In talking about Muck & Brass recently I mentioned that there were no tiebreakers. Your net worth was your score and that was it. This was not popular. The general response was that tie breakers were necessary and required, that there always had to be, if at all possible, a singular clear winner. Examples such as money in Power Grid, track in Age of Steam, and the ever so many layers of tiebreakers in King of Siam were given as the Way It Should be Done
Other’s more public comments on ties (in no particular order):
Shannon offers three acceptance criteria for tiebreakers:
- unique (ideally)
Which on the face of it is reasonable. If you are to have a tiebreaker then by the Principle of Least Surprise and be obvious and fair as anything else would be potentially surprising. The uniqueness requirement merely prevents a chain or cascade of tie breakers, with satisfies both Occam’s Razor and the general rules of simplicity. However Shannon doesn’t really attempt to justify the existence of tie breakers behind the somewhat circularly self-justifying:
Either the game explicitly says there is no tie-breaker, or else just doesn’t mention one. Besides being anticlimatic, it feels lazy on the part of the designer. I think some game designers feel like they can get away with it because you earn enough points that a tie is pretty unlikely … but they will come up sometimes.
I’m less convinced that tie breakers are either an automatic default design assumption or default requirement.
Two quotes appear to sum the brunt of Jim’s arguments:
Why? Is it really a further test of skill to have a sudden death? Is it really a test of skill in a board game to have a tie breaker that has nothing to do with the normal goal of the game?
Yes and no.
The obvious answer is that since the rules of the game include rules for breaking ties, then players must account for any and all possible outcomes. This affects their choices during the game. It is a skill to be able to win by rule A, and if not then to win by rule B, etc.
But at some point–in some games–it seems like the rules go to great length to pick an arbitrary winner from the set of those players who tied. This really doesn’t interest me. Might as well roll a die to see who wins. Might as well just share it.
…I do feel in many cases that tie-breakers are thrown in at the last minute. They have no relationship to the flow of the game, have some player order bias, or are simply based on luck.
This appears to be a rephrasing of Shannon’s arguments around obviousness, fairness etc.
Seth Jaffee argues two sides: first that ties and ties breaks are a reasonable form of measurement of the accomplishment of the player and second, that one player should win the tie breaker because they took a more difficult route to the tie, or somehow accomplished more or accomplished it more efficiently.
The accomplishment measurement argument for tie breaks is reasonable. It makes sense from the view of game scoring as a measurement of the incremental solution of the central game problem but in doing so it unflatteringly reveals the weakness of the original game’s scoring method. Seth argues that some measured incremental items are worth more than other such items; ie doing X which is rewarded with 2 VPs is somehow worth marginally more than doing Y which is also rewarded with 2 VPs. In which case, why isn’t X worth 3 VPs or the whole scoring system scaled so that X is worth 2,001 VPs and Y worth 2,000 VPs or some other such disambiguation ratio?
Such combinations of large/small values is fiddly and annoying to score as well as rather distracting for the players. I just got 37,000,000,000,003 points for building that bridge and you only got 37,000,000,000,001 for that redoubt! Ptui. Clearly such a scoring method is inconsiderate and incompletely designed. Or is it? Having X be worth 2+epsilon VPs and Y be worth 2 VPs really just establishes that there are two ranks of scoring: the big important values (whole VPs) and the tiny details (epsilon) where the epsilons don’t matter unless the items need to be sequenced in value order. The assumption is that players will rarely need to sequence order and that the primary focus is on broad score patterns and not epsilon details. Fair dinkum.
Seth’s second argument is where I think the argument begins to break down: that one player should win the tie break because they took a more difficult route to the tie, or somehow accomplished more during the course of the game or accomplished it more efficiently. At a simple level this is just another case of the epsilon argument discussed immediately above: there are primary scoring items and some of them are accompanied by epsilon scoring riders where the epsilons are only calculated in the event of a tie as they are otherwise negligible. At that simple level I have no over-riding problem with such tie breakers though I find the extra layer of epsilons annoying and almost certainly unnecessary.
On the gripping hand outside of the epsilon argument, the implication that there is some sort of should, that somehow the players morally deserve to win the tie breaker because of in-game activities is preposterous. The game defines a win-metric. The players either accomplish that win metric or they don’t. It is a binary condition. There is no place for external morality in gaming or win-determination – the game rules define the only morality measured in the game.. It is a simple question of logical definition: the win-condition is XYZ and they either meet that criteria or they don’t. If multiple players meet the win-criteria then multiple players win. Each of them, individually, satisfies the win-definition defined by the game, ergo they win. At this level the win-criteria trump and there are no other discriminating or disambiguating factors. Whether the racers ran uphill or down hill before crossing the finish line is irrelevant: did they cross the finish line first? The finish line –that’s the only metric that the game’s win-condition supplied and thus it is the only thing measured. Of course if the designer deigns to provide additional criteria the situation is different because the win-conditions are different.
