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Fritzlein
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Re: 2013 World Championship Format
« Reply #105 on: Apr 28th, 2012, 5:52pm »
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Thanks Omar.   On the second try the two 11-digit codes were accepted.  There was no indication of duplicate account creation to get more votes.  That gives us 42 completed surveys with a valid code.  What an amazing response from the Arimaa community!  If the enthusiastic participation in the survey is any guide, we are going to get plenty of volunteers to make the tournament a reality.
 
Three of the questions were not about tournament preferences, but about the respondent.  Those are “filter questions” that can be used to see if different subgroups responded differently.
 
Quote:
If the actual structure of the tournament were close to your preferred structure, how likely would you be to participate as a player?

90% - 100%  14      
75% - 90%    8      
50% - 75%    9      
25% - 50%    7      
0% - 25%     3
No answer    1
 
I will split this between the 22 who said they were more than 75% likely to play and the 20 others.
 
Quote:
How many Arimaa World Championships have you participated in?

None  28
One    4
Two    4
Three or more  6
 
I will split this between the 14 who have played in a World Championship before and the 28 who haven't.
 
Quote:
Approximately what is your Arimaa rating?

under 1600  13
1600-1800    8
1800-2000    9
2000-2200    9
over 2200    3
 
I will split this between the 21 over 1800 and the 21 under 1800.
 
Quote:
The 2013 Arimaa World Championship will be played at the pace of one round per week. A player who has lost three games can no longer become World Champion. Given this information, how many games would you like to play?

I would like to stop playing as soon as I have lost three games      18
I would like to play six games guaranteed      16
I would like to play seven games guaranteed      1
I would like to play eight games guaranteed      2
I would like to play nine games guaranteed      1
I would like to play ten or more games guaranteed      3
No answer      1
 
It was close between a desire to have a consolation bracket or not.  A majority wanted to keep on playing, and of those, most only wanted six games.
 
participation: 61% of likely players wanted guaranteed games.
experience: 50% of experienced players wanted three and out.
rating: 50% of high-rated players wanted three and out.
 
What we decide on this one is critical to my motivation.  Given my personal goal of maximizing participation, and given that the respondents most in favor of three-and out were less likely to be playing, I will unilaterally decide that the 2013 World Championship will have six guaranteed rounds.  There was no consensus anyway; a decision must be made for us to progress, so I will make the decision that I personally think is best for the Arimaa Community.
 
Quote:
Would you like the tournament to have rest weeks in the middle?

No rest weeks      20
One rest week      19
Two or more rest weeks      2
No answer      1
 
There was an even split between wanting a rest week or not.
 
participation: 56% of likely players wanted no rest week
experience: 71% of experienced players wanted no rest week
rating: 65% of higher-rated players wanted no rest week
 
The skew of the more critical groups was against having rest weeks, so I'm pretty sure we don't want a rest week during the first six rounds.  I am, however, still open to having a rest week between the six guaranteed rounds and the remaining elimination rounds.
 
Quote:
Would you prefer a qualifying tournament followed by a elite final, with losses from qualifying forgiven before the final, or a unified tournament in which losses from any round count equally?

Qualifying / Final  23
Unified Tournament  17
No Answer    .    .  2
 
A majority preferred the split format with loss forgiveness.
 
participation: 52% of likely players wanted a split format
experience: 71% of experienced players wanted a unified format
rating: 50% of high-rated players wanted a unified format
 
When we look at the more critical groups, the majority for a split format disappears.  Indeed, among the players who know best what it is like to play in a split format, the support for a unified format is strongest.
 
Therefore I am still torn between re-creating the success of 2011 with exactly the same format (6-round Swiss Open Classic followed by top-eight finals) and making the small experiment of a 6-round Swiss Divider, where Round 7 and onward let the eliminated players go home, but preserve the early-round losses to eliminate all edge effects and all incentives for intentional losses.  The latter is my personal preference, but perhaps there is some benefit in having a format that the hoi-polloi can understand?  But no, I think people will love Swiss Divider once they no what it is.  It is not hard to understand; just unfamiliar.  I think the experiment is small enough and the potential gain great enough that we try it out at least once.  Also it shortens the tournament by about one round, and nobody likes a long tournament (see below).
 
