The Conundrum Of Coincidence

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The concept of “coincidence” was a thorny problem for philosophers starting from the ancient Greeks. Plato, in Phaedo, defined “inquiry into nature” as a search for “the causes of each thing; why each thing comes into existence, why it goes out of existence, why it exists”. Aristotle went further, developing a theory of causality, commonly known in modern times as “the doctrine of the four causes” which made the search for cause and an explanation of the processes which lead from cause to outcome the central tenet of what would become “natural philosophy” and, eventually, “physics”. The Aristotelean view of the universe is one in which all events, by definition, have a cause, and there is no such thing as chance; and without chance, coincidence cannot exist, only the illusion of coincidence.
It was early research into quantum theory that challenged and overthrew this deterministic perception of reality, but because Quantum Mechanics is perceived as hard to understand, there were many people who had philosophical objections, most famously including Einstein. Nevertheless, the Quantum view of reality has slowly won on every point in the debate, and is no longer under any serious doubt.
Nor, for the purposes of examining the role of chance in the universe, and hence the scope for coincidence, is it all that difficult to understand. Essentially, it comes down to:
- Chance determines the outcome of certain subatomic events – not just when they will happen, and what the outcome will be, but whether or not they will happen at all.
- This is not a completely random selection of outcome, it is a chance determination of which of a narrow group of possible outcomes will result.
- These events normally occur on too small a scale to affect the macroscopic world, but occasionally, consequences can cascade like falling dominoes to have an impact on a larger scale.
- The probability of this happening on any given case is infinitesimal but there are so MANY different particles experiencing random outcomes that it is inevitable that macroscopic chance events occur constantly. The larger the system under observation, the more such events will occur.
- Nevertheless, the observable trends dictated by natural law are so dominant, and the random chance events are so constrained by the limited potential for interactions that result from those limited choices of outcomes, that the universe has an emergent property of apparent determinism. Only in inherently unstable systems can outcomes become impossible to predict over any length of time.
- ALL systems are inherently unstable to some degree, and the level of instability therefore determines the difficulty in predicting events and outcomes within that system over a given period of time. Or, to put it another way, the reliability of a forecast is dependent on the interval into the future of the forecast and the level of instability of the system.
- Thus, weather is very hard to predict reliably; and when we roll a die, the number that comes up is essentially random, but the certainty that one of the numbers showing WILL come up is incredibly high. much higher than the probability of the dice standing on an edge, even on an inclined surface (what my gaming group calls a “cocked die”, requiring a re-roll), and much, MUCH higher than the likelihood of the dice spontaneously becoming a lemon tart when rolled.
- One of the most unstable situations that can be contemplated involves human perceptions and decision-making. We still don’t clearly understand the role that individual neurons have in behavior, but the reality is that only a relatively small number need to experience a different outcome to significantly change the behavioral choices of the individual. Again, established patterns and trends dominate sheer chance – so people tend to have relatively consistent personalities and abilities – but chance has a far greater role in decision-making, and hence is far more likely to cascade into measurable differences in outcomes where a single individual is concerned.
- Which means that coincidences in the field of human behavior, and the consequent interactions between people, can and do happen, and are a real and measurable phenomenon.
Yet, the Aristotelean, Deterministic, Newtonian, “Classical Physics” understanding of the universe implicitly denies chance. Hence the problems, and the conflicts, between that view of the universe and the world of Quantum Mechanics.
It’s not much less of a problem for GMs.
Coincidence, for better or worse, is a recognized phenomenon whenever random chance dictates the outcome of events, and that happens in the real world all the time at a quantum level, and quantum effects cascade and grow into manifestly different outcomes at the macroscopic scale. It is also a recognized phenomenon that occurs whenever free will enters the picture, because people are almost as unpredictable as quantum collapse, or perhaps even more so – at least a quantum possibility can only collapse into a small number of pre-definable outcomes. Thinking is fuzzier, and more flexible, than that.
It follows that coincidence is necessary within any game world for credibility, and therein lies the paradox; players know that the GM controls the world, and therefore that the world they inhabit is inherently deterministic. Coincidence cannot occur in such an environment, not by chance; and so the presence of coincidence undermines credibility. Whenever something happens by coincidence, players assume that “coincidence” is GM code for “important piece of the plot”!
How can this dilemma be resolved?
Past practice
In the past, it was my practice to simply avoid coincidence at all costs. I would ensure ironclad justification for everything that happened, even if the mechanisms were not always evident to the players at the time. In many ways, this policy served me well; months after the event, the players might stumble across some scrap of paper or planning that locked into game canon part of this justification, and by the time the campaign came to an end, the whys and wherefores had all been explained. The only X-factors with which they had to contend were their own decisions and random rolls of the dice – and they expected me to fudge those from time to time, despite ample evidence that I didn’t do so.
But that involved a lot of work, and I was never completely convinced that all of it was necessary.
The Possibility Of Justification
Eventually, I realized that the possibility of justification was enough. It didn’t matter if there was genuinely a plausible explanation or not, just that such an explanation was possible; there was no need to provide verifiable proof.
Surprisingly (to me at the time), my games markedly improved immediately. This was because I didn’t have to labor at cementing every logical brick into place; I simply ensured that there could be a logical explanation and moved on. This freed up considerable time to polish other aspects of the game. When the players encountered an apparent coincidence, they either formulated their own explanation or simply assumed (from my past practice) that there was one that they weren’t seeing, and moved on. Play sped up, and became more dynamic.
Still, the conundrum that I posed at the start of this article nagged at me, until relatively recently, I instituted a change of GMing policy, quietly and without fanfare.
