Author |
Topic: World Championship tournament format (Read 9313 times) |
|
99of9
Forum Guru
Gnobby's creator (player #314)
 
Gender: 
Posts: 1413
|
 |
Re: World Championship tournament format
« Reply #105 on: Jul 31st, 2005, 10:50pm » |
 Quote  Modify
|
on Jul 31st, 2005, 9:03pm, omar wrote:| But when going from triple to quadruple the increase in percentage is not much and not worth adding three more rounds. |
|
There is a statistical anomaly in there (FTE performs *better* than FQE at inacc=50). I think it might be worth running some of the most important formats with more than 2000 trials.
I'd say 10.3 consecutive rounds is already very long to have people guaruntee they can participate (2.5 months!). It could be even longer if we have more entries than last year. I personally would prefer the 7.7 round option.
Quote:
I also tried a slight variation which I called floatTripElim2. It is identical to the original except that when selecting the second player in the pairing we chose a player having the most loses instead of least loses. It seems to perform about the same as the original, but adds an additional round.
|
|
Although this is a reasonable alternative, I think it is socially bad. This method means that the bottom ranked player gets smashed in his first 3 games against the top 3 ranked players (assuming the outcomes are predictable).
Quote:
I also compared the FTE against a double RR for the 4 player case (as in the computer championships). Here's the results:
Rating inacc 50 200 400
FTE (6.7) 66.0% 62.9% 65.4%
DRR (6.0) 55.2% 56.9% 56.4%
It's almost 10% better with only about one extra round. I think FTE is also a good format for the computer championship. It eliminates having to break ties based on moves per game as we encounted in the last tournament. Also it can scale up nicely by keeping the number of rounds fairly low if we allow for more players.
|
|
Interesting. I'd really like to see unlimited entries in the CC (max 1 per human of course). Then we'll never have to rely on the December ratings, which are certainly open to manipulation since humans are better than bots at the present.
Note that extra games are not really that painful in computer tournaments, because they can be run automatically. In fact I'd say some extra games would add to the interest of spectators.
You might want to think about how minor places are awarded. That would be less straightforward if the tournament was not round robin.
Quote:
we did not try out real swiss style tournaments.
...
I will venture to guess that the performance of a real swiss style tournament will be about equal to the floatingDoubleElim format.
|
|
That depends how long the swiss tourney goes for, and exactly how you handle players who are in their own score bracket (especially up the top), and how you handle players who've played each other before. If you give it the same number of rounds as floating_Triple_Elim, and allow players to play previous opponents, I expect it would be about equal with FTE. Why do you think it will be worse?
|
|
 IP Logged |
|
|
|
omar
Forum Guru
Arimaa player #2
Gender:
Posts: 1003
|
|
Re: World Championship tournament format
« Reply #106 on: Jul 31st, 2005, 10:51pm » |
Quote Modify
|
I wanted to see how much of the FTE's performance was due to the careful pairing of the players. So I created a version called floatTripElimRand which was identical to the original floatTripElim except that the second player in the pairing is chosen at random from among the players that the first player has played againt the least number of time (instead of in favor of having fewest losses, and further ties broken in favor of lower pre-tournament rating).
I was suprised to see that the random version performed as well as the original version that carefully selected the opponent. The number of rounds increased slightly. This suggests that the details of the pairings don't matter as much as we think they do. Amazing 
|
|
IP Logged |
|
|
|
Fritzlein
Forum Guru
Arimaa player #706
Gender:
Posts: 5928
|
|
Re: World Championship tournament format
« Reply #107 on: Jul 31st, 2005, 11:17pm » |
Quote Modify
|
Wow, we all three posted withing 3 minutes of each other. Some more responses:
I agree with 99of9 that pairing by fewest losses vs. most losses is socially bad. Let's give even the bottom seed a shot a redemption in game three. But more than that, it slows down the sorting of players. Of course we can expect the tournament to take longer, because we delay the point at which the top dogs have to prove anything against each other. It's no accident that traditional Swiss pairings match people with similar records so as to speed up the sorting.
