(Metagame Archive) Strength in Numbers: Just My Luck

By Olav Rokne

My recent trip to Atlanta has me thinking about luck.

I arrived at the airport at 8 AM with lots of time before my flight. The weekend started out with my flight being delayed seven hours. There were seventy-five flights that left Edmonton International Airport that day and only five of them were delayed, two for five hours or more. If we accept that my plane was probably of average size, then every passenger in the airport had about a 3% chance of being delayed by five hours.*

When I got onboard my aircraft, we discovered that there were more passengers than there were seats. There were fifty seats on the aircraft and fifty-three passengers. By random selection, I was determined to be one of three passengers to lose my seat. Any particular passenger had a 6% chance of losing his or her seat.

Because I had, at this point, missed several connections and every airplane seemed to be fully booked, I was unable to get a new flight until half past midnight. A very nice young woman at the ticketing counter told me that fully booked days like that one happen about twenty times a year. If you are just as likely to fly on any particular day (not deciding specifically to go on Spring Break or Christmas), you have about a 5.5% chance of flying on a fully booked day.**

It all seemed like bad luck.

But what are the chances of the stars aligning such that those circumstances get me to Atlanta at noon on Friday rather than on Thursday evening? About 0.009% (rounding up)—which means that what I experienced happens to about one in every 11,409 passengers.

The odds of that sound fairly bad until you consider that there are more than 1,000,000 people flying over the U.S.A. every day.

So (on top of the other two people who were booted from the same flight that I was), I experienced a set of circumstances that 31,990 people experience every year in the United States alone.

My frequent flyer card has racked up a rather shocking number of miles on it; between a dozen or so trips to Europe, scores of flights to and from the U.S., round-tripping to Australia, and miscellaneous trips within Canada, I would estimate that I’ve taken more than 200 flights. About one in fifty people who take that many flights will have the sort of delay I experienced on my trip to Atlanta.

So really, I was neither lucky nor unlucky. I experienced a somewhat negative event that had to happen to someone sometime.

Now what, you may ask, does this have to do with Vs. System? While I was in Atlanta on Metagame-related business, I had the opportunity to pay close attention to several drafts, games, and Sealed Pack constructions. The advantage of being an outside observer during games and drafts is that one can be far more sanguine about low-probability events of negative outcomes than those directly involved in the game.

Let us conservatively say that there are twenty cards in each deck without which a player cannot win unless he or she has drawn one of those cards by turn 3. We’ll term this low probability event of negative outcome a “deck implosion.” In a Squadron deck, this event works out to not playing a single character before turn 4.

Without taking into account a mulligan, every player has a 3.3% chance of a deck implosion in any particular game. When you consider that on the first day of the Pro Circuit, 1,650 games of Vs. were played, there were likely 55 deck implosions in the Constructed portion of the tournament. Since there were 330 players, there’s about an even chance that one of them accounted for more than one deck implosion.***

Multiple deck implosions mean the difference between a 7-3 record and a 5-5 record. There were likely players who were skilled and hardworking enough to make Day 2 but didn’t because of low probability events with negative outcomes.

It’s important to note, however, that the inverse is not true; it is usually not possible to salvage a game from a deck implosion through skillful play, but the associated positive event (which we’ll call a “deal of divine origin”) can be ruined by poor play. To compound this, if we accept that deals of divine origin are as uncommon as deck implosions, then such deals are unlikely to account for a 6-4 record.

When you’re looking at the numbers from the perspective of an overall tournament, these low probability events with negative outcomes look normal. But from the perspective of the poor sod whose deck has just collapsed, it seems like the universe is conspiring against them, and so they perceive it as luck.

A study conducted by Richard Wiseman of the University of Hertfordshire revealed that people who thought they were lucky in general in fact had statistically identical numbers of low probability events of a negative outcome as people who considered themselves unlucky.

Where the perception of “bad luck” becomes important, according to Wiseman’s recent book, The Luck Factor, is that those who think of themselves as lucky are more likely to see the opportunities presented by low probability events of a positive outcome.

The lesson for Vs. players is then evident—when things are not going your way, it isn’t useful to decry your luck. Rather, if you accept small negative events as something statistically inevitable, you can then look at the upswings of chance and be ready to take better advantage of them.

In Sealed format tournaments, perceptions of bad luck become even more prevalent. With the random element of pack contents, there are more opportunities for low probability negative events.

For example, in JLA Draft (the format that I observed over the course of the Pro Circuit), a number of players went with the understanding that the set had specific “power cards” that were vital to any Draft deck. These included but were not limited to: Gorilla Grodd; Sinister Citadel; and Martian Manhunter, J’onn J’onzz. These are clearly very good cards, but players can’t rely on getting exactly what they want in a draft. A complaint I overheard at mid-level Draft tables was, “I didn’t see a Grodd, so I don’t have a chance.”

Bad luck, as a concept, is particularly enticing because it makes it possible to blame chance for one’s failings.

$10K winner and all-around good guy Josh Wiitanen provided a perfect example of being prepared for different low-probability events. During his first draft of Day 2, I watched every card he drafted and thought he’d suffered a terrible bout of bad luck.

To my surprise, he told me later that it was “possibly the best deck he had ever drafted.” Despite a lack of the classic “power cards,” he had seen opportunities in what was passed to him. He went 2-1 in that pod.

* All numbers in this article have been rounded for the sake of convenience and ease of understanding. There are obvious assumptions made in the construction of this article, which I hope you will forgive me for. As an example, I have no way of knowing if the number of delays per flight on March 24 was indicative of larger trends, but it was the number I had to go on.

** Please forgive me for not taking leap years into account. The extra day makes very little statistical difference. Plus, this set of events did not occur on a leap year.

*** Since my starting premise was exceptionally conservative regarding what would constitute a deck implosion, it’s likely safe to say that this happened to more than one player on the first day of the Pro Circuit.

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