C Dutch System Version as agreed by the 83rd FIDE Congress in Istanbul 2012

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1 Dutch System Version s greed y the 83rd FIDE Congress in Istnul 2012 A Introductory Remrks nd Definitions A.1 Initil rnking list A.2 Order See 04.2.B (Generl Hndling Rules - Initil order) For pirings purposes only, the plyers re rnked in order of, respectively A.3 Score rckets A.4 Flots A.5 Byes. score. piring numers ssigned to the plyers ccordingly to the initil rnking list nd susequent modifictions dependent on possile lte entries Plyers with equl scores constitute homogeneous score rcket. Plyers who remin unpired fter the piring of score rcket will e moved down to the next score rcket, which will therefore e heterogeneous. When piring heterogeneous score rcket these plyers moved down re lwys pired first whenever possile, giving rise to reminder score rcket which is lwys treted s homogeneous one. A heterogeneous score rcket of which t lest hlf of the plyers hve come from higher score rcket is lso treted s though it ws homogeneous. By piring heterogeneous score rcket, plyers with unequl scores will e pired. To ensure tht this will not hppen to the sme plyers gin in the next two rounds this is written down on the piring crd. The higher rnked plyer (clled downfloter) receives downflot, the lower one (upfloter) n upflot. Should the totl numer of plyers e (or ecome) odd, one plyer ends up unpired. This plyer receives ye: no opponent, no colour, 1 point or hlf point (s stted in the tournment regultions). A.6 Sugroups - Definition of P0, M0 To mke the piring, ech score rcket will e divided into two sugroups, to e clled S1 nd S2, where S2 is equl or igger thn

2 S1 (for detils see 2 to 4) S1 plyers re tenttively pired with S2 plyers. c P0 is the mximum numer of pirs tht cn e produced in ech score rcket. P0 is equl to the numer of plyers divided y two nd rounded downwrds. M0 is the numer of plyers moved down from higher score groups (it my e zero) A.7 Colour differences nd colour preferences The colour difference of plyer is the numer of gmes plyed with white minus the numer of gmes plyed with lck y this plyer. After round the colour preference cn e determined for ech plyer who hs plyed t lest one gme. c An solute colour preference occurs when plyer s colour difference is greter thn +1 or less thn -1, or when plyer hd the sme colour in the two ltest rounds he plyed. The preference is white when the colour difference is less thn -1 or when the lst two gmes were plyed with lck. The preference is lck when the colour difference is greter thn +1, or when the lst two gmes were plyed with white. A strong colour preference occurs when plyer s colour difference is +1 or -1. The strong colour preference is white when the colour difference is -1, lck otherwise A mild colour preference occurs when plyer s colour difference is zero, the preference eing to lternte the colour with respect to the previous gme. Before the first round the colour

3 preference of one plyer (often the highest one) is determined y lot. d e f While piring n odd-numered round plyers hving strong colour preference (plyers who hve hd n odd numer of gmes efore y ny reson) shll e treted like plyers hving n solute colour preference s long s this does not result in either dditionlfloters or floters with n higher score or pirs with higher score difference of the pired plyers. While piring n even-numered round plyers hving mild colour preference (plyers who hve hd n even numer of gmes y ny reson) shll e treted nd counted s if they would hve mild colour preference of tht kind (white resp. lck) which reduces the numer of pirs where oth plyers hve the sme strong colour preference. Plyers who did not ply the first rounds hve no colour preference (the preference of their opponents is grnted) A.8 Definition of X1, Z1 Provided there re P0 (see A6) pirings possile in score rcket: the minimum numer of pirings which must e mde in the score rcket, not fulfilling ll colour preferences, is represented y the symol X1. in even rounds the minimum numer of pirings which must e mde in the score rcket, not fulfilling ll strong colour preferences (see A7.e), is represented y the symol Z1 X1 nd, in even rounds, Z1 cn e