Sensei’s wiki/blog discusses a number of tie-breaker methods, albeit with a rather Go-centric focus (please see the source page for links to the discussion and more detailed evaluations and definitions):
Rematch: Breaks ties by having the players play extra rounds. Also known as play-off. This is generally considered a good method, but its use is often not possible due to time constraints.
Direct Comparison: Often used in a tie between only two players, considering the match between these players as a substitute for a play-off. Called “Face to Face Result” by the AGA. Not widely implemented in software.
SOS: sum of the opponents scores, also know as Buchholz or Solkoff in Chess. Several variants exist which attempt to eliminate noise by discarding some results (eg: SOS-1, SOS-2, Median or Modified Median). Does not work for round robin.
SOSOS: sum of the opponents of the opponents scores. Generally only used as a secondary tie breaker after SOS.
SODOS: sum of the defeated opponents scores, also known as SonnebornBerger in Chess. Is adviced against in McMahon tournaments, because players with the same score do not necessarily have the same number of wins. Often used in round robin tournaments.
CUSS: expected average strength of the opponents, also known as Sum of Progressive Scores (or, simply Progress) in chess
ROS: expected average strength of the opponents with extra bonus for winning more games
IROS: inverse ROS, see ROS-Page
SOP: (theoretical) sum of placing of opponent (nickname suposition)
SOR: (theoretical) sum or ranks
Maximum Likelihood: a mathematical method to determine the player most likely to win, not easily calculated by hand.
Random tie-breaker: tie-breaking at random, used as a last resort.
OOF: Order of Finishing
A nicely thorough list.
What is more interesting is that the list is almost exclusively phrased in terms of tournament ranking systems (and he’s not the only one to take that focus). There is also some discussion that none of the the listed tie-breaker methods are ideal; they are all compromises. This should begin to ring bells and prompts my observation that:
Tie breakers are tools to disambiguate and order members of a set in a “fair” way based on subjective evaluation of supposedly objective criteria.
Yeah, functionally tie breakers are voting or election systems. Tie-breakers order members of a set by previously established preference criteria. Hang on, so do voting systems, just with the addenda of polling/metrics gathering and also with all the same systems-gaming that tie-breakers have. Happily voting and election systems are a well-known field. What’s most useful about this observation is that, simply, there are no fair and equitable voting or election systems. Without exception they all have weaknesses, weaknesses that their counter-representations in tie-breakers also share.
A few key quotes:
In a number of games I own there is no provision made for what happens when two or more players wind up with the same score. The creators of these games either imply or outright say that both players are winners. Now this does not sit well with me. I want clearcut rules of victory and defeat, with each player knowing where they stand at game’s end and why.
This is not simply an ego issue (“me better than you; me win”). But in running games at cons, there are often prizes that ride on wins and losses. When I look at games that do have good rules for resolving ties, I place these into my “con-friendly” list.
I like ties, as long as they aren’t too frequent. It’s a matter of taste as to what counts as “too frequent”, and probably depends on the game.
I actually like games that can end in ties, and in fact tend to feel that roughly 25-30 percent of a game’s outcomes should be ties. I also find it particularly annoying when a game includes tie-breaker provisions that are clearly arbitrary add-ons to the game (rather than carefully thought out design elements) in order to cater to the hard-line “there can be only one” crowd.
Then you don’t understand the real problem–a tiebreaker should not be arbitrary, but somehow naturally flows from the flow & goals of the game. If not, then you are not playing the to be the best player of the game, but of some unplaytested variant.
I dislike the possibilities of a tie. There should, in my simple dualistic mind, be only one victor. This is, again, fairly important for those of us who run tournaments. But I also walk away dissatisfied when there are multiple winners in a game – unless it’s a co-op.
How about a disclaimer stating that this game is prone to ending in ties and that if the tournament ends in a tie, that the winners will be splitting the prize equally?? (i.e., assuming it is a cash prize).
I think we are solving the wrong problem. I don’t mind a tie score in a game, if the game play was even. It is playing in a tournament that is the problem!
In short these sum to two dialectic pairs:
- Ties are utterly unacceptable, there must be only one winner and some number of losers, always
- Ties are acceptable and even desirable as long as they’re not too frequent (by some subjective evaluation)
- Tournaments require unambiguous winners, thus ties are unacceptable in tournaments
- Tournaments could be (re-)defined to accept and respond appropriately to ties
The first dialectic pair is a preference statement. It is undebatable. That is what they prefer for unquestionable internal reasons. Whatever logic may be externally applied to it, their emotive bindings are set and thus unquestionable.