A Change of Policy
Besides the obvious and established “not a coincidence” explanation afforded by the possibility of justification, I introduced three other explanations for coincidences occurring:
- Coincidences just happen sometimes
- The convergent evolution of plot events
- Predestiny doesn’t have to be predictable
Coincidences Just Happen Sometimes
Every now and then – and I’ll get into the timing in a moment – I simply have something happen by coincidence, with no master plan, no relevance to events, and quite evidently, no need for explanation beyond these four words: “Coincidences Just Happen Sometimes.”

Logo of the villainous corporation, “Monochrome”
The Convergent Evolution Of Plot Events
Sometimes, what appears to be coincidence isn’t, but instead is an inevitability in some shape or form.
For example, one of the PCs in the Zenith-3 campaign was putting in some hours at a nominated charity – working in a soup kitchen for the homeless – when she was approached by a homeless man and asked to help find his friend, Harry. At the same time, another PC, in a completely different part of the city, was encountering four homeless people who had been subjected to experimental cyber-surgery and sent to rob a bank in order to test the military-spec prototype upgrades, the established M.O. of a shady organization known as Monochrome. (These four were not informed that they had also been fitted with phosphorous grenades to ensure that no matter how the experiment turned out, no evidence would lead back to the perpetrators).
This seems, on initial glance, to be coincidence of the most heavy-handed kind, but was it? The missing person had been gone for long enough to have the cyber-surgery and for the wounds so inflicted to heal. PC one works with the homeless regularly, and is known to help many people who ask for it; with the Police uninterested, the NPC had little choice but to accept the situation until the opportunity to approach the PC presented itself. In any event, this was the first opportunity that he would have had, because the PC had been busy doing other things recently.
Nor could Monochrome wait very long before testing their prototype hardware. There was always a risk that this time, the police would take an interest, or that the publicly-known and recognized PCs would tumble to things. So it was inevitable that the disappearance report and the criminal activity would be closely-connected in time.
Finally, given who the PCs were (the superheroes of this world, complete with government sponsorship), when four cyberpunks of unknown capability with unrecognizable equipment made a public appearance, if a PC had not happened to be nearby, the PCs would have been called in to deal with the situation.
The dominoes were in motion, and their fall, inevitable. This, of course, is an example of “The Possibility Of Explanation”.
Predestiny Doesn’t Have To Be Predictable
Thirdly, let us say that for plot needs, it is predestined, predetermined, or prophesied that a given event will take place. It might even be predestined that it involve one of the PCs. None of that explains why or how the PC becomes involved; chance or coincidence can be just as plausible a reason as any. But, if the event is occurring for metagame reasons, is that really chance? This takes the frequent player assumption, and accepts it – some things DO happen for metagame reasons.
The Inevitability of Causality
Finally, things aren’t a coincidence if someone deliberately engineers them to occur that way. If a villain has been heavily investing his time in, say, Temporal Magic, or Energetic Particle Research, it’s not exactly a surprise when they make a breakthrough in the field, nor that they would turn this discovery to villainous ends. Their involvement in a plotline that starts with the deployment of such technology is therefore no coincidence at all – they are either responsible, or they want the knowledge of the person who is.
The 1:3:1:1 ratio
I said earlier that I would get into the question of timing, i.e. the frequency of coincidence after explaining the different “modes” of coincidence.
I try to maintain the ratio given in the subsection title overall. The first number is the occurrence of true coincidence, no matter how trivial; the second refers to the “Possibility Of Explanation”; the third to an occasion in which the appearance of coincidence is actually an error in logic, or to metagame causes in other words; and the fourth to the frequency of occurrences that aren’t coincidences at all.
This ratio permits enough randomness for coincidence to be plausible, while ensuring that most of the time (five-sixths, in fact) there is some other explanation – only one of which is the GM metagaming, and a relatively minor one at that. It keeps everything at acceptable and plausible levels.
Player Dismissal
Players will not accept coincidence as an explanation for events save as a last resort. That’s fine by me; let them think paranoid thoughts, it’s very entertaining to watch!
There is no such thing as coincidence – in reverse
Often, as a result, players will go to great lengths to explain away apparent coincidence. That’s fine, too – I listen to them speculate, and if I like their line of thought, I give it a home in the game reality. If not, I assume that there’s some other explanation.
That’s where things get interesting. Their decisions and actions will be derived from a mis-perception as to the cause of events. If there’s an obvious error in logic, I give a character – PC or NPC – who hasn’t yet voiced enthusiastic support for the theory an intelligence check to spot the flaw; if they fail, they fail. If everyone has come out in favor of it, I make a secret roll for the character with the highest INT to spot the flaw just after the PCs have gotten themselves in trouble through their incorrect assumption.
This only becomes a problem when there is too great a gap between interpretation and correction. After a while, what was speculation becomes accepted dogma, and that’s far harder to correct. As soon as I get the impression that this is taking place, someone will raise doubts about the conclusion.
Sometimes, a coincidence is just a coincidence
More often, though, players will simply default to dues-ex-machina assumptions, i.e. that it’s the GM pulling strings. But, so long as they can also assume that the motivation for doing so is to create more fun for everyone, neither they nor I have any reason to complain. And that’s how I solve the Coincidence Conundrum.
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October 16th, 2015 at 1:36 am
It’s when GM has coincidence and the players want an explanation. That gets my cogs spinning. Good read, yet again Mike
October 16th, 2015 at 3:23 am
Thanks, Symatt. Yes, it can present quite an opportunity to the GM if he can take advantage of it!
October 20th, 2015 at 5:14 am
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May 5th, 2017 at 1:45 am
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