One issue that doesn't get talked about that much, but is a real difficulty for people who write regular articles is coming up with a new topic to write about each week. I'm going to be honest, I've gotten pretty decent at solving that particular problem over the years, but this week was particularly tricky for me to figure out what I should write about.

Often, it's easiest to just write about whatever you've been doing lately. What deck are you playing? Write about that. What format have you mastered? That's a great topic. However, I've been focused almost exclusively on best-of-one play on MTG Arena lately in preparation for the Mythic Invitational so that's all I really feel comfortable writing about when it comes to decks that I know and understand on a high enough level to impart my knowledge to others. The problem is, that's a fairly narrow topic, in that it won't help anyone playing in paper events and I have to keep some information close to the chest in order to give myself and teammates the best chance to succeed at the event.

Fortunately, I have a document with random ideas on my phone that I can fall back on in times like these. And that's exactly where we find ourselves right now. I only had two things written in that document. One was "Font of Agonies in Modern Death's Shadow" and the other was talking about odds and how we as humans tend to fail when it comes to odd calculations, and not necessarily for the reasons people believe.

Odds it is! I'm sure as hell not writing about Font of Agonies. Nobody wants to read three thousand torturous words about Comic Sans or Times New Roman.

Never Tell Me the (Wrongly Calculated) Odds

I ran into a situation on my stream last month where someone suggested I take a certain line of play because it was "more likely my opponent had X than Y in their hand based on odds" and if I took that line of play and got punished I could at least take comfort in the knowledge that I made the right play. When I say I ran into this situation, what's more appropriate is that I rant into this situation, because I firmly disagreed with that analysis, and I thought it would make a good discussion point in an article.

When you boil things down, basically everything in Magic is related to math in some way. Building a deck involves math, figuring out our mana bases involves math, as is calculating the likelihood of drawing specific cards at specific times. So if our opponent has four copies of Vraska's Contempt in their deck and three copies of Cast Down, we should generally play around Vraska's Contempt over Cast Down because it's more likely that they have Vraska's Contempt, right?

Wrong. Well, sort of. It is true that in the dark, with no other knowledge, mathematically speaking, it is more likely that they have a Vraska's Contempt. Their opening hand, for example, is more likely to contain that card. However, games aren't played in a vacuum and we shouldn't use math as a blunt instrument to fit our needs unless we actually know how we are using it.

Every turn that we play a game of Magic, we learn things about the contents of our opponent's deck and what they are likely to have in their hand. Some of this is more obvious information like "my opponent keeps passing every turn with a single blue mana open, they are probably more likely to have a Spell Pierce in their hand than not." So if my opponent keeps representing Spell Pierce in spots where it would be inconvenient for them to do so and they also keep tapping down to exactly one mana, then I would wager it's more likely that they have a Spell Pierce in their hand than a Negate, even if they play more copies of Negate in their deck.

Some kinds of information are not as obvious. For example, our opponent might cast Vraska's Contempt on our creature, and then on the next turn cast another Vraska's Contempt on another creature. We might then think, oh our opponent only has two Vraska's Contempts left in their deck but they haven't cast any of their (presumably) three copies of Cast Down yet, so they are now more likely to have a Cast Down in their hand than a Vraska's Contempt. That's just math!

However, that's not math. That's our interpretation of math without incorporating all the variables involved. We failed to factor in that our opponent might have chosen on a previous turn to Cast Down one of our creatures if they had it instead of using a Vraska's Contempt, which lowers their odds of having a Cast Down. We have failed to factor in that our opponent might have been willing to use their second Vraska's Contempt on a mediocre creature of ours because they were holding another copy or even two more in their hand and thus felt safe to spend one, increasing the odds of them having a Vraska's Contempt.

We also, except in situations with perfect decklist information, don't actually know the exact contents of our opponent's deck. We can guess, based on past history and lists that we've seen, but it's likely that our opponent has adjusted the numbers in some capacity to fit their preferences.

Now, if our opponent has no unknown cards in their hand and we're deciding whether to play around them drawing Kaya's Wrath or not, then we can certainly calculate the odds of how likely it is for them to draw that card on the next turn, based on how many we believe they have left in their deck and how many cards remain for them to draw, and so on and so forth. However, even then, those calculations do not tell the full story.

"Should I play around Kaya's Wrath or should I play around Cast Down" is not a question that can be answered solely by the odds of which they are more likely to draw next. That analysis should also be weighted by how likely we are to win if they do draw one of those cards. Our opponent might be more likely to draw Kaya's Wrath than Cast Down against us, but if we are extremely likely to lose if they draw Kaya's Wrath, even if we do choose to play around it, then our best play might be to not play around Kaya's Wrath—even though it's more likely that they draw it than the alternative.

I do believe it is possible to calculate the odds for which card, or even combination of cards we should play around in any given situation. I think math is an incredibly powerful tool and capable of making these kinds of seemingly subjective calculations. If Magic were a bigger game, I believe there would already be AI developed to make these kinds of decisions, and maybe eventually make them better than the top professionals. However, I think these calculations involve significantly more variables than just figuring out how many copies of any given cards our opponent is playing in their deck and thus which ones they are more likely to have. Some of those variables include things like body language, how they've played every turn up to that point, and how we believe they've constructed their deck.

I'll Take My Chances

I don't think we, as humans, are capable of calculating those odds. I don't think we even know all the variables that go into these kinds of calculations, let alone be able to figure out how much to weight each one, or which ones matter. However, there is one aspect of our minds that is actually capable of attempting an estimation on these kinds of odds. That would be our subconscious.

Our subconscious mind is constantly weighing different variables it picks up on over the course of a game and updating to give us it's best guess on what our opponent might have. So if we ever think a thought like "Our opponent has already played three Vraska's Contempts, but I still think they probably have the fourth in their hand, even though it's unlikely, statistically" it may actually be less unlikely than we think. It might be likely that they have it in their hand, based on all the other reads we have picked up on over the course of the game, and our subconscious mind figured it out where our conscious, attempting-but-failing-to-be-logical mind could not.

Our subconscious can also be hilariously wrong in many spots, and is not something that we should rely exclusively on for our decision making. Our subconscious mind sometimes gets so mired in the "gut reads" it provides us that sometimes it can overlook obvious, on-board information.

As a result, I think the best way to play Magic is to use our conscious mind's logic to reason through situations that involve known information, but also to trust and incorporate our subscious mind's gut reads in situations where we need to make judgment calls that rely on unknown information. Being able to use the two harmoniously in tandem with each other is the most effective way to "play the odds."

So to go back to the initial point, if our opponent is more likely, based on their deck construction, to have X in their hand over Y, and we choose to play around them having X and lose, can we at least rest easy in the fact that we made the right play? I say no. Because I don't think we necessarily made the right play. If we ignored our gut screaming out that they had Y instead, we made the wrong play. If we decided to take and throw away a lot of the information that is gleaned over a game of Magic and focus instead on numbers, and only some of the numbers, then we didn't actually make the right play, we made the comforting play.

Our odds calculation may have told us to make a certain play, but I wouldn't rest easy in it or take comfort in it being right because I think we rarely get our odd calculations right—and what's more, I don't think we as humans are even capable of making those calculations in most situations. There is so much information that goes into it all, and not just the raw statistics of which cards are more likely to be drawn than others. Magic is a game where there's a lot more than what initially meets the eye, and we do ourselves no favors by attempting and failing to make plays based on flawed odds than to just follow our instincts and do what we deem best.