I agree with Omar (not 99of9) that a traditional Swiss tourney of length equal to FTE would not do quite as well at picking a winner. This is because traditional Swiss absolutely forbids repeat pairings. But it provides less information to have the ninth round consist of, say #1 vs #7 and #2 vs #8 (or something like that because of avoiding repeat pairings) than it provides to have #1 play #2 because everyone else has been knocked out. The early rounds are used to determine who #1 and #2 are, but eventually they have to fight each other to the death rather than trying to rack up points against players who have no more hope of winning.
I agree with 99of9 that it would be cool to let all bots into the championship tourney as long as they meet the public play requirements. It wouldn't add too many rounds either, I believe. (Side note: with only four entrants, the first three rounds of FTE are guaranteed to be a round robin.)
And finally, I too am surprised that floatTripElimRand did almost as well as my FTE. You think of the most interesting things to test, Omar. But anyway it isn't surprising that randomness takes a round longer to sort things out, and I also think random pairings are socially worse than letting losers play losers and winners play winners.
|
| « Last Edit: Aug 1st, 2005, 9:45pm by Fritzlein » |
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #108 on: Jul 31st, 2005, 11:24pm » |
Quote Modify
|
on Jul 31st, 2005, 10:48pm, Fritzlein wrote:| Also, you never had to face the same guy twice no matter what. |
|
I didn't realise this was a fundamental part of the swiss system. I think that is a major disadvantage (for the reason you later describe Fritz). Can't that condition be relaxed?
Quote:| But the hugest advantage of elimination formats is that your fate remains in your hands until elimination. Until you get the third loss, you can always rest secure in the knowledge, "If I win the rest of my games I will still be champion." Each player retains the power to single-handedly vanquish the field. In traditional Swiss this is not true: if you are behind you need to win plus you need the leaders to lose. |
|
You are thinking of "your fate" being simply in terms of winning or not winning the overall tournament. Those of us who are not at the top  are also interested in contesting lower ladder-places, especially if it means that we get a few games against people of similar standard (even if we've lost the chance at winning overall).
How's this for a format proposal:
Each round:
(1) Players are sorted from first to last in order of
(a) tournament score
tiebroken by
(b) total score of opponents
tiebroken by
(c) original rating (seeding)
(2) If there are an odd number of players, the player at the bottom of the tournament gets a bye which is counted as a win (2 points).
(3) The others pair off from the top of the sorted list [eg 1 plays 2, 3 plays 4 etc]. 2 points for a win, 1 for a draw, 0 for a loss.
Iterate this for as many rounds as you want in your tournament. At a bare minimum you will need a similar number to swiss, but if you test this out I'd prefer you ran it with 5,6,7,8,9,10.... rounds to see how much better it got with increasing rounds (and so it could be directly compared with other formats of the same number of rounds).
[EDIT: Of course if there is a tie in the tournament score at the end, it is tiebroken the same way as the sorting is done - whoever had the hardest tournament wins.]
I've designed this to get as many confrontations between top players as possible (as in swiss), and in particular have deliberately included repeat clashes. This means that for a fewer number of rounds, a better discernment is done between the top few players. (it would certainly give the tournament leader a high-difficulty tournament!)
I think by Omar's metric this method will perform nearly the best for a given number of rounds [but I understand that there are other important metrics that are important to how good a competition is].
What do you guys think of it?
|
| « Last Edit: Jul 31st, 2005, 11:48pm by 99of9 » |
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #109 on: Jul 31st, 2005, 11:29pm » |
Quote Modify
|
on Jul 31st, 2005, 11:17pm, Fritzlein wrote:| I agree with Omar (not 99of9) that a traditional Swiss tourney of length equal to FTE would not do quite as well at picking a winner. This is because traditional Swiss absolutely forbids repeat pairings. |
|
Agreed - I hadn't realised this was part of the construct (I should have actually followed Omar's wiki link ).
