug 20th, 2006, 8:59am » |
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I just noticed that a floating double elimination tournament with 2^N players will, after N rounds of play, have exactly one undefeated player and N players with one loss. This suggests that the formula for maximum number of rounds in a FDE tournament of X players is 2+lg(X)+lg(lg(X)). Given that lg(lg(X)) is so tiny, we essentially do get to double the number of players for each additional round we are willing to play.
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| « Last Edit: Aug 20th, 2006, 9:05am by Fritzlein » |
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seanick
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Re: 2007 World Championship Format
« Reply #7 on: Aug 22nd, 2006, 11:18am » |
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these are usually played at about one round a week, right? so 12 rounds is 3 months?
after that it starts to be kind of a long tournament.. having to go that long without, say, a 2 week vacation away from any computers. so there is some sense to keep it under 256 players.
hmm, one month is all that is necessary to square the number of people that could enter.
That in mind, I agree it seems not to make sense to limit the entries to the top 16 by rating.
(even though I think it will probably be one of the top 6 by rating that wins. its a few months away though so if nothing else those ratings might change by then... )
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PMertens
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Re: 2007 World Championship Format
« Reply #8 on: Aug 22nd, 2006, 1:24pm » |
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on Aug 22nd, 2006, 11:18am, seanick wrote:
(even though I think it will probably be one of the top 6 by rating that wins. its a few months away though so if nothing else those ratings might change by then... ) |
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at least it is not reduced to 2 titans like last year
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Fritzlein
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Re: 2007 World Championship Format
« Reply #9 on: Aug 22nd, 2006, 4:14pm » |
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on Aug 22nd, 2006, 1:24pm, PMertens wrote:| at least it is not reduced to 2 titans like last year |
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Yeah, we all know that last year only two people had a realistic chance of winning according to the ratings at that time. In fact, playing out the games last year was wasted motion, since everyone knew it was between me and 99of9.
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seanick
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Re: 2007 World Championship Format
« Reply #10 on: Aug 22nd, 2006, 10:55pm » |
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I would like to be wrong here, for sure. but I think you (by which I mean you collectively, those in the top 6) are slightly better prepared for new styles and paying more attention than last year. even so, the top 6 includes some serious talent. Sure, it might be someone ranked 17th or 18th or something (especially if they just barely make the cutoff should Omar decide top 16 by rating only, and a couple people don't enter thus leaving open spots for 17 and 18 to join...), but my gut tells me it will be someone in the top 6. maybe 8 if Jean comes back by then.
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robinson
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Re: 2007 World Championship Format
« Reply #11 on: Aug 23rd, 2006, 4:55am » |
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i want to argue for an open tournament, too
first i think it is a big motivation for newcomers, as it was for me when i first visited this site, to keep on playing here, knowing that evryone could take part and match up with the big ones.
and second i think it cant reduced to any count untill we have no clear rating system ( or maybe ratingsystem for only human games ) if someone havent time to play much bots to increase his rating, it wouldnt be fair not to allow him to play.
for the tournament i would prefer something were we have a clear final and maybe semi-final. so maybe we can play doubleelimination untill there are 4 players left and the best of 3 or something like this.
i havent liked last years situation that the game between me and adanac decided if paulM would be in the final...even though he got a second chance after it...
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Adanac
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Re: 2007 World Championship Format
« Reply #12 on: Aug 23rd, 2006, 7:09am » |
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on Aug 23rd, 2006, 4:55am, robinson wrote:i want to argue for an open tournament, too
first i think it is a big motivation for newcomers, as it was for me when i first visited this site, to keep on playing here, knowing that evryone could take part and match up with the big ones.
and second i think it cant reduced to any count untill we have no clear rating system ( or maybe ratingsystem for only human games ) if someone havent time to play much bots to increase his rating, it wouldnt be fair not to allow him to play.
for the tournament i would prefer something were we have a clear final and maybe semi-final. so maybe we can play doubleelimination untill there are 4 players left and the best of 3 or something like this.
i havent liked last years situation that the game between me and adanac decided if paulM would be in the final...even though he got a second chance after it... |
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I'd vote for an upper limit on the number of players such as 128, which would realistically allow all interested players to join every WC for the rest of the decade but will limit the field once we have hundreds or thousands of active Arimaa players. If Omar specifies is an upper limit maximum for the number of weeks, I would prefer a 128 double-elimination tournament rather than a triple-elimination with a smaller number of players.
And with 128 players, I think the prediction contest should be reserved for spectators only - but that's not an issue for the next few years. For now, I really enjoy player participation in both competitions 
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PMertens
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Re: 2007 World Championship Format
« Reply #13 on: Aug 27th, 2006, 11:59am » |
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I propose a randomized pairing instead of the folded pairing of last year.
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Fritzlein
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Re: 2007 World Championship Format
« Reply #14 on: Sep 10th, 2006, 4:10pm » |
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on Aug 27th, 2006, 11:59am, PMertens wrote:| I propose a randomized pairing instead of the folded pairing of last year. |
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I think you don't mean completely random pairings, do you? Certainly no one should have to face the same opponent twice if there is another pairing that prevents repeat matchups. Also, I quite like having winners play winners and losers play losers.
But if what you mean is simply ignoring the ratings for the purposes of pairing, I think it would be an interesting experiment. 99of9 once posted some axioms for pairing, including things like
* A higher rating never hurts you
* A lower rating never helps you
* The player with the highest true skill has the best chance of winning.
* etc. etc.
I note that if you completely ignore the ratings for the purposes of pairing, 99of9's axioms are satisfied. The player with the highest true skill still has the best chance of winning, and inflating your rating neither hurts nor helps you.
I expect some people will object to ignoring ratings for pairings, because failing to seed the tournament makes it less likely that best player will win. Maybe in a seeded tournament the #1-rated player has a 35% chance to win, and in an unseeded tournament has a 25% chance to win. The latter might still be higher than any other player's chance, but not as high as before. This goes against the principle of choosing a format with the highest possible chance of crowning the best player champion.
I see a tension between using ratings to help pick the best player, which is good, and inflating your own rating to increase your chance of winning the tournament, which is bad. We all know the ratings can be manipulated in several ways. If we put too much emphasis on the rating, then there is a huge incentive to protect one's rating and inflate it before the tournament by botbashing.
Maybe a better idea is this: instead of ignoring the ratings for the purposes of pairings, calculate seeding based on anti-human performance. For example, take every human's last 30 games against human opponents, calculate their performance rating based on those games, and seed the World Championship with those ratings.
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