4 clculted s follows: w in odd rounds: 0; in even rounds: numer of plyers who hd n odd numer of unplyed gmes which hve mild colour preference for white (see A7.e) in odd rounds: 0; in even rounds: numer of plyers who hd n odd numer of unplyed gmes which hve mild colour preference for lck (see A7.e) W (remining) numer of plyers hving colour preference white B (remining) numer of plyers hving colour preference lck numer of plyers who hve not plyed round yet X1 If B+ > W+w then else If X1 < 0 then In even rounds: X1 = P0 W w -, X1 = P0 B -. X1 = 0 Z1 If B > W then else If Z1 < 0 then Z1 = P0 - W - - w - Z1 = P0 - B - - w -. Z1 = 0 A.9 Trnspositions nd exchnges In order to mke sound piring it is often necessry to chnge the

5 order in S2. The rules to mke such chnge, clled trnsposition, re in D1 In homogeneous score rcket it my e necessry to exchnge plyers from S1 to S2. Rules for exchnges re found under D2. After ech exchnge oth S1 nd S2 re to e ordered ccording to A2. A.10 Definitions: Top scorers, Bcktrcking Top scorers re plyers who hve score of over 50% of the mximum possile score when piring the lst round. Bcktrcking mens to undo the pirings of higher score rcket to find nother set of floters to the given score rcket. A.11 Qulity of Pirings - Definition of X nd P The rules C1 to C14 descrie n itertion lgorithm to find the est possile pirings within score rcket. Strting with the extreme requirement: P0 pirings with P0 X1 pirings fulfilling ll colour preferences nd meeting ll requirements B1 to B6 If this trget cnnot e mnged the requirements re reduced step y step to find the est su-optiml pirings. The qulity of the pirings is defined in descending priority s the numer of pirs the closeness of the scores of the plyers plying ech other the numer of pirs fulfilling the colour preference of oth plyers (ccording to A7) fulfilling the current criteri for downfloters fulfilling the current criteri for upfloters During the lgorithm two prmeters represent the progress of the itertion: P is the numer of pirings required t specil stge during the pirings lgorithm. The first vlue of P is P0 or M0 nd is decresing. X is the numer of pirings not fulfilling ll colour preferences which is cceptle t specil stge during the pirings lgorithm. The first vlue of X is X1 (see A8) nd is incresing. B Piring Criteri Asolute Criteri (These my not e violted. If necessry plyers will e moved down to lower score rcket.) B.1 Two plyers shll not meet more

6 thn once. A plyer who hs received point or hlf point without plying, either through ye or due to n opponent not ppering in time, is downfloter (see A4) nd shll not receive ye. B.2 Two plyers with the sme solute colour preference (see A7.) shll not meet (therefore no plyer s colour difference will ecome >+2 or < -2 nor plyer will receive the sme colour three times in row) Note: If it is helpful to reduce the numer of floters or the score of floter when piring top scorers B2 my e ignored. If top scorer is pired ginst non-top scorer, the ltter is considered top scorer for colour lloction purposes. Reltive Criteri (These re in descending priority. They should e fulfilled s much s possile. To comply with these criteri, trnspositions or even exchnges my e pplied, ut no plyer should e moved down to lower score rcket). B.3 The difference of the scores of two plyers pired ginst ech other should e s smll s possile nd idelly zero (note for progrmmers: see section D.4 regrding how to use this criterion fter repeted ppliction of rule 13) B.4 As mny plyers s possile receive their colour preference B.5 No plyer shll receive n identicl flot in two consecutive rounds. B.6 No plyer shll hve n identicl flot s two rounds efore. C Piring Procedures Strting with the highest score rcket pply the following procedures to ll score rckets until n cceptle piring is otined. The colour lloction rules (E) re used to determine which plyers will ply with white. 1 Incomptile plyer If the score rcket contins plyer for whom no opponent cn e found within this score rcket without violting B1 (or B2, except when piring top scorers) then: if this plyer ws moved down from higher score rcket pply C12. if this score rcket is the lowest one pply C13. in ll other cses: move this plyer down to the next score rcket Determine P0, P1, M0, M1, X1, Z1