|
| « Last Edit: Jul 31st, 2005, 11:30pm by 99of9 » |
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #110 on: Jul 31st, 2005, 11:38pm » |
Quote Modify
|
on Jul 31st, 2005, 9:03pm, omar wrote:| Also a swiss tournament lacks the climax ending of a knockout style format. |
|
This is an important metric that is not included in Omar's tables. The format I just proposed also does not necessarily have a climactic final round. But unless one player is much stronger than all the others, I'd suggest that the final round will often be very important to the overall winner result (more often than swiss), and will certainly be important for determining minor placings.
|
| « Last Edit: Jul 31st, 2005, 11:39pm by 99of9 » |
IP Logged |
|
|
|
omar
Forum Guru
Arimaa player #2
Gender:
Posts: 1003
|
|
Re: World Championship tournament format
« Reply #111 on: Jul 31st, 2005, 11:39pm » |
Quote Modify
|
on Jul 31st, 2005, 10:50pm, 99of9 wrote:
That depends how long the swiss tourney goes for, and exactly how you handle players who are in their own score bracket (especially up the top), and how you handle players who've played each other before. If you give it the same number of rounds as floating_Triple_Elim, and allow players to play previous opponents, I expect it would be about equal with FTE. Why do you think it will be worse?
|
|
Yes, I agree it depends on the length of the tournament. But usually the number of rounds of a swiss tournament has to be preannounced and is usually just long enough for one player to score one point more than the next highest. About two rounds more than what a single elimination requires is usually enough. That happens to be about how long a floating double elimination is.
|
|
IP Logged |
|
|
|
Fritzlein
Forum Guru
Arimaa player #706
Gender:
Posts: 5928
|
|
Re: World Championship tournament format
« Reply #112 on: Aug 1st, 2005, 12:54am » |
Quote Modify
|
on Jul 31st, 2005, 11:24pm, 99of9 wrote:
How's this for a format proposal:
Each round:
(1) Players are sorted from first to last in order of
(a) tournament score
tiebroken by
(b) total score of opponents
tiebroken by
(c) original rating (seeding)
(2) If there are an odd number of players, the player at the bottom of the tournament gets a bye which is counted as a win (2 points).
(3) The others pair off from the top of the sorted list [eg 1 plays 2, 3 plays 4 etc]. 2 points for a win, 1 for a draw, 0 for a loss.
|
|
Wow, very interesting idea. I would love to see how it performs. One proviso is that you would have to have several extra rounds. If you have just 4 rounds for 16 players, then it's single elimination with horrible seeding. Even if you have just five rounds, I expect it would get weird. But after eight or nine rounds, you would have had a heck of an interesting tournament.
Here are my attempts at pairings in the "favorites always win model":
1v2, 3v4, 5v6, 7v8, 9v10, 11v12, 13v14, 15v16
1v3, 5v7, 9v11, 13v15, 2v4, 6v8, 10v12, 14v16
1v5, 9v13, 2v3, 6v7, 10v11, 14v15, 4v8, 12v16
1v9, 5v13, 2v10, 6v14, 3v11, 7v15, 4v12, 8v16
1v5, 2v9, 6v3, 13v7, 10v4, 14v11, 8v15, 12v16
1v2, 5v3, 9v4, 6v7, 10v11, 13v8, 14v12, 15v16
Notes: for the first four rounds, the standings correspond less and less to player strength. (Not a good thing for a format to achieve when there are 2nd and 3rd place prizes to be given out?) After 5 rounds, things are sorting back out, but #8 seed was still rooked by the pairings and #9 vaulted into fifth place. Sadly, after 6 rounds, there is almost no chance I have done the calculation correctly.