Quote:
Which time control would you prefer for the fastest games of the tournament?

45 seconds per move   9
60 seconds per move  22
90 seconds per move   7
120 seconds per move  2
No Answer    .    .   2
 
The clear preference is for 60 seconds/move to be the fast time control.
 
participation: 69% of likely players chose 60 seconds.
experience: only 50% of experenced players chose 60 seconds; still the median choice
rating: 67% of likely players chose 60 seconds.
 
This decision is a slam dunk.
 
Quote:
Which time control would you prefer for the slowest games of the tournament (i.e. the deciding games among top players)?

45 seconds per move    1
60 seconds per move    4
90 seconds per move   15
120 seconds per move  21
No Answer    .    .    1
 
A teensy majority wanted 120 seconds per move for the final games.  An obvious compromise is to switch from 60 seconds to 90 after six rounds, and then to 120 seconds when only a small number of players (three?) remain.  Or we could just stick with the 60/90 division that has worked well in the past.
 
participation: similar distribution
experience: fewer experienced players wanted 120 seconds; more wanted 90.
rating: fewer high-rated players wanted 120 seconds; more wanted 90.
 
Quote:
The tournament will be run by volunteers who take care of pairings, scheduling, trouble-shooting, and refereeing games. Additionally there might be live audio commentary, recordings of commentary, written game summaries, fundraising to increase prizes, promotion to increase the audience, and so on. It is likely that not all extra roles will be filled if we rely purely on volunteers. Would you support some of your entry fee compensating volunteers so that the tournament will likely have more extra features?

I would like my entire entry fee to be distributed as prizes. (Volunteers would not be compensated at all.)      4
I would like my entry fee split between prizes and compensating volunteers for extra features.      31
I would like my entire entry fee to compensate volunteers. (The prize fund would come from donors and sponsors.)      5
No answer 2
 
The overwhelming consensus is to split entry fees between prizes and compensation.  Not too surprising, since this is what every chess tournament does, every poker tournament does, etc.  This is another slam-dunk decision.
 
participation: Likely players were more polarized; unlikely players universally wanted a split.
experience: similar distribution
rating: similar distribution
 
Quote:
Which prize payout structure (in order of player finish) is closest to your preference?

50-30-20      9
40-20-15-10-7-5-3      14
30-15-10-8-6-5-4-4-3-3-3-3-2-2-2      5
Prize fund divided proportional to number of wins; everyone who wins a game gets something.      12
No answer      2
 
This one doesn't seem to have a clear consensus or even a good compromise.  We'll have to think more about prizes distribution.
 
participation: 46% of likely players picked the second option.
experience: 50% of experienced players picked the second option.
rating: similar distribution
 
Quote:
Please rank in order which of these would make you most likely to participate as a player:

It is hard to present complete data on this one, so I present only averages.
 
2.78 Low entry fee
2.85 Good chance of playing opponents near my level
4.02 My preferred time control
4.02 Good chance of playing opponents higher than my level
4.39 My preferred tournament length
4.44 Good chance of my games being commentated
5.22 Large prize fund
 
Low entry fee and evenly matched games dominated people's concerns, while a desire to be commentated and have a large prize fund brought up the rear.  This is consistent with the consensus that was developing in the thread pre-survey.
 
participation: Likely participants ranked near opponents #1, low entry fee #2, otherwise similar.
experience: Experienced players rated all factors nearly equal, except for a large prize fund still being least important.
rating: similar distribution
 
Quote:
Supposing you could not participate as a player, please rank in order which of these would create the World Championship tournament you would like to become a reality.