7 2 Determine P0 ccording to A6.. Set P1 = P0 Determine M0 ccording to A6.c. Set M1= M0 Determine X1 ccording to A8. In even rounds: determine Z1 ccording to A8. 3 Set requirements P, B2, A7d, X, Z, B5/B6 c d e f g h In homogeneous score rcket set P = P1 In heterogeneous score rcket set P = M1 (top scorers) reset B2 (odd rounds) reset A7.d Set X = X1 (even numered rounds) Set Z = Z1 (rcket produces downfloters) reset B5 for downfloters (rcket produces downfloters) reset B6 for downfloters (heterogeneous score rckets) reset B5 for upfloters (heterogeneous score rckets) reset B6 for upfloters 4 Estlish su-groups Put the highest P plyers in S1, ll other plyers in S2. 5 Order the plyers in S1 nd S2 According to A2. 6 Try to find the piring Pir the highest plyer of S1 ginst the highest one of S2, the second highest one of S1 ginst the second highest one of S2, etc. If now P pirings re otined in complince with the current requirements the piring of this score rcket is considered complete. in cse of homogeneous or reminder score rcket: remining plyers re moved down to the next score rcket. With this score rcket restrt t C1.

8 in cse of heterogeneous score rcket: only M1 plyers moved down were pired so fr. Mrk the current trnsposition nd the vlue of P (it my e useful lter). Redefine P = P1 M1 Continue t C4 with the reminder group. 7 Trnsposition Apply new trnsposition of S2 ccording to D1 nd restrt t C6. 8 Exchnge In cse of homogeneous (reminder) group: pply new exchnge etween S1 nd S2 ccording to D2 nd restrt t C5. In cse of heterogeneous group: if M1 is less thn M0, choose nother set of M1 plyers to put in S1 ccording to D3 nd restrt t C5 9 Go ck to the heterogeneous score rcket (only reminder) 10 Terminte the piring of the homogeneous reminder. Go ck to the trnsposition mrked t C6 (in the heterogeneous prt of the rcket) nd restrt from C7 with new trnsposition. Lowering requirements c d e f (heterogeneous score rckets) Drop B6 for upfloters nd restrt from 4 (heterogeneous score rckets) Drop B5 for upfloters nd restrt from 3.h (rcket produces downfloters) Drop B6 for downfloters nd restrt from 3.g (rcket produces downfloters) Drop B5 for downfloters nd restrt from 3.f (odd numered rounds) If X < P1, increse X y 1 nd restrt from 3.e (even numered rounds) If Z < X, increse Z y 1 nd restrt from 3.e. If Z = X nd X < P1, increse X y 1, reset Z=Z1 nd restrt from 3.e (odd numered rounds) Drop A7.d nd restrt from 3.d

9 g (top scorers) Drop B2 nd restrt from 3.c Any criterion my e dropped only for the minimum numer of pirs in the score rcket 11 Deleted (see 10.e) Bcktrck to previous Score rcket If there re moved down plyers: cktrck to the previous score rcket. If in this previous score rcket piring cn e mde wherey nother set of plyers of the sme size nd with the sme scoreswill e moved down to the current one, nd this now llows P1 pirings to e mde then this piring in the previous score rcket will e ccepted. Bcktrcking is disllowed when lredy cktrcking from lower score rcket Lowest Score Brcket In cse of the lowest score rcket: if it is heterogeneous, try to reduce the numer of pirle moved-down plyers (M1), s shown in C14.2. Otherwise cktrck to the penultimte score rcket. Try to find nother piring in the penultimte score rcket which will llow piring in the lowest score rcket. If in the penultimte score rcket P ecomes zero (i.e. no piring cn e found which will llow correct piring for the lowest score rcket) then the two lowest score rckets re joined into new lowest score rcket. Becuse now nother score rcket is the penultimte one, C13 cn e repeted until n cceptle piring is otined. Such merged score rcket shll e treted s heterogeneous score rcket with the ltest dded score rcket s S1. Decrese P1, X1, Z1, M1 For homogeneous score rckets: As long s P1 is greter thn zero, decrese P1 y 1. If P1 equls zero the entire score rcket is moved down to the next one. Strt with this score rcket t C1 Otherwise, s long s X1 is greter thn zero, decrese X1 y 1. In even rounds, s long s Z1 is greter thn zero, decrese Z1 y 1. Restrt from C3. For heterogeneous score rckets: 1 If the piring procedure hs got to the reminder t lest once, reduce P1, X1 nd, in even rounds, Z1 s in the homogeneous score rckets

