Author Paulo Vitor Damo Da Rosa (PV)

PV’s Playhouse – Game Theory


I’ll start by apologizing for not having written last week – I was in Argentina playing the South American Junior Bridge Tournament (!). For that same reason, I didn’t get to read the comments until I came back, so I didn’t reply to any of them. I’ll say, though, that I did write the article before Atlanta.

So, speaking of Bridge I have been playing Bridge for a few years now, and though I have a decent grasp of it, I am by no means a professional player. That puts me in the position that I assume most of the readers of this article are – an okay player, but struggling to get better than okay, and wondering what I can do to improve, because there are certainly a lot of people who are much better than me and I refuse to think it is just a matter of talent.

Though Magic and Bridge are not really related in any way, it is not uncommon that I find myself relating Magic and Bridge concepts in my head from time to time. Often, much to my surprise, it is something that I already know from Magic but for some reason was not applying in the other game. For example, some time ago, my friend was telling me that, against a certain kind of hand, we had to be aggressive and take our tricks quickly without giving them time to take theirs, whereas against other kinds of hands all you have to do is be passive and not play the cards they want you to play and then in the end they will be short on tricks as long as you don’t mess up. In my mind, that brings an instant reference to tempo in Magic, and though it is not exactly the same, it helps my understanding of it if I see one type of hand as a tempo hand and the other not, because this concept is already stuck in my head.

Applying Bridge Concepts for Magic

Some months ago, I was defending a hand that I considered to be particularly tricky. I played my cards in a certain sequence that made the contract go down but not as much as it could (if you don’t know Bridge, it essentially means we got points, but not as many as we could have gotten had I played optimally), and my partner (who was a better player) asked why I had played them in that particular order. I told him that I had played that way so that, even if Declarer (the opponent) had Ace and King of spades in his hand, I would ensure that we would beat them. He then asked me “But do you think that, if Declarer had AK of spades, he would have played spades this particular way? Do you think he is an idiot?”

The answer was no, obviously not. It was rather easy to see once I stopped to look at it this way – if I had the declarer’s cards, and they were the cards I feared, then I would have played in a completely different way, and assuming he had even remotely a clue of what he was doing, so would he. It was the first time, in Bridge, that I understood I could figure out what other people had in their hands by the way they are playing.

But this article is not about Bridge, it is about Magic. The reason I brought this example up is because this concept is as true in Magic as it is in Bridge, yet many people fail to apply it when they are playing, like I failed to do it with Bridge. Basically, Magic is a game of incomplete information – we do not know what they are holding, what they are going to draw (or even what they might draw at some point), what is in the top of our decks. There is something we do know, though – we know that they want to win the game. This is precious information, and by basing all their action on this premise, we can try to figure out what they are going to play next, or what they have access to. I know that there are some people who use little tells, like the twitch of an eye, or particular behaviors and patterns, such as playing your cards with conviction or with doubt, to determine if their opponents think to be in a winning or losing position, if they are bluffing, etc. I do not possess this skill, so I have to do the best I can with the only bit of information I can get.

I have already talked a little bit about this in other articles, but today I will expand on it. To do so, I will invoke two examples that I have also already used, as well as some new ones.

This happened at a prerelease in our local store:

Player 1: You’re at eight, right?
Player 2: Yes.
Player 1: Do you want to gain 2 life?
Player 2: Hm, sure.
Player 1: Hidetsugu’s Second Rite you.

I like this example because it illustrates so perfectly that what the opponent is doing is never for your benefit. Every time your opponent does something, he is doing it because he wants to win the game, just like you – there are no friends here. In this scenario, Player 2 is obviously extremely silly, as it is clear that even if you don’t know about the existence of Second Rite you are just going to say “no” to this no matter what.