1.83 All top-level players participating
2.85 A large number of players participating
2.86 Much live commentary
3.24 Many games evenly-matched
3.52 Much permanently saved commentary
4.85 A long tournament
 
Few spectators care for a long tournament, but almost all spectators want all the top players to participate.  Live commentary beat out saved commentary, and large participation beat out even games.  Contrasted to the previous question, it is clear people want different things as players than they want as spectators.
 
participation: similar distribution
experience: similar distribution
rating: similar distribution
« Last Edit: Apr 28th, 2012, 6:02pm by Fritzlein » IP Logged

Thiagor
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Re: 2013 World Championship Format
« Reply #106 on: Apr 29th, 2012, 2:12am »
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Interesting results! Thanks for carrying out and evaluating the survey. Let me mention two additional thoughts that just came to my mind:  
 
Firstly, on the question about Qualifying & Final vs Unified Tournament, I don't have a strong opinion as a participant or spectator. However from the point of view of encouraging participation, I guess the format of 2011 might give additional motivation: As many players don't have any serious hope to win the tournament, they can stick to the more modest goal to make it into the finals, which is still a big achievement.
 
Secondly, concerning the distribution of prize money: As Fritzlein decided to guarantee each player at least six games, I would prefer a distribution that gives an incentive to win even after having lost three times. That would mean either the distribution proportional to the number of wins, or (my personal preference) a distribution proportional to 1/n^2 (or a similar function), where n is the place in the position table.
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browni3141
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Re: 2013 World Championship Format
« Reply #107 on: Apr 29th, 2012, 1:41pm »
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on Apr 29th, 2012, 2:12am, Thiagor wrote:
a distribution proportional to 1/n^2 (or a similar function), where n is the place in the position table.

I like this idea very much. It seems to fit my opinion of what prize distribution should be like.
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Re: 2013 World Championship Format
« Reply #108 on: Apr 30th, 2012, 6:15am »
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It seems to me that taking the current unified FTE format and adding second- and third-place consolation brackets to it would satisfactorily address several issues at once in a relatively simple fashion: No arbitrary choice of what tiebreakers to pick to determine these places and in what order, and everyone would be guaranteed of playing at least five games.
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omar
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Re: 2013 World Championship Format
« Reply #109 on: May 4th, 2012, 8:57pm »
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Thanks for running this survey and analyzing the results Karl.
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Fritzlein
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Re: 2013 World Championship Format
« Reply #110 on: May 5th, 2012, 9:26am »
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on Apr 29th, 2012, 2:12am, Thiagor wrote:
Secondly, concerning the distribution of prize money: As Fritzlein decided to guarantee each player at least six games, I would prefer a distribution that gives an incentive to win even after having lost three times. That would mean either the distribution proportional to the number of wins, or (my personal preference) a distribution proportional to 1/n^2 (or a similar function), where n is the place in the position table.

 
on Apr 29th, 2012, 1:41pm, browni3141 wrote:
I like this idea very much. It seems to fit my opinion of what prize distribution should be like.

You two make me regret not including this option in the poll, especially since it was suggested earlier in the discussion.  I initially thought the 1/n^2 distribution was plausible, but when I tried it out myself I found it too steep at the top for my liking.  Then I imposed this conclusion on the group by leaving it out of the poll.  So let me remedy the situation and re-open the possibility here.
 
For 2012, the 1/n^2 distribution would have been as follows:
 
hanzack  $734.32  
chessandgo  $183.58  
Adanac  $81.59  
Nombril  $45.90  
Fritzlein  $29.37  
Tuks  $20.40  
rabbits  $14.99  
ocmiente  $11.47  
Harren  $9.07  
Simon  $7.34  
woh  $6.07  
 
It seems strange to me that chessandgo would have gotten only 1/4 the money hanzack did, and also strange that Adanac would make it to the podium and barely get back his entry fee.  Take nothing away from hanzack's great performance, but he would have walked away with 64% of the prize money.  If there had been more participants it would have been approximately 61-15-7-4 at the top.
 
