Section 3 – Tie-breaks

While Sonneborn-Berger and/or Bilbao systems are often sufficient to break a tie in a tournament, the systems above as any other truly fair tie-break system don’t always can break a tie in a match.
The ranking from the double-round-robin can be used in the subsequent matches as further tie-break (Sys.15 below, as seen in Opt.2.1 and Opt.3.1). However it’s rare but also all the mentioned systems could fail to break a tie in a tournament: the most evident case is a tournament 100% full of draws.
So, when all is done, a final “luck based” tie-break is necessary. Before making “Heads or Tails” (drawing of lots or coin flip), however, in my opinion it’s better to consider the player’s results from the previous Cycle, as tie-break (especially if some privilege for the Word Champion is taken into consideration, see Section 4): in this case who is the title-holder (i.e. he is the reigning World Champion), has an higher rank, then who won a final in the previous Cycle, then who won a semi-final, then who had an higher score in the double-round-robin of the previous Cycle.
To have an overall view, these below are all the systems used in the Cycle:

Tournament.
Sys.1) Normal score (Win=1, Loss=0, Draw=½).
Sys.1c) Bilbao score conditioned (Normal score, if 1st halfgames=75%draws then Win=3,Draw=1)
Sys.2) Sonneborn-Berger (sum of opponents score in wins + ½ sum of opponents score in draws).
Sys.2c) Sonneborn-Berger conditioned (sum of opponents “Bilbao score conditioned” in wins + ½ sum of opponents “Bilbao score conditioned” in draws).
Sys.3) Score in games played between the tied players.
Sys.4) Bilbao score (Win=3, Loss=0, Draw=1).
Sys.5) Sonneborn-Berger for Bilbao score (sum of opponents Bilbao score in wins + ½ sum of opponents Bilbao score in draws).
Sys.6) Sonneborn-Berger modified (Sonneborn-Berger - ½ sum of opponents score in draws with <40 moves as White).
Sys.6c) Sonneborn-Berger modified conditioned (“Sonneborn-Berger conditioned” - ½ sum of opponents “Bilbao score conditioned” in draws with <40 moves as White)
Sys.7) Sonneborn-Berger for Bilbao score modified (Sonneborn-Berger for Bilbao score - ½ sum of opponents Bilbao score in draws with <40 moves as White).
Sys.8) Koya System (sum of score of opponents with score>50%max, if it ties then>49%,>51%,...).
Sys.9) Ranking from the previous Cycle (better results gives an higher ranking, as seen above).
Sys.10) Drawing of lots.[the Black-privileging Sys.12 below is used as last resort in tournament]

Match.
Sys.11) Number of games won.
Sys.12) Number of games won as Black.[more a Black-privileging tie-break than an anti-draw Sys.]
Sys.12c) Number of games, after the 4th game, won with <60 moves as Black.
Sys.13) Number of games drawn with <40 moves as Black.
Sys.14) Vella System (lower least number of moves in games drawn with <40 moves as Black).
Sys.15) Ranking from the previous double-round-robin tournament (where Sys.2-9 was used)
Sys.15L) Drawing of lots (Sys.10 wasn’t used for Sys.15 to not begin a “luck-privileged” Match).

Play-off mini-match.
Sys.16) Play-off mini-match system.
The player who has the higher ranking from the tie-breaks in match (from Sys.12-15L, as seen in Section 2 giving him a “colour-choice-privilege” or a “colour-decisive-privilege”) will play all games as White. If he wins a game then he wins the match, if he loses a game then he loses the match, if he draws a game then he will play the next game. I’d advice 2 games for this mini-match, but it’s not necessary: likely an organizer may not offer it at all for the further days in scheduling.


Play-off last game.

Sys.17) Armageddon with “colour-choice-privilege”.
The player who has the higher ranking from the tie-breaks in match (from Sys.12-15L, as seen in Section 2 giving him a “colour-choice-privilege”) or in tournament (Sys.2-10, if the organizer offer a play-off game after the double-round-robin) will play the final game as Black, in which if Black wins or draws then Black wins the match (he relies on a forcing draw preparation), or if he prefers as White in which only if White wins then White wins the match (he relies on an aggressive preparation); if he doesn’t win the match in this way then he lose the match.