Well, I wonder what Omar's tests will reveal. It is an intriguing idea, but I say that unless these pairings are unequivocaly better at picking a winner than floating elimination is, then the early mayhem caused in the standings is simply not worth it. For psychological reasons, the #4 seed should not have to get rocked twice at the start and fall behind some schmoe from the bottom of the bracket who got two wins against other low seeds.
|
|
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #113 on: Aug 1st, 2005, 2:36am » |
Quote Modify
|
on Aug 1st, 2005, 12:54am, Fritzlein wrote:| Sadly, after 6 rounds, there is almost no chance I have done the calculation correctly. |
|
Miracles can happen. My calculation (some bits by hand, some by spreadsheet) gives exactly the same first 6 rounds as you. I'll post more when I get them (But I see why you gave up!!! Tourneys using this format would have to be administrated by a computer!).
|
| « Last Edit: Aug 1st, 2005, 8:14am by 99of9 » |
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #114 on: Aug 1st, 2005, 3:55am » |
Quote Modify
|
I wrote the code Fritz, here are the pairings and intermediate scorecards if the better seeded player wins every time. From round 6 onward you are in a situation where #1 is tested against #2 and #3 until somebody cracks. One downside: in this "perfect seeding" model #2 and #3 only get one game against each other (because one of them is usually busy playing #1). But I think that for humans, upsets are sufficiently likely that there would be enough variation in the results to prevent endless cycles in the pairings.
Round 1 - Current Standings:
player 1 score: 0 oppscore: 0
player 2 score: 0 oppscore: 0
player 3 score: 0 oppscore: 0
player 4 score: 0 oppscore: 0
player 5 score: 0 oppscore: 0
player 6 score: 0 oppscore: 0
player 7 score: 0 oppscore: 0
player 8 score: 0 oppscore: 0
player 9 score: 0 oppscore: 0
player 10 score: 0 oppscore: 0
player 11 score: 0 oppscore: 0
player 12 score: 0 oppscore: 0
player 13 score: 0 oppscore: 0
player 14 score: 0 oppscore: 0
player 15 score: 0 oppscore: 0
player 16 score: 0 oppscore: 0
1 v 2
3 v 4
5 v 6
7 v 8
9 v 10
11 v 12
13 v 14
15 v 16
Round 2 - Current Standings:
player 1 score: 1 oppscore: 0
player 3 score: 1 oppscore: 0
player 5 score: 1 oppscore: 0
player 7 score: 1 oppscore: 0
player 9 score: 1 oppscore: 0
player 11 score: 1 oppscore: 0
player 13 score: 1 oppscore: 0
player 15 score: 1 oppscore: 0
player 2 score: 0 oppscore: 1
player 4 score: 0 oppscore: 1
player 6 score: 0 oppscore: 1
player 8 score: 0 oppscore: 1
player 10 score: 0 oppscore: 1
player 12 score: 0 oppscore: 1
player 14 score: 0 oppscore: 1
player 16 score: 0 oppscore: 1
1 v 3
5 v 7
9 v 11
13 v 15
2 v 4
6 v 8
10 v 12
14 v 16
Round 3 - Current Standings:
player 1 score: 2 oppscore: 2
player 5 score: 2 oppscore: 2
player 9 score: 2 oppscore: 2
player 13 score: 2 oppscore: 2
player 2 score: 1 oppscore: 2
player 3 score: 1 oppscore: 2
player 6 score: 1 oppscore: 2
