My friend and former ARG writer, Johnny Li, once told me about a common practice in Magic where instead of rolling a dice, players had two sets of Rock-Paper-Scissors cards. Each player would shuffle the cards face down and randomly pull a card. The card drawn would then be paired against the card the opponent had pulled and they would play Rock-Paper-Scissors with them as a means of determining who would go first. There was apparently quite a bit of statistical proof that this was a “more random” way to determine who would go first. After thinking about it for a minute, I told him I wouldn’t use this method. If the dice the dice gave you a better chance of getting lucky, I’d want to take the increased chance that I might get lucky for multiple rounds, despite the fact that there was an increased risk of my opponents getting lucky over multiple rounds. Today’s article is going to talk about the need to get lucky to win a tournament.
I love to contradict myself. It’s a great way to learn about something and it helps you avoid one of the most common biases; arguing to win the argument instead of arguing to find the right answer. If you think about it, it makes a lot of sense. If you don’t care about winning the argument and only care about figuring out whether or not something is right, you don’t have any incentive to develop this bias.
Contradicting yourself is an excellent check on your ability to be unbiased. If you read my article last week, you’ll notice how my opening statement contradicts the entire purpose of my last article, where I made the controversial claim that luck does not exist. This week I’m going to be talking about the necessity of luck in success? What kind of cop out is this?
Contradicting one’s self is actually just a way to apply divert thinking, or looking at something in multiple ways, to a situation and is a necessary part of the developmental process.
At this point I need to make a very important distinction for my argument. There an exceedingly common notion that having multiple possible answers implies that there will be more than one way to accomplish your goal, whatever it may be. In many cases this is correct. Let’s say your goal is to make it to your flight for YCS Tacoma this weekend. That involves making it to the airport before the plane leaves. To get to the airport you could take a variety of different routes. To keep it simple, we’ll limit it by saying that there are only two options: you can either take the I75/I85 straight through downtown Atlanta, or you can take the 285, the perimeter that encircles Atlanta. Both routes will get you to the airport and they will both allow you to make your flight on time. In that respect, there were multiple answers that resulted in you accomplishing your goal of making your flight.
That does not mean that one route is not better than another.
Objectively, if you had gone one way it would have taken some number of minutes and if you had gone the other way, it would have also taken some number of minutes. But if you’re directly North of the city and the airport is directly South of the city, it might stand to reason that the route that leads you directly through the middle will get you there quicker than the one that made you go all the way around the city. If at this time “rush hour” has crossed your mind, you’ve missing the point. Go back and reread it (while rush hour is completely irrelevant to my point, you don’t know Atlanta very well if you think traffic will be anything short of terrible on both of these roads).
The point is this; despite the fact that there may be multiple ways to reach your goal, one of those ways will almost certainly be better than every one of those other solutions.
Let me bring this full circle by saying that contradicting yourself is a good thing, because it allows you to see multiple solutions to a problem and identify the best aspects of each solution, so that you may reach the single best solution. Similarly, though only marginally related, yet still worth bringing up, is the idea that two solutions implies an even split in the chance that one will result in a better outcome than the other. Two solutions come with the connotation that each one has a 50% chance of being the right solution. This simply isn’t true. It makes sense that going directly through something will be a shorter distance than having to go around it, so it stands to reason that the shorter distance will likely correlate to the shorter amount of travel time spent. Both routes do not have a 50% chance of being the quicker route.
Now that we’ve set the stage for the argument, allow me to contradict myself by talking about why you need to get lucky to win, even though a week ago I seemingly didn’t believe in luck!
Earlier today I was discussing theory with a friend of mine by typing up a self-evaluation for my tournament experiences in Charleston and Fort Worth. The point I made about luck hinges on the card Good & Evil of the Burning Abyss. This was the argument I put forth:
I played 2 Good & Evil in Texas, something I fully believe was more correct than playing only a single copy on the basis that I want to give myself the chance to get lucky. Playing a second copy gives us a tradeoff: we are able to mill it off Dante more often than we would have if we only played a single copy, but we also have to draw it more often than if we only played a single copy. For the sake of this argument, we’re going to ignore the benefits and costs of any card that would replace the 2nd copy by assuming the net benefit was close to that of Good & Evil in the long run.
Milling Good & Evil off of a Dante is amazing! It puts you so far ahead in the game. Drawing it, on the other hand, has few applications outside of discarding it for Virgil. I’d like to call your attention back to the first part of this article. One way or another, it was better to play 1 instead of 2 or 2 instead of 1. They are not equal. Objectively, one is the smarter choice and there is not a 50% chance it’s one option and 50% chance it’s the other.