Sys.18) Armageddon with “colour-decisive-privilege”.
The player who has the higher ranking from the tie-breaks in match (from Sys.12-15L, as seen in Section 2 giving him a “colour-decisive-privilege”) will play the final game as White, in which if White wins or draws then White wins the match (White could easily force a draw and Black has only a desperate last chance); if he doesn’t win the match in this way then he lose the match.

I haven’t specified but it’s obvious: there are no rapid or blitz games.
In my opinion a World Champion with some “Forcing draw” specialization is most reliable than a World Campion with “Blitz games” specialization.
After all each player is there just to play Classical Chess, and organizers could easily arrange the usual one additional day for tie-breaks (for the “Armageddon”, while “Play-off mini-match” and “Two-stages system” remain an option for organizers to be elected, see Section 1).

Resuming, Sys.1-18 will be applied according to elections from Q.2 + Q.3 (see section 2) in this way (the order between “-“ signs means that if a system doesn’t break the tie, then the subsequent is applied, while the “*” means that the system could not to be applied due to organizer’s scheduling):

Opt.2.1+3.1 > Sys.1-((2-3-8-9-10)+17*) + 11-((15-15L)+16*+17)
Opt.2.2+3.1 > Sys.1c-((2c-4-5-3-8-12-9-10)+17*) + 11-((12c-15-15L)+16*+17)
Opt.2.3+3.1 > Sys.4-((5-3-8-12-9-10)+17*) + 11-(12+16*+18)-((15-15L)+16*+17)
Opt.2.1+3.2 > Sys.1-((2-3-8-6-12-9-10)+17*) + 11-((13-14-15-15L)+16*+17)

Opt.2.2+3.2 > Sys.1c-((2c-4-5-3-8-6-12-9-10)+17*) +
11-((12c-13-14-15-15L)+16*+17) (default)

Opt.2.3+3.2 > Sys.4-((5-3-8-6-12-9-10)+17*) +
11-(12+16*+18)-((13-14-15-15L)+16*+17)

Opt.2.1+3.3 > Sys.1-((6-3-8-2-12-9-10)+17*) +
11-((13-14)+16*+18)-((15-15L)+16*+17)

Opt.2.2+3.3 > Sys.1c-((6c-3-8-2-12-9-10)+17*) + 11-(12c-((13-14)+16*+18)-((15-15L)+16*+17))

Opt.2.3+3.3 > Sys.4-((7-3-8-2-12-9-10)+17*) +
11-((12-13-14)+16*+18)-((15-15L)+16*+17)


I suppose the most probable elected (obviously after Opt.2.2+3.2 because it’s the default, without unanimity) would be Opt.2.1+3.2 (if all players trust on fighting and valuable draws in tournament) and Opt.2.2+3.3 (if all players strongly try to avoid any short-draw in matches, or they just want to highly privilege Black who force a draw in less than 40 moves), then Opt.2.1+3.3.
One who doesn’t like the abovementioned privileges in matches probably doesn’t like any privilege at all in matches, and he’d vote for “Non-punishing short draws system” (Opt.3.1): unfortunately it means that he likes “Head or Tails” (because organizers don’t like any “unlimited games” format, as suggested by Fischer and as adopted in the 1984 Karpov-Kasparov match, left unfinished after 48 games). However, also in case of that unanimous vote (to elect Opt.3.1), the players might use “Heads or Tails” in the end of the match, but it doesn’t mean that a lucky winner will take home the match victory and the resigned loser will not have a chance to break the match tie: it means that the “Heads or Tails” loser will have a last chance trying to win with White pieces in an “Armageddon” Classical Chess game: if he lose or if he draw, with White, then he will lose that match.