player 7 score: 1 oppscore: 2
player 10 score: 1 oppscore: 2
player 11 score: 1 oppscore: 2
player 14 score: 1 oppscore: 2
player 15 score: 1 oppscore: 2
player 4 score: 0 oppscore: 2
player 8 score: 0 oppscore: 2
player 12 score: 0 oppscore: 2
player 16 score: 0 oppscore: 2
1 v 5
9 v 13
2 v 3
6 v 7
10 v 11
14 v 15
4 v 8
12 v 16
Round 4 - Current Standings:
player 1 score: 3 oppscore: 5
player 9 score: 3 oppscore: 5
player 5 score: 2 oppscore: 6
player 13 score: 2 oppscore: 6
player 2 score: 2 oppscore: 5
player 10 score: 2 oppscore: 5
player 6 score: 2 oppscore: 3
player 14 score: 2 oppscore: 3
player 3 score: 1 oppscore: 6
player 11 score: 1 oppscore: 6
player 7 score: 1 oppscore: 4
player 15 score: 1 oppscore: 4
player 4 score: 1 oppscore: 3
player 12 score: 1 oppscore: 3
player 8 score: 0 oppscore: 4
player 16 score: 0 oppscore: 4
1 v 9
5 v 13
2 v 10
6 v 14
3 v 11
7 v 15
4 v 12
8 v 16
Round 5 - Current Standings:
player 1 score: 4 oppscore: 11
player 5 score: 3 oppscore: 11
player 2 score: 3 oppscore: 10
player 9 score: 3 oppscore: 9
player 6 score: 3 oppscore: 8
player 3 score: 2 oppscore: 10
player 13 score: 2 oppscore: 9
player 7 score: 2 oppscore: 8
player 10 score: 2 oppscore: 8
player 4 score: 2 oppscore: 7
player 14 score: 2 oppscore: 6
player 11 score: 1 oppscore: 8
player 8 score: 1 oppscore: 7
player 15 score: 1 oppscore: 6
player 12 score: 1 oppscore: 5
player 16 score: 0 oppscore: 5
1 v 5
2 v 9
6 v 3
13 v 7
10 v 4
14 v 11
8 v 15
12 v 16
Round 6 - Current Standings:
player 1 score: 5 oppscore: 16
player 2 score: 4 oppscore: 16
player 5 score: 3 oppscore: 18
player 3 score: 3 oppscore: 17
player 9 score: 3 oppscore: 15
player 4 score: 3 oppscore: 13
player 6 score: 3 oppscore: 13
player 7 score: 3 oppscore: 11
player 10 score: 2 oppscore: 14
player 11 score: 2 oppscore: 12
player 13 score: 2 oppscore: 12
player 8 score: 2 oppscore: 10
player 14 score: 2 oppscore: 8
player 12 score: 2 oppscore: 7
player 15 score: 1 oppscore: 9
player 16 score: 0 oppscore: 9
1 v 2
5 v 3
9 v 4
6 v 7
10 v 11
13 v 8
14 v 12
15 v 16
Round 7 - Current Standings:
player 1 score: 6 oppscore: 21
player 2 score: 4 oppscore: 26
player 3 score: 4 oppscore: 23
player 4 score: 4 oppscore: 20
player 6 score: 4 oppscore: 18
player 5 score: 3 oppscore: 25
player 9 score: 3 oppscore: 21
player 7 score: 3 oppscore: 18
player 10 score: 3 oppscore: 18
player 8 score: 3 oppscore: 15
player 12 score: 3 oppscore: 11
player 11 score: 2 oppscore: 18
player 13 score: 2 oppscore: 16
player 14 score: 2 oppscore: 13
player 15 score: 2 oppscore: 10
player 16 score: 0 oppscore: 15
1 v 2
3 v 4
6 v 5
9 v 7
10 v 8
12 v 11
13 v 14
15 v 16
Round 8 - Current Standings:
player 1 score: 7 oppscore: 28
player 3 score: 5 oppscore: 30
player 2 score: 4 oppscore: 36
player 5 score: 4 oppscore: 34
player 4 score: 4 oppscore: 27
player 6 score: 4 oppscore: 27
player 7 score: 4 oppscore: 25
player 8 score: 4 oppscore: 21
player 9 score: 3 oppscore: 28
player 10 score: 3 oppscore: 24
player 11 score: 3 oppscore: 22