My argument for why 2 is better than 1 is that you have to get lucky to win a tournament. Let’s say, for example, that if you played 10,000 matches with Burning Abyss, you win 75% of all the matches. That’s not a bad percentage, but guess what? You’re not going to win the tournament winning 75% of your matches.
To even make top cut at a Circuit Series, you’d have to go 7-1-1 in matches. If you’re x-1 and can tie the last round, that’s 8 rounds you have to play. Winning 75% of those only gives you a record of 6-2 going into the final round. Instead of leaving yourself praying for good tiebreakers, you could instead try and raise that percent.
The thing about 10,000 matches is that it’s a lot of matches. You could win a bunch, but if after that many games you won 75% of them, that’s a very strong indicator of your deck’s mean performance. Thankfully we don’t have to play 10,000 matches to determine the outcome of a tournament. If we’re playing for a Circuit and need to be 7-1 to draw the last round, we only need to play 8 to make it to top cut. However, we aren’t trying to make it to top cut, we’re trying to win! That’s 4 more matches that we have to play, which means we’re going to need an impressive record of 11-1 in matches played to actually win the tournament. That’s a much better record than our 75% mean performance.
The distinction? 12 matches may feel like a lot that you have to perform well in, but it’s actually a very low sample size. All tournaments are played in the short run. We can use this knowledge to our advantage.
What’s the actual difference between short-run and long run? Well in the long run, it’s unlikely you’re going to score much different than your mean deck performance percentage. As a matter of fact, it’s not only unlikely, it’s not going to happen. If the percent of matches you should win is 75% and you play 10,000, you’re going to find you won a number of matches that is very close to 7,500.
In the short-run, we have this thing called variance. It’s what most of you guys think of as luck. If your opponent has 30 cards in deck and tops Snatch Steal as his only out to beat you, you’ve lost the game. If we use this game to represent a match (perhaps it was game 3), your opponent only had a 1/30 chance of winning, but they still won 1 of the 12 rounds you need to win the event. It’s impossible to draw Snatch, it’s just unlikely. In the long run, they’ll draw it 1/30 games. In the short run, that’s like 3 tournaments. We’re just looking at trying to win a single tournament. Essentially, in the short-run, you’re much more likely to deviate from the deck’s mean performance. Variance is going to have a much greater impact on your games than it would in the long run.
While people see this as a flaw in the game, I use it to my advantage to help me win tournaments. I acknowledge variance and embrace it. Why? Because if I need 11-1 to win the tournament and 75% is the amount of matches I should win, I’m not winning any tournament. I need my deck to over perform.
By throwing cards that “allow me to get lucky” in, I increase my variance. These results in an increased chance that my deck will over perform and allow me to go 11-1 and win the tournament, but it comes with the tradeoff of an increased chance that my deck will underperform as well and I will be out at an earlier round.
Guess what? Underperforming doesn’t matter. It’s underperforming as compared to the 75% standard, the number that wouldn’t allow us to make top cut anyway. We don’t want the standard because the bar for success is higher than the standard. We can never be successful if we only perform at the mean every time. Essentially, the standard 75% is equal to underperforming, as it doesn’t matter if you’re out round 3 or round 8, either way, you’re out. This makes the increased chance of underperforming irrelevant, but still leaves us with the increased chance of over performing and winning the tournament!
This effect is decreased if this had been a YCS instead of an ARG. At a YCS you are allowed to go 10-2 in the constructed portion and still win the YCS. This is much closer to the 75% standard that we’ve been working with. In such a case, it may not be worth it to increase the chance that you will get lucky by increasing the chance that you will underperform, because you don’t need to get as lucky. Here you only have to win 83.33%, or over perform by 8.33%. At a Circuit, you have to win 91.66%, or over perform by 16.66% in order to win the tournament. You don’t need to take as many risks at a YCS because the result needed at a YCS is much closer to the median, perhaps to the point that it is not worth the added risk of underperformance.
So now that I’ve fully fledged out my argument, am I actually getting lucky? Or am I taking what everyone else complains about as a disadvantage and making it work to my advantage? How do I resolve my contradictory statement that I do not believe in luck, yet I think you need luck to win an event? I think it is safe to say that my true beliefs on the matter are that you make your own luck. Until next time, play hard or go home!