The second dialectic pair derives directly from the first and is thus also undebatable. If there must be only one winner of a game then by logical extrapolation, given that a tournament is merely a meta-game, there must also be only one winner of the tournament. This also works reflectively. Given that there must also be only one winner of the tournament meta-game, none of the component games may result in a tie as that would ambiguate the meta-game results. After all, were the tied component game resolved to an unambiguous winner, it could change the win-determination of the tournament. Clearly however there is nothing inherent in a tournament-definition that requires a single-winner determination. Tournaments could allow ties just as easily as their component games.
Much as I dislike tournaments (in sympathy with Tradewinds Ted above), it would be interesting to attempt a well-defined tournament system which both accepted ties in component games and attempted (or demanded) a single-winner determination for the tournament meta-game.
Tie-breaker justification – J C Lawrence
None of the above directly addresses the justification of tie-breakers as design components in the first place. Are tie breakers a valid component in game designs? From the emotive aspect of the dialectics just discussed they are clearly valid – some players demand them as part of the emotional coherence of the game definition. From a more mechanical vantage however they don’t seem either required or necessarily justified in the general case.
Mostly, I view tie-breakers as clearly visible and even flaunted flaws in their subject game designs.
There are of course exceptions. I’ll discuss one below.
Tie-breakers suggest a few things:
- Ties are common
- Ties are hard for the players to prevent/beat
- Ties should be avoided.
That last one is of course a doozie. As there’s no reasoning with it I won’t attempt to reason with it. To ape the great Bugs Bunny, It is a maroon.
The first two are more interesting. Some games inherently encourage ties. In fact a few games, such as King of Siam, are explicitly based on the premise that the game will naturally tend toward ties. King of Siam has an extensive cascade of tie breakers and during the course of the game the players attempt to wield that cascade of tie-breakers offensively in a massive iterated game of Chicken, putting the system into un-tied win-conditions for themselves and at other levels back into a tied lose-condition against the other players (King of Siam is an unusually clever game) at different levels of the tie-breaker cascade. Clearly such a game depends utterly on the manipulation of tie-breakers and thus must have those tie-breakers merely to function. By definition tie-breakers are a valid design tool for such games. But, most games aren’t so focussed on tie-breakers. In most games, ties are rare and it is the rest of the field I question.
Most of the apparent need for tie-breakers appears to be emotional. I won’t address that. However what do tie-breakers offer game definitions and thus what do they offer game designers? Seth Jaffee again:
A tiebreak rule can be used to subtly counterbalance a favorable (or unfavorable) starting position, much the same way that the first player in some games starts with fewer actions in the first round, fewer points, or less money than the later players. Nobody complains about those rules being arbitrary.
Tiebreak rules can be used to reward a player for accomplishing the game’s goals more efficiently than another player - to finish with the same score, but with resources to spare.
Tiebreak rules can also be used by a designer to show a preference for a particular strategic path - be that for thematic reasons, or because that path was the one the designer thought most interesting.
- Tie-breaker as a game-balance factor
- Tie-breaker for efficiency
- Tie-breaker as incentive toward desired play-paths/patterns
The efficiency argument and even the game balance factor are a restatement of the epsilon argument addressed above. The game balance point is perhaps a little more subtle, but in essence is the same as the many majority/plurality games which state that the first one in is the default winner of the contest (eg Medieval Merchant, Die Neuen Entdecker, etc): another phrasing of epsilon.
I’m not aware of any games which use the incentive argument in their designs. It also isn’t compelling. The concepts of the right way to play game or the spirit of a game or the significance of the designers intent for the game are all external valuations that don’t bear on a game’s definition:
A game is an isolated self-defined logic system that consists of a number of goals, defined abilities that may be used to accomplish those goals, and barriers that hinder accomplishment of those goals.
Everything else is post-definition subjective evaluation.
A game is a goal-focussed system for players to manipulate in a laissez faire manner within the constraints of the game rules.
There’s no style or spirit of designer’s intent there, just goal-based player self-interest. To quote the immortal Michael Lawrie:
Do what thou wilt shall be the whole of the law. I am the law!
The game rules are the law and that leaves the mechanical value of tie-breakers (for most games) as epsilon systems, and much more interestingly, as epsilon systems whose simplest and clearest definition is null! If a player wants to unambiguously win a tie-breaker-less game they must end the game without a tie.
A game without a tie-brekaer offers a tri-state:
And that is the challenge: The winner must clearly exceed the other players, ergo they must provide their own disambiguating epsilon to give themselves the clear win or risk losing the tie. A designer-provided tie-breaker removes that challenge and arguably to that extent weakens the game definition and the required quality of play. It also makes the game more forgiving: players can win without unambiguous excess and for some games and designers that may be a desirable game-quality. Those qualities of forgiveness and weak/gentility are simply uninteresting for me and my designs. I don’t want to design either weak or forgiving games, I’d rather design games that punish and stress-exercise their players, and as a result I do not expect to use tie-breakers in the final scoring methods of any of my games unless the base game is explicitly tie-focussed.
As always, you get to pick. Pick wisely.