player 13 score: 3 oppscore: 22
player 12 score: 3 oppscore: 15
player 15 score: 3 oppscore: 13
player 14 score: 2 oppscore: 19
player 16 score: 0 oppscore: 21
1 v 3
2 v 5
4 v 6
7 v 8
9 v 10
11 v 13
12 v 15
14 v 16
Round 9 - Current Standings:
player 1 score: 8 oppscore: 37
player 2 score: 5 oppscore: 45
player 3 score: 5 oppscore: 43
player 4 score: 5 oppscore: 34
player 7 score: 5 oppscore: 30
player 5 score: 4 oppscore: 42
player 9 score: 4 oppscore: 36
player 6 score: 4 oppscore: 35
player 11 score: 4 oppscore: 29
player 8 score: 4 oppscore: 28
player 12 score: 4 oppscore: 22
player 10 score: 3 oppscore: 34
player 13 score: 3 oppscore: 30
player 14 score: 3 oppscore: 21
player 15 score: 3 oppscore: 19
player 16 score: 0 oppscore: 27
1 v 2
3 v 4
7 v 5
9 v 6
11 v 8
12 v 10
13 v 14
15 v 16
Round 10 - Current Standings:
player 1 score: 9 oppscore: 46
player 3 score: 6 oppscore: 52
player 2 score: 5 oppscore: 60
player 5 score: 5 oppscore: 53
player 4 score: 5 oppscore: 45
player 6 score: 5 oppscore: 43
player 7 score: 5 oppscore: 42
player 8 score: 5 oppscore: 36
player 9 score: 4 oppscore: 45
player 10 score: 4 oppscore: 39
player 11 score: 4 oppscore: 38
player 13 score: 4 oppscore: 36
player 12 score: 4 oppscore: 28
player 15 score: 4 oppscore: 21
player 14 score: 3 oppscore: 29
player 16 score: 0 oppscore: 35
1 v 3
2 v 5
4 v 6
7 v 8
9 v 10
11 v 13
12 v 15
14 v 16
Round 11 - Current Standings:
player 1 score: 10 oppscore: 57
player 2 score: 6 oppscore: 71
player 3 score: 6 oppscore: 69
player 4 score: 6 oppscore: 53
player 7 score: 6 oppscore: 48
player 5 score: 5 oppscore: 64
player 6 score: 5 oppscore: 54
player 9 score: 5 oppscore: 54
player 8 score: 5 oppscore: 46
player 11 score: 5 oppscore: 46
player 12 score: 5 oppscore: 36
player 10 score: 4 oppscore: 52
player 13 score: 4 oppscore: 47
player 14 score: 4 oppscore: 31
player 15 score: 4 oppscore: 29
player 16 score: 0 oppscore: 43
1 v 2
3 v 4
7 v 5
6 v 9
8 v 11
12 v 10
13 v 14
15 v 16
Round 12 - Current Standings:
player 1 score: 11 oppscore: 68
player 3 score: 7 oppscore: 80
player 2 score: 6 oppscore: 90
player 5 score: 6 oppscore: 76
player 4 score: 6 oppscore: 67
player 6 score: 6 oppscore: 63
player 7 score: 6 oppscore: 63
player 8 score: 6 oppscore: 55
player 9 score: 5 oppscore: 66
player 10 score: 5 oppscore: 58
player 11 score: 5 oppscore: 58
player 13 score: 5 oppscore: 54
player 12 score: 5 oppscore: 45
player 15 score: 5 oppscore: 31
player 14 score: 4 oppscore: 41
player 16 score: 0 oppscore: 53
1 v 3
2 v 5
4 v 6
7 v 8
9 v 10
11 v 13
12 v 15
14 v 16
|
|
IP Logged |
|
|
|
99of9
Forum Guru
Gnobby's creator (player #314)
Gender:
Posts: 1413
|
|
Re: World Championship tournament format
« Reply #115 on: Aug 1st, 2005, 3:59am » |
Quote Modify
|
Omar, here is the code. If you can turn it into a probabilistic one based on ratings which integrates with your validation system, I'd be very interested, but don't worry about it too much - having seen the early round pairings I'm less gung-ho about it.