For comparison, see the prizes for the 2012 Masters golf tournament:
http://www.augusta.com/masters/story/blog/2012-masters-tournament-prize- money
 
That looks an awfully lot like 1/n distribution.  Given the $8M total fund, the top players received a 18-11-7-5-4 payout.  This is more in line with my idea of fairness.  But I certainly don't want to cut off discussion.  Please discuss further if giving over 3/5 of the money to first place seems most appropriate to you.
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Re: 2013 World Championship Format
« Reply #111 on: May 5th, 2012, 10:25am »
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on Apr 30th, 2012, 6:15am, aaaa wrote:
It seems to me that taking the current unified FTE format and adding second- and third-place consolation brackets to it would satisfactorily address several issues at once in a relatively simple fashion: No arbitrary choice of what tiebreakers to pick to determine these places and in what order, and everyone would be guaranteed of playing at least five games.

If I understand what you are proposing, it is like quintuple elimination except that players with four losses can only play each other (they are only eligible for 3rd place), and players with three losses can only play each other (they are still eligible for 2nd place, but if they lose they would drop down to join the 3rd place bracket).  Let me try to get my head around the consequences.
 
* Clearly, everyone would get to play at least five games, which I like.  (Actually, I would like at least 10 games guaranteed Smiley, but of the choices I provided in the poll, 6 games guaranteed was the median choice.)
 
* Everyone who was not eliminated would still be playing for something, albeit not for the championship.  I like this as well.
 
* One difference from a full floating-quintuple elimination would be a shorter tournament for the winner.  The World Champion wouldn't have to keep playing until all his opponents had five losses.  He would already be on the sideline with his crown while the other players squabbled for the lower places.
 
* In past tournaments, the tiebreaker for 3rd/4th has been concurrent with 1st/2nd still playing, while the tiebreaker for 2nd/3rd happened the week after the champion was determined.  In your proposal, however, it seems the third-place bracket would go on for about four weeks after the champion was determined, assuming 64 participants.  It would have to go on for at least two additional weeks for the person who lost to the champion to get his two extra losses, but would generally go even longer due to the greater number of people in the lowest bracket.  If the World Championship went on for a month after the champion was determined, it would be weird.
 
* I can imagine a scenario in which a moderately good player (but not a true contender) gets knocked into the third-place bracket fairly early in the tournament, and then wins through to third place without ever having to play the two people who end up in first and second place.  Meanwhile the person who ends up in fourth place might have ended up playing (and losing to) the top two players in a total of three or four games.  The dividers would make cross-group pairings impossible, whereas in a unified tournament avoiding cross-group pairings is a lower priority than avoiding repeat pairings.  In a unified tournament that moderately good player staying alive with early losses is eventually forced to play the top players.
 
* The division into brackets could cause byes to be unevenly distributed.  This would be fine if the higher bracket gave out a bye while the lower bracket didn't, but it seems the reverse could also happen.  Currently, if the last player knocked out of the top bracket has one more win than any other eliminated player, we call them 2nd place with no tiebreaker.  Under your proposal, it would seem routinely possible for them to then lose in the consolation bracket, ending with an equal number of wins as the player your proposal would crown 2nd place, which seems weird.  But weirder still would be a scheduling quirk under which the last eliminated player would have two more wins than the player he meets in the 2nd-place bracket, due to uneven assignment of byes.  That player could then get knocked down to third with a single loss, while still having one more win than the player walking away with second place.
 
* In addition to balancing byes, we seem to be generally tweaking the format to compensate easy pairings in earlier rounds with tougher pairings in later rounds, and vice versa.  Dividing the tournament into a main bracket and consolation brackets prevents any even-out mechanisms from working.
 
Obviously I am still just brainstorming about this format, so I am probably not seeing exactly how it would work.  My first impression, however, is that if we want everyone to keep playing until they have lost five, it would be better to have a unified quintuple elimination with no dividers.  My fundamental intuition is that number of wins is a better way to determine second place than a playoff/consolation system that might give the prize to someone with only an equal number of wins or (gasp) even someone with one win fewer.
 