10 nd restrt from C3. 2 Otherwise, s long s M1 is greter thn 1, reduce M1 y 1 nd restrt from C3. If M1 is one, set M1=0, mnge the rcket s homogeneous, set P1=P0 nd restrt from C2.. D Trnsposition nd exchnge procedures D.1 Trnspositions D1.1 Homogeneous or reminder score rckets Exmple: S1 contins 5 plyers 1, 2, 3, 4, 5 (in this sequence) S2 contins 6 plyers 6, 7, 8, 9, 10, 11 (in this sequence) Trnspositions within S2 should strt with the lowest plyer, with descending priority

11 : To e continued. (t ll 720 figures) D1.2 Heterogeneous score rckets The lgorithm is in principle the sme s for homogeneous score rckets (See D1.1), especilly when S1 = S2, If S1 < S2 the lgorithm must e dpted to the difference of plyers in S1 nd S2. Exmple: S1 contins 2 plyers 1, 2, (in this sequence) S2 contins 6 plyers 3, 4, 5, 6, 7, 8 (in this sequence)

12 The trnspositions within S2 re the sme s in D1.1. But only the S1 first listed plyers of trnsposition my e pired with S1. The other S2 S1 plyers remin unpired in this ttempt. D.2 Exchnge of plyers (homogeneous or reminder score rcket only) When pplying n exchnge etween S1 nd S2 the difference etween the numers exchnged should e s smll s possile. When differences of vrious options re equl tke the one concerning the lowest plyer of S1. Then tke the one concerning the highest plyer of S2. Generl procedure: Sort the groups of plyers of S1 which my e exchnged in decresing lexicogrphic order s shown elow in the exmples (List of S1 exchnges) Sort the groups of plyers of S2 which my e exchnged in incresing lexicogrphic order s shown elow in the exmples (List of S2 exchnges) The difference of numers of plyers concerned in n exchnge is: (Sum of numers of plyers in S2) (Sum of numers of plyers in S1). This difference shll e s smll s possile. When differences of vrious options re equl: Tke t first the option top down from the list of S1 exchnges. Tke then the option top down from the list of S2 exchnges. After ech exchnge oth S1 nd S2 should e ordered ccording to A2 Remrk: Following this procedure it my occur tht pirings lredy checked will pper gin. These repetitions re hrmless ecuse they give no etter pirings thn t their first occurrence. Exmple for the exchnge of one plyer: S S

13 exchnge plyer 5 from S1 with plyer 6 from S2 : difference 1 2. exchnge plyer 5 from S1 with plyer 7 from S2 : difference 2 3. exchnge plyer 4 from S1 with plyer 6 from S2 : difference 2 Etc. Exmple for the exchnge of two plyers: S1 5,4 5,3 5,2 5,1 4,3 4,2 4,1 3,2 3,1 2,1 S2 6, , , , , , , , , , , , , ,

14 10, Exchnge 5,4 from S1 with 6,7 from S2: difference = 4 2. Exchnge 5,4 from S1 with 6,8 from S2: difference = 5 3. Exchnge 5,3 from S1 with 6,7 from S2: difference = 5 4. Exchnge 5,4 from S1 with 6,9 from S2: difference = 6 5. Exchnge 5,4 from S1 with 7,8 from S2: difference = 6 6. Exchnge 5,3 from S1 with 6,8 from S2: difference = 6 Etc. Exmple for the exchnge of three plyers: List of S1 exchnges: 5,4,3 5,4,2 5,4,1 5,3,2 5,3,1 5,2,1 4,3,2 4,3,1 4,2,1 3,2,1 List of S2 exchnges: 6,7,8 6,7,9 6,7,10 6,7,11 6,8,9 6,8,10 6,8,11 6,9,10 6,9,11 6,10,11 7,8,9 7,8,10 7,8,11 7,9,10 7,9,11 7,10,11 8,9,10 8,9,11 8,10,11 9,10,11 1. Exchnge 5,4,3 from S1 with 6,7,8 from S2: difference = 9 2. Exchnge 5,4,3 from S1 with 6,7,9 from S2: difference = Exchnge 5,4,2 from S1 with 6,7,8 from S2: difference = Exchnge 5,4,3 from S1 with 6,7,10 from S2: difference = Exchnge 5,4,3 from S1 with 6,8,9 from S2: difference = Exchnge 5,4,2 from S1 with 6,7,9 from S2: difference = 11 Etc. Exct procedure for exchnge of N (N= 1,2,3,4..) plyers in scoregroup of P plyers Sort ll possile susets of N plyers of S1 in decresing lexicogrphic order to n rry S1LIST which my hve S1NLIST elements. Sort ll possile susets of N plyers of S2 in incresing lexicogrphic order to n rry S2LIST which my hve S2NLIST elements To ech possile exchnge etween S1 nd S2 cn e ssigned difference which is numer defined s: (Sum of numers of plyers in S2, included in tht exchnge) - (Sum of numers of plyers in S2, included in tht exchnge) In functionl terms: DIFFERENZ(I,J) = sum of numers of plyers of S2 in suset J sum of numers of plyers of S1 in suset I This difference hs minimum DIFFMIN = DIFFERENZ (1,1) nd mximum DIFFMAX = DIFFERENZ (S1NLIST, S2NLIST)