In the default system in match (Opt.2.2+3.2), the main “degeneration” could be the pre-arranging #moves in dead draws to avoid the last resort to punish the draws (as short draws): i.e. if both players has voted Opt.3.1, then they don’t like the draws to be punished, and then they would prefer to pre-agree to stop all quick dead draws conventionally at move 25, in order to boycott the system and not being punished, but going in the further tie-break which considers the score in the previous tournament. In fact that pre-agreement shouldn’t be convenient for the player who has a lower score, so it’s not a real degeneration, rather it’s a way to try to degenerate the system, so I defy anyone to find a way to degenerate this system.
Note that in privileging Black when he is able to break White’s winning opportunities in <40 moves, this way not only deter White to play safe in surviving till move #40 in possible desired draws, but it also gives a balanced slight colour-privilege to Black: it’s more or less as statistics says (i.e. if this Black’s ability is roughly equivalent to the 5% of White’s wins in <30 moves, it’d cover the known 45% Black average score), but it’d be noticeable also in case I draw a game with the variant in my Black repertoire “1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.Nf3 g6 5.Bc4 Nb6 6.Bb3 Bg7 7.a4 dxe5 8.a5 N6d7 9.Bxf7+ Kxf7 10.Ng5+ Kg8 11.Ne6 Qe8 12.Nxc7 Qd8 13.Ne6 Qe8 14. Nc7 Qd8 ½-½” and I could give more value to my variant (instead of replacing it with another where White is better, possibly disliking the entire Alekhine Defense), pushing opponents to find other variants in their White repertoire not only to always have a way to try to win (at least against any Black variant like mine) but also to not give me a further privilege when I want to draw as Black.
On the other hand, to demonstrate how other proposed anti-draw systems are unbalanced (as the flat Bilbao system too or as the so-much-extolled BAP system which gives a seriously unbalanced colour-privilege to Black: Black win=3, White win=2, Black draw=1,White draw=0, any loss=0), there are innumerable examples of fine played draws, with or without a narrow or lucky way to save the game, which deserve half the value of a win (not only by an objective chess-playing point of view, but also statistically), but many people deter its value usually preferring exciting (are you sure?) lot of wins, instead of an elite of top-level played games.
To know more about the actual opinions regarding the tie-breaks go to these links:
http://en.wikipedia.org/wiki/Tie-breaking_in_Swiss-system_tournaments
[Excerpt: “Harry Golombek points out deficiencies in most of the tie-break systems and recommends a playoff if there is time. If not, he recommends Sonneborn-Berger and then the player who has the most wins”]
http://main.uschess.org/content/view/8602/468/
[Excerpt (GM Joel Benjamin agrees): “Full-length playoffs are the best solution if a tie must be broken. Organizers should set aside the time and money for a proper playoff if one is necessary.”]
http://www.chessbase.com/newsdetail.asp?newsid=7257
[Excerpt (Vladimir Kramnik interview): “If the match system is used, there must be definitely six or even eight games matches, because otherwise most of the matches might be decided in rapid or blitz, like in Kazan, and it makes little sense because it is a classical chess championship”]
http://www.chessbase.com/newsdetail.asp?newsid=2729
[Excerpt (John Nunn statements): “The Linares 2004 event has become notorious for its high draw percentage (79% draws and 33% short draws), but is this typical?”. “The three points for a win plan really makes a huge difference to tournament results and fundamentally changes the game. I don't see that such a drastic change is necessary”]
http://www.chessbanter.com/rec-games-chess-politics-chess/17978-bap.html
[Excerpt: “In an interview before his loss, Kramnik claimed that short draws were unavoidable because one needed an advantage in the opening to defeat a top grandmaster, and the best players are so well prepared that one must introduce a surprising new idea in the opening to obtain any advantage. This is a modern form of the "draw death" argument that world champion Jose Raul Capablanca raised in the 1920s. Fortunately, Kramnik is wrong. In the next game, his opening preparation extended all the way to a slightly inferior endgame that Black is supposed to be able to draw. Leko won anyway. Chess is not exhausted yet!”]