Contrariwise, if we simply want to guarantee everyone a certain number of games, it would be better to have only one divider, and that between players who have something to play for and players who are just playing for fun.  Then everyone still playing for the podium would be in a unified group where the pairing algorithm was able to balance things out as well as possible, including by forcing pairings which haven't happened yet.
 
The past system of ranking by number of wins satisfied my intuition of fairness.  Unfortunately, even in a unified format, the number of byes given out may be unequal by one, so we require a small kludge: a playoff game when when eliminated players have the same number of wins.    It seems like a small kludge, though, whereas expanding the playoff into a tournament-long consolation bracket seems to expand the kludginess.
 
This is just my first impression; I welcome further discussion.
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Re: 2013 World Championship Format
« Reply #112 on: May 5th, 2012, 1:33pm »
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Perhaps I am missing some subtleties, but a single elimination winners bracket with a consolation bracket for eliminated players is common in Go. You run the consolation bracket so that the players who are knocked out of the original tournament later effectively have byes in the consolation tournament. See this page for an example:http://hiddema.nl/L19.html  
 
I'm not sure it's possible to merge that with floating elimination or it solves all the problems, but if possible, I think it may address some of your concerns, Fritzlein.
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Re: 2013 World Championship Format
« Reply #113 on: May 5th, 2012, 2:46pm »
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on May 5th, 2012, 9:26am, Fritzlein wrote:

I initially thought the 1/n^2 distribution was plausible, but when I tried it out myself I found it too steep at the top for my liking.  

 
Ok, I must admit that I hadn't really thought about this steep descend at the top. However, if people think this distribution is otherwise fine, we could just fix it an ad-hoc way, e.g. use 1/(n+1)^2 instead.
 
Another suggestion: Has anyone already thought about combining different distributions? For instance, we could award half of the total prize fund to the top 3 finishers (say 50-30-20), while the other half is given to all players, proportional to their number of wins. This would also, in some sense at least, give justice to the survey results Wink
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Re: 2013 World Championship Format
« Reply #114 on: May 5th, 2012, 4:41pm »
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on May 5th, 2012, 1:33pm, hyperpape wrote:
Perhaps I am missing some subtleties, but a single elimination winners bracket with a consolation bracket for eliminated players is common in Go. You run the consolation bracket so that the players who are knocked out of the original tournament later effectively have byes in the consolation tournament. See this page for an example:http://hiddema.nl/L19.html  
 
I'm not sure it's possible to merge that with floating elimination or it solves all the problems, but if possible, I think it may address some of your concerns, Fritzlein.

If the Arimaa World Championship were single-elimination, there would be no difficulties, and no need for fancy formats.  First place and second place would be obvious: the winner and loser of the last game, respectively.  And, as is common in single-elimination tournaments, the two losers of the second-to-last round would play each other for third place.  If other losers wanted to play each other for fun, that would be fine too.
 
The subtleties start to arise when someone is still in contention after losing a game.  In double-elimination tournaments, anyone with one loss is not playing in a "consolation bracket"; they are still playing for the title.  Brackets like the one you linked are common (at least in the United States) with the addition that the winner of the losers' bracket gets to play the winner of the winners' bracket, and can at that point claim the title with two consecutive wins.
 
The typical fixed bracket for a double-elimination tournament is straightforward.  Say after one round there are 32 winners and 32 losers.  Each group plays internally leaving 16 WW players, 16 WL players, 16 LW players, and 16 LL (eliminated) players.  As you note, the second-round losers can be neatly paired with the first-round losers, after which there remain 16 in the winners' bracket and 16 in the losers' bracket.
 
However, everyone in the loser's bracket has now played three games instead of only two.  Suppose that someone who lost in the first round wins every game from then on.  By the time only one winner remains, his score line will be WWWWWW.  The first-round loser, however, will have a score line of LWWWWWWWWWW, having had to win ten games for the privilege of trying to win two more against top player.  I saw something nearly this ridiculous happen in a pool (pocket billiards) tournament once, and it was obviously unjust; the player from the losers' bracket was exhausted by the time he won through, while his opponent from the winners' bracket was still fresh.
 