It is not always this obvious, though – sometimes the exact same scenario will happen and you will fall for it, partly because you just want to believe they are giving you a free win and partly because sometimes you don’t even understand what is going on. There isn’t really a hard rule to figure out if your opponent’s actions are part of a greater scheme or if he is really just handing you a gift, but generally the better the player, the more likely you are to be able to trust his actions to make sense. A lot of good players have told me that they play better against other good players, and it is the case with me too, because I can make better sense of their actions. I remember reading Conley’s article and thinking the exact opposite of what he was saying – that is, that you most definitely should play differently against different players. After I finished it, though, it became clear that we were not thinking of the same thing – he was saying that you should enter the game with the same mindset, and that I agree with. It is clear to me, though, that your plays cannot be the same, because the inferences you get are different.

Take, for example, the scenario where your opponent plays turn one Forest, Noble Hierarch, turn two Island, pass, into your empty board. If your opponent is a kid in a GPT that you’ve never seen before and who doesn’t look particularly professional or even good, then you might be inclined to think that he simply forgot to attack with his guy. Now, what if it is LSV you are playing against? I find it hard to believe that he would simply forget to attack with his Exalted guy, so you can safely put him on something – Cancel, Bant Charm, Vendilion Clique, Aven Mindcensor – you don’t know what, but be sure that he has something, or he would have attacked. Even if he does not play anything that particular turn, do not forget this turn – the card is still in his hand for later use.

I was playing with a friend not long ago and on turn four I played a Jace, the Mind Sculptor, and looked at the top card of his library, which was an All is Dust, and I left it there. Many turns later, with my opponent stuck on six mana, I played an extra guy into my already dominating board position, leaving UU up. He drew his seventh land and then said something like “unless you’ve gone totally insane, you have a counter for the All is Dust you know I have, so I guess I just have to play this other guy instead”. In the end, I did not have the counter, but drew it in the extra turn he gave me and won the game because of that. Nah, just kidding – I had the counter. In this situation it didn’t matter because I had two counters, so I countered both his other threat and the All is Dust, but the moral of the story here is that my opponent acknowledged that I was a rational being – if I knew he had the Wrath in hand, would I really have overextended without a reason? Am I an idiot? (Don’t answer.) He didn’t believe so, nor did he believe I had forgotten he had it, so he tried to play something else, that would enable him to survive but not be as swingy, to try to bait a counter and resolve the All is Dust next turn.


The example I like the most about this (and it is example I have already used #2) comes from a playtesting session of Time Spiral Block Constructed decks – Pickles and Teachings, where Luis and Paul Cheon were playing and I was watching (for some reason I like watching playtesting matches a lot, I think I can learn a lot about how both decks work). Paul had an Ancestral Visions with one counter, and was tapped out. Luis drew and passed his turn. Then, on Paul’s upkeep, when Visions was about to resolve, Luis played Pull from Eternity. Paul thought for a while and then said out loud, “Why would you play this on my upkeep, when I have mana to counter it, when you could have played that last turn? You must have Imp’s Mischief, nice try Luis, you might get worse players with it,” – he then let the Pull resolve and Luis did have the Mischief in his hand. I like this example a lot, because both players have to be very good for the situation to go like this, and they have to respect each other – if his opponent was not good, it could very well be that Paul would just think his opponent forgot about Ancestral Visions until it was about to resolve, for example. As it was, Paul knew Luis had to have a reason to do what he did – he was certainly not giving his opponent any free help.

Another situation where this applies and people seem to ignore is with opening hands. When we look at their 5 cards left on turn 3, we think they have 5 unknown cards we have no information about, but we forget that those are not 5 random cards, but 5 random cards that they kept! Imagine you are playing Dark Depths Thopter against Saito playing Zoo (and when I say Saito, or LSV, it doesn’t have to be this class of pro player, it could be anyone good), and he goes turn one Go, turn two Tarmogoyf. Now you have the option of going for the 20/20 the next turn or you can wait a couple turns to build some defense, do you go for it? Of course not! If Saito didn’t play a one drop, what does he have in his hand that made him keep it? Would he keep Tarmogoyf, Bolt, Helix, 4 lands? He clearly has disruption for your combo if he is not playing anything else. Again, if someone is not very good, it becomes a lot harder to judge on that – maybe they think this hand is good, how are you supposed to know? But if they are decent players, you can judge what they have by the fact that they kept their hand and have not played anything that would be a requirement for them to keep yet.