#include <stdio.h>
#include <stdlib.h>
#define ROUNDS 12
#define PLAYERS 16
int score[PLAYERS];
int oppscore[PLAYERS];
int seed[PLAYERS];
int opponent[PLAYERS][ROUNDS];
int ranking[PLAYERS];
int Sort_Players() {
/* I know this is a very inefficient sort method, but I needed to be quick */
int pos=0;
int cp;
while (pos!=PLAYERS-1) {
if (( score[ranking[pos]] <score[ranking[pos+1]])||
((score[ranking[pos]]==score[ranking[pos+1]])&&(oppscore[ranking[pos]]<oppscore[ranking[pos+1]]))||
((score[ranking[pos]]==score[ranking[pos+1]])&&(oppscore[ranking[pos]]==oppscore[ranking[pos+1]])&&(seed[ranking[pos]]<seed[ranking[pos+1]]))){
cp = ranking[pos+1];
ranking[pos+1] = ranking[pos];
ranking[pos] = cp;
pos = 0;
} else {
pos++;
}
}
}
int Winner (int a, int b) {
if (a<b) return 1;
else return 0;
}
int main () {
int round, rnd;
int player;
int game;
for (player=0; player<PLAYERS; player++) {
ranking[player]=player;
score[player] = 0;
oppscore[player] = 0;
seed[player] = PLAYERS - player;
}
for (round=0; round<ROUNDS; round++) {
Sort_Players();
printf("Round %2d - Current Standings:\n", round+1);
for (player=0; player<PLAYERS; player++) {
printf("player %2d score: %3d oppscore: %4d\n", ranking[player]+1, score[ranking[player]], oppscore[ranking[player]]);
}
for (game=0; game<PLAYERS/2; game++) {
printf("%2d v %2d\n", ranking[game*2]+1, ranking[game*2+1]+1);
opponent[ranking[game*2]][round] = ranking[game*2+1];
opponent[ranking[game*2+1]][round] = ranking[game*2];
if (Winner(ranking[game*2],ranking[game*2+1])) {
score[ranking[game*2]]++;
} else {
score[ranking[game*2+1]]++;
}
}
if (PLAYERS%2) {
score[ranking[PLAYERS-1]]++;
opponent[ranking[PLAYERS-1]][round] = -1;
}
/* last on board gets a bye and a point,
and their opponent for that round is set to be themselves*/
for (player=0; player<PLAYERS; player++) {
oppscore[player] = 0;
for (rnd=0; rnd<=round; rnd++) {
if (!(opponent[player][rnd]==-1))
oppscore[player] += score[opponent[player][rnd]];
}
}
printf("\n");
}
}
|
| « Last Edit: Aug 1st, 2005, 9:29pm by 99of9 » |
IP Logged |
|
|
|
jdb
Forum Guru
Arimaa player #214
Gender:
Posts: 682
|
|
Re: World Championship tournament format
« Reply #116 on: Aug 1st, 2005, 8:25am » |
Quote Modify
|
Quote:But the hugest advantage of elimination formats is that your fate remains in your hands until elimination. Until you get the third loss, you can always rest secure in the knowledge, "If I win the rest of my games I will still be champion." Each player retains the power to single-handedly vanquish the field. In traditional Swiss this is not true: if you are behind you need to win plus you need the leaders to lose.
|
|
I agree with this 100%. The climatic final game is also good public relations.
Quote:| I agree with Omar (not 99of9) that a traditional Swiss tourney of length equal to FTE would not do quite as well at picking a winner. This is because traditional Swiss absolutely forbids repeat pairings. |
|
If a Swiss and FTE have the same number of rounds, and the number of participants is sufficiently large, the Swiss will perform better. While each individual game in the Swiss is not as effective at determining the winner, in the latter rounds, the Swiss has more total games. Which one is better for a 16 person tourny, I have no idea.
|
|
IP Logged |
|
|
|
omar
Forum Guru
Arimaa player #2
Gender:
Posts: 1003
|
|
Re: World Championship tournament format
« Reply #117 on: Aug 4th, 2005, 12:30am » |
Quote Modify
|
Toby, I'll try out your method once I get some time.
Jeff, Im starting to get the feeling that the total number of games does not matter too much. What I think matters more is the average number of rounds a tournament has. Also another thing that seems to matter is how many rounds are played before making a decision about eliminating players. Im also getting the feeling that the details of how the pairs are chosen do not matter much compared to these other two factors.