15 Now the procedure to find the exchnges in correct order: 1 DELTA = DIFFMIN 2 I=1 J=1 3 If DELTA = DIFFERENZ(I,J) then do this exchnge, fter tht goto 4 4 if J < S2NLIST then J=J+1 goto 3 5 if I<S1NLIST then I=I+1, J=1 goto 3 6 DELTA =DELTA+1 7 if DELTA > DIFFMAX goto 9 8 goto 2 9 The possiilities to exchnge N plyers re exhusted After ech exchnge oth S1 nd S2 should e ordered ccording to A2 D.3 Moved-down plyers exchnge Exmple: M0 is 5; The plyers originlly in S1 re {1, 2, 3, 4, 5} The elements in S1 strt with the M1 highest plyers, then with descending priority: S1 elements in descending priority M1 = 5 M1 = 4 M1 = 3 M1 = 2 M1 = M0 = D.4 Note for progrmmers: B.3-fctor in the lowest score rcket After repeted pplictions of rule C13, it is possile tht the lowest score rcket (LSB)

16 contins plyers with mny different scores nd tht there re multiple wys to pir them. Such rcket either is homogeneous (when the numer of plyers coming from the penultimte score rcket is equl or higher thn the numer of LSB plyers) or eventully produces homogeneous reminder. The following rule must e followed y piring progrms: The est piring for such homogeneous score rcket or reminder is the one tht minimizes the sum of the squred differences etween the scores of the two plyers in ech pir (clled B3- fctor). Getting the ye is equivlent to fce n opponent with one point less thn the lowest rnked plyer (even if this is resulting in -1). Exmple: Let the following e the plyers in the LSB: 3.0 : A 2.5 : B, C 2.0 : D 1.5 : E 1.0 : F F cn only ply ginst A. The piring will initilly strt with S1={A,B,C} S2={D,E,F} nd, fter few trnspositions, it will move to Png1: [S1={A,B,C} S2={F,D,E}]. Work is not finished, though. Some exchnges must e pplied to get to Png2: [S1={A,B,D} S2={F,C,E} ] which is the est possile piring. This is ecuse of the B3-fctor. Let us compute it: Png1: (A-F, B-D, C-E) => (2.0* * *1.0) = 5.25 Png2: (A-F, B-C, D-E) => (2.0* * *0.5) = 4.25 Wrning: if there is seventh plyer (G) with less thn 2.5 points, who is the only one who cn get the ye, the LSB is heterogeneous nd no exchnges in S1 re llowed. In such n instnce, the piring of the LSB is: A-F, B-D, C-E, G(ye) Remrk: This lgorithm is nothing especil. It is the est mthemticl method to find the pirings which n riter seeing ll the plyer s dt nturlly will chieve. E Colour Alloction rules For ech piring pply (with descending priority): E.1 Grnt oth colour preferences E.2 Grnt the stronger colour preference E.3 Alternte the colours to the most recent round in which they plyed with different colours E.4 Grnt the colour preference of the higher rnked plyer E.5 In the first round ll even numered plyers in S1 will receive colour different from ll odd numered plyers in S1

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