This happens in draft too; Imagine your BR opponent in Rise Sealed kept his 7 and played turn three Gloomhunter, and then didn’t play a spell in turns four or five and passed with RRRBB up. You have Drake Umbra. Do you play it? You can’t! Do you seriously think your opponent kept Gloomhunter, 6 lands (and then proceeded to draw all lands on top of that)? Or perhaps he kept Gloomhunter, Emrakul, 5 lands? Unless you know him to be particularly not-good, then you should give him some credit and hold your aura for when he taps out. You can be sure that, if you play against me and this situation happens, either your guy is dying in response or I am playing a gigantic mythic rare dragon next turn, possibly both.

Inferring to Win

I believe Josh Utter-Leyton has already written about this, but you can also infer if your opponent believes his deck to be controllish or aggressive, if he thinks he has enough bombs to win the late game no matter what or if his cards are more race-type cards based on whether he is blocking or not, trading damage or not. If your opponent blocks your “inferior” guys and does not mind trading them for his better guys, then it is probably because he believes he has the tools necessary to win the game if it goes long, and doesn’t feel pressured to kill you – he thinks surviving is his first priority. On the other hand, if your opponent doesn’t block your 3/2 with their 2/2 or 2/1 flier, then you should know that their intentions are different – they probably have cards they believe will tip the race in their favor, like Fog or Falter effects, or a bunch of removal that they will start playing soon to the point where they value more their creature than their removal. The easiest way to try to figure out what their actions mean is to put yourself on their place – what cards would you need to not trade in that situation if you were him? What combination of cards would lead to thinking taking four to deal two is worth it?

Other instances in which this happens is when, for example, you attack, they take the damage, you pass with no play and they kill your guy at the end of the turn. They opted to take damage and only then to kill it – why did they do that? They like taking damage? Clearly they had a reason – if they are playing blue, it might be that they have a counterspell in hand and didn’t want to tap out. If they are not, then it is possible that they do not have many removal spells in hand, and they wanted to make sure that you didn’t play a bigger threat before spending their card on your guy (because with the likes of three removal spells in hand, they would probably not wait). Or, alternatively, it might be that they have a Wrath effect, and were waiting for you to play another creature to get card advantage out of it, but since you didn’t they decided to just use the spot removal – there are many reasons why they might have played like this, but there is certainly a reason and you can try to figure it out.

Also worth noting is that, most of the time (but not always), when people think it is for a reason they are thinking. I remember a match against Gabe Walls in a team draft, for example – it was game three, so we already knew most of each other’s decks. I played a black one-drop, and he was playing UW and drew his card and thought hard on his first turn, only to play Plains, go. From that pause, I already knew three other cards in his hand – I knew that he had to have an Island, or he wouldn’t be thinking about which land to play. He also had a WW drop (in this case a Kazandu Blademaster), but no second Plains, or he wouldn’t have been thinking about it either, he would just have played Plains and passed. And, finally, he also had to have a Blue card he could have played turn one in his hand – in this case it had to be Kraken Hatchling. Remove any of those pieces, and his pause to think does not make sense. Sure enough, he played Island, Kraken Hatchling on turn two and then Plains, Blademaster on turn three. The only reason I was able to figure this out is that I know Gabe is good and plays fast – if he is making a decision, there is a decision to be made (in this case either playing his wall on turn one to stop my one drop or taking one attack and trying to draw a Plains to play his Ally turn two).

This is why I advise people to think in “groups” – When you are deciding whether to keep your hand, think of your early plays too (of course, sometimes it is impossible – imagine that Gabe just drew the 0/4, for example) so that your opponent does not know what exactly you are thinking – this way you give them less information. Conley Woods wrote in his article that he kept a hand based on the fact that his opponent thought hard before keeping his own, and it is certainly valid inference, though it might easily be misleading – when I see my opening hand with Zoo, for example, I think of whether I am keeping, which land I am going to play on turn one, which dual land I am going to get with my fetch in turns one and two and which one drop I am going to play – after I have it all figured out, and only then, I say, “keep”, so someone who is playing against me will have a hard time figuring out if my hand is good, explosive, flooded, if it needs a certain piece, etc, based on the time I took to keep it.