Here's a trivial sounding math question for anyone who wants to take a crack at it:
If a player A can defeat player B with a probability p then what is the probability that player A will win if they play a series of N games?
I was wondering about this because it will set an upper bound on how well we can expect a tourament to perform. Knowing the number of players and the range of their true ratings we can come up with an average difference in rating between the best and second best player and from that the probability of the best player winning a game against the second best. Then from the number of rounds the tournament runs for we can determine the probability of the best player winning and get an upper bound on what the best the tournament can do.
|
|
IP Logged |
|
|
|
jdb
Forum Guru
Arimaa player #214
Gender:
Posts: 682
|
|
Re: World Championship tournament format
« Reply #118 on: Aug 4th, 2005, 9:26am » |
Quote Modify
|
Quote:If a player A can defeat player B with a probability p then what is the probability that player A will win if they play a series of N games?
|
|
Here's a little program that should compute this.
public class GameTest {
public static long factorial(int n) {
assert( n>=0 && n<=60);
long result = 1;
for ( int i=1; i<=n; i++ ) {
result *= i;
}
return result;
}
public static long nCr(int n, int r) {
return factorial(n)/factorial(r)/factorial(n-r);
}
public static void main( String args[] ) {
int num_games = 5;
double game_win_prob = .3;
if ( args.length == 2 ) {
num_games = Integer.parseInt(args[0]);
game_win_prob = Double.parseDouble(args[1]);
}
assert( num_games >=1 );
assert( game_win_prob>=0 && game_win_prob <=1.0 );
double total = 0;
double match_win_prob = 0;
for ( int i=0; i<=num_games; i++ ) {
double a_win = Math.pow(game_win_prob,i);
double b_win = Math.pow(1-game_win_prob,num_games-i);
double ways = nCr(num_games,i);
double item_win = a_win * b_win * ways;
System.out.println(i+" "+item_win);
total += item_win;
match_win_prob += (i>num_games/2) ? item_win : 0;
}
System.out.println("Total: "+total);
System.out.println("Match Length: "+num_games);
System.out.println("Individual Win Prob: "+game_win_prob);
System.out.println("Match Win Prob: "+match_win_prob);
}
}
|
|
IP Logged |
|
|
|
omar
Forum Guru
Arimaa player #2
Gender:
Posts: 1003
|
|
Re: World Championship tournament format
« Reply #119 on: Aug 4th, 2005, 5:20pm » |
Quote Modify
|
Thanks for the program Jeff.
Since Im learning Ruby, I rewrote this in Ruby. Here it is in case anyone is interested:
#!/usr//local/bin/ruby
# N choose M = N! / (N-M)!*M!
def NcM(n, m)
b = [];
b[0] = 1
for i in 1 .. n
b[i] = 1
j = i-1
while j>0
b[j] += b[j - 1]
j -= 1
end
end
return b[m]
end
# compute probability of winning as:
# pW = 1 - [ T0 + T1 + T2 ... + Tk ]
# where Ti = Nci*q^(N-i)*p^i
# q = 1-p
# k = int(N/2)
#
def pW(p, n)
q = 1-p
k = n/2
wp = 0.0
for i in 0 .. k
j = n-i
y = NcM(n,i)
x = NcM(n,i) * q**j * p**i
wp += NcM(n,i) * q**j * p**i
end
wp = 1.0 - wp;
return wp
end
p = ARGV[0].to_f
n = ARGV[1].to_i
if p < 0 or p > 1
print "probability is out of range [0, 1]\n"
exit
end
if n < 1
print "number of games must be at least 1\n"
exit
end
wp = 100*pW(p, n)
print "chance of winning is #{wp}%\n"
To run it just pass the probability of winning for the stronger player and the number of games. For example:
chance 0.6 11
and it will print:
chance of winning is 75.349813248%
|
|
IP Logged |
|
|
|
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print