This injustice was exactly what prodded me to propose a floating (as opposed to fixed-bracket) double-elimination tournament for the Arimaa World Championship.  If I beat you in the first round, the number of wins you need to become champion should be one more than the number of wins I need to become champion.  That's fair (isn't it?) because I have only one more win than you so far.  This fairness criterion is what a floating elimination tournament achieves.  Yet in a 64-player fixed-bracket double-elimination, a first-round winner needs six more wins for the title while a first-round loser needs twelve more, which is twice as many, not one more.
 
Let me stress again that fairness concerns like this one only apply when losers are still in contention for the title.  If there is a consolation bracket purely for the losers to have fun in, then fairness is unimportant and what matters most is pairing evenly-matched games, because evenly-matched games are the most fun.
 
What aaaa was proposing (if I read it correctly) was a triple-elimination tournament with an additional 3-loss and 4-loss bracket to determine 2nd and 3rd place respectively.  My thought is that for the purpose of determining order of finish, this is a strictly worse system than having a quintuple-elimination tournament from the get-go, because everyone who is not eliminated is still fighting for something, so fairness matters.  Those two extra brackets are not just for fun, they are for eternal glory and (at least a little) money.
 
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Re: 2013 World Championship Format
« Reply #115 on: May 5th, 2012, 4:54pm »
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on May 5th, 2012, 2:46pm, Thiagor wrote:
Another suggestion: Has anyone already thought about combining different distributions? For instance, we could award half of the total prize fund to the top 3 finishers (say 50-30-20), while the other half is given to all players, proportional to their number of wins. This would also, in some sense at least, give justice to the survey results Wink

Actually, by the survey we would need 22.5% distributed 50-30-20, 35% distributed 40-20-15-10-7-5-3, 12.5% distributed 30-15-10-8-6-5-4-4-3-3-3-3-2-2-2, and 30% distributed proportional to number of wins.  Tongue
 
The problem with the survey question is that both the shape and extent of the distribution matter.  Since there are two concepts in dispute, there isn't really a "middle" or a "compromise" answer.  The first three options I presented were all roughly 1/n, with the difference being how many people got something.  The last option garnered support perhaps because everyone got something, but if you plot the prize versus place, it is weirdly S-shaped rather than falling off in orderly fashion.
 
At the moment I am leaning toward prizes as 1/n, extended to the place of anyone who won even one game.  In a six-round 64-player tournament, that means only one person (other than dropouts) gets nothing, and the top places are about 21-11-7-5-4.  But no, that doesn't leave as much money at the top as most people were voting for.  This is oddly similar to allotting half per win and half per 1/(n+1)^2 but the shape of the distribution gets weirder, with the top still about 21-11-7-5-4 and a flattening through the middle when the steep half is mostly gone so it is by wins instead, each worth about 0.25 share.  I'm just not sure what to do.  Maybe 1/n extended to the people who "make the finals" by being alive after six rounds?  This would mean that in a 64-player tournament, about 22 places would pay out, with the top getting about 27-14-9-7-5.  That last idea might be as close to matching the survey as we can get.  (Recall that a slim majority wanted only 7 or 3 places to pay out.)
« Last Edit: May 5th, 2012, 5:17pm by Fritzlein » IP Logged

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Re: 2013 World Championship Format
« Reply #116 on: May 5th, 2012, 8:43pm »
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I see my post was too unclear. I wrote it as if I'd already been participating in the thread, so my intentions would be clear.  
 
Anyway, I meant to not be talking about a single elimination plus consolation bracket, or standard double elimination bracket, but a way of implementing aaaa's idea: if there are n players, wait for the first n/2 to be eliminated in a quadruple floating elimination or triple floating elimination, then pair them. The n/4 winners face the next n/4 players to be eliminated, and so on.  
 