Of course, there will always be those people who try to bluff a counterspell no matter what – for example, it is turn 7 and you play Boil for their entire board. They start thinking, tap two Islands, untap, say, “Hmmm” and then, “ok, resolves.” Now, everyone knows they would have countered the Boil if they could, so you can’t base your inferences on the fact that they paused – in this case, the fact that Boil resolved trumps everything and they most definitely do not have a counter in hand. There are also people who do the same when you play a turn 10 Llanowar Elves – everyone knows that they are not going to counter it, even them, so it doesn’t matter if they pause or not, you cannot take any information from it.

It also works backwards – the “if they had this card, they would have played this way. Since they did not, then it follows logically that they do not have this card” thought process. This is easy to do on early plays, for example – if your Zoo opponent did not play a one drop turn one, it follows logically that he does not have a one drop in hand, because it is in his best interest, as far as winning the game is concerned, to play it on turn one if he has it. Basically you do not play around cards that you believe they would have used already if their intention is to win the game, or that would have caused them to play differently.

I remember a match of Black/Red against Green/Red, a long time ago. Both players were at two life, and one of them played Obliterate (don’t ask me what it was doing in that match). Player A hit three lands and played Call of the Herd, and played B hit his fourth drop and was faced with the decision of playing either Blazing Specter or Flametongue Kavu. After thinking long and hard, player B played Flametongue killing the Elephant, and next turn played the Specter and killed player A when this one tapped out to flashback the Call of the Herd. My friend who was watching the match asked player B why he hadn’t simply played the Blazing Specter and killed his opponent, and played B answered that he was playing around Shock, which is obviously bad – his opponent cannot possibly have Shock in his hand, because, if he had, he would have used it already to kill him!

This gets trickier once the game goes on, though, because you and your opponent place different values for different cards. It might be that you think your Umezawa’s Jitte is invaluable, and therefore, if your opponent did not counter it, he cannot possibly have a counterspell, but maybe he does and simply doesn’t deem it worth countering. I remember once I was playing a playtest match and I figured that, if my opponent held a particular card combination, he would have killed me the previous turn, and since I was not dead, that meant he did not have those cards, so I played in a certain way that would leave me vulnerable to those cards (because I knew he didn’t have them). Next turn he played the exact sequence of cards and killed me.

“Did you have those or did you draw this?”
“No I had them all.”
“And why didn’t you kill me last turn?”
“Oh, I missed it.”

This will happen in matches, and you will lose games because of this – I know I have. It is like they try to throw the game away, and you simply refuse to believe that they would do so, and then do not take your opportunity. It is hard to judge – everyone makes mistakes, even the best players, and if you fail to believe every single one of them you will fail to capitalize – you have to try and figure out how likely it is that it is a mistake, and how likely it is that they have a plan. If you’re playing against LSV again, for example, and he forgets to use his Vithian Stinger to ping you at the end of the turn, you don’t have to start playing around a Mirror Universe effect – chances are he just forgot it.

It gets even worse once you get to more levels of analysis – you have to be careful not to assume they have information they do not, just because you have it. For example, you will know you don’t have a removal spell, so the train of thought “if they had cards this and this they would have played in a certain way” might not hold true, because they might not know that you don’t have anything. Depending on how good they are, you can apply the thought process as if you were them to see if they know something – for example, it might be that if you had a removal spell, you would have played it already. If they know that, they will know that you logically cannot have the removal spell, so if they can kill you with that knowledge they will, and the fact that they didn’t means they themselves do not have the necessary cards.

So, basically, to sum this all up – Magic is a game where information is very precious, and your opponent is a constant source of information that you would be a fool not to use. If you establish that he is a decent player and that he wants to win, then most of his actions will lead to logical conclusions about cards he probably has, or cannot have, or about the way his deck is designed, and if you put yourself in his place and think, “would I have played like this if I had card X?”, or “what would have caused me not to trade in this situation?” you will have a greater understanding of what is going on and will be better able to play the cards you have, because you understand more.

I hope you’ve enjoyed this, and see you next week!


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