Hence the rather cryptic comment about merging a double elimination format with floating elimination.
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Re: 2013 World Championship Format
« Reply #117 on: May 6th, 2012, 9:34am »
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on May 5th, 2012, 8:43pm, hyperpape wrote:
Anyway, I meant to not be talking about a single elimination plus consolation bracket, or standard double elimination bracket, but a way of implementing aaaa's idea: if there are n players, wait for the first n/2 to be eliminated in a quadruple floating elimination or triple floating elimination, then pair them. The n/4 winners face the next n/4 players to be eliminated, and so on.

Only single-elimination eliminates half as many people each round as the round before.  A multiple-elimination format will have a more complex progression.  For example, a 64-player triple-elimination eliminates 8 people in the third round, 12 people in the fourth round, 12 people in the fifth round, 10 people in the sixth round, 7 or 8 people in the seventh round, and a variable number of people in the following rounds.  You can't simply match new losers to old losers; there must be some sort of floating pairing in the consolation bracket.
 
But maybe I am still missing the point of your proposal: Why not have everyone (losers as well as winners) play at the rate of one game per week?  Why have one bracket move at a different pace than the other?  What is the aim of your proposal, i.e. what benefit are you trying to achieve?
« Last Edit: May 6th, 2012, 9:39am by Fritzlein » IP Logged

Marty
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Re: 2013 World Championship Format
« Reply #118 on: May 6th, 2012, 3:02pm »
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on May 5th, 2012, 4:41pm, Fritzlein wrote:
...
 
However, everyone in the loser's bracket has now played three games instead of only two.  Suppose that someone who lost in the first round wins every game from then on.  By the time only one winner remains, his score line will be WWWWWW.  The first-round loser, however, will have a score line of LWWWWWWWWWW, having had to win ten games for the privilege of trying to win two more against top player.  I saw something nearly this ridiculous happen in a pool (pocket billiards) tournament once, and it was obviously unjust; the player from the losers' bracket was exhausted by the time he won through, while his opponent from the winners' bracket was still fresh.
 
...

[technical] it seems to me that for 64 players in a fixed double elimination tournament you need only 7-8 wins to win the loser's bracket and face the winner of the winner's bracket (who'd scored 6 wins)
 
this detail aside, i agree that the floating elimination is fairer than the simpler fixed elimination and i like it better.
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Re: 2013 World Championship Format
« Reply #119 on: May 6th, 2012, 10:08pm »
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on May 6th, 2012, 3:02pm, Marty wrote:
[technical] it seems to me that for 64 players in a fixed double elimination tournament you need only 7-8 wins to win the loser's bracket and face the winner of the winner's bracket (who'd scored 6 wins)

I could be wrong, but let's break it down.
 
I lose my first game.  I am one of 32 losers.
I win my second game.  I am one of 16 losers.
16 losers join my bracket.  I am one of 32 losers again.
I win my third game.  I am one of 16 losers again.
I win my fourth game.  I am one of 8 losers.
8 losers join my bracket.  I am one of 16 losers again.
I win my fifth game.  I am one of 8 losers again.
I win my sixth game.  I am one of 4 losers.
4 losers join my bracket.  I am one of 8 losers again.
I win my seventh game.  I am one of 4 losers again.
I win my eighth game.  I am one of 2 losers.
2 losers join my bracket.  I am one of 4 losers again.
I win my ninth game.  I am one of 2 losers again.
I win my tenth game.  I am the only loser.
1 loser joins my bracket.  I am one of 2 losers again.
I win my eleventh game.  I am the only losers again.
 
That makes one loss and ten wins.  Now to win the tournament I need two more against the winner of the winners' bracket, i.e. a total of twelve straight wins.
 
Am I doing the math correctly?
 
Quote:
this detail aside, i agree that the floating elimination is fairer than the simpler fixed elimination and i like it better.

I'm glad you like floating elimination.  Also, thanks for posting, and don't hesitate to post with any further questions, suggestions, or general comments!
« Last Edit: May 6th, 2012, 10:09pm by Fritzlein » IP Logged

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