Weak Among the Strong: Bluffing, Imperfect Information and the Myth of the Single Correct Play

What can you say about Chad Ellis’s fundamentals articles? That Chad Ellis is a respected Magic theorist capable of taking complex concepts and making them simple to understand. That Chad is respected by the best theorists and players in the game. That every time you read a Chad Ellis article, you will learn something and become a better player. If that’s not enough, check out the guest appearance from “The Donald” in this exceptional article.

Before I get into the article, a warning: if you want to learn how to read people, pick up on tells, or otherwise gain information from someone’s demeanor, the speed with which they play, etc., read another article. I’m okay at it, but not great – and certainly not good enough to write an article about it. Instead I’m going to write about bluffing from a strategic/objective point of view, in terms of information, risk/reward and percentages. Go read a poker book if you want to learn how to tell whether someone has a trick by whether he looks at you or at the board.

In an article bemoaning his team’s defeat by mine at a Neutral Ground PTQ, Mike Flores wrote:

It is empowering to realize that there is only one right play on every priority of every stack…

Empowering, but flat-out wrong. Not only is there not “only one right play” on every priority, there may not even be only one right play on most – and almost certainly not on most skill-testing priorities.

Similarly, I must disagree with Mike Clair when he says that in a given situation, “Obviously there is only one right play” and cites the following maxim to “ensure that you’re making the right decision”:

In order to advance to the midgame with the largest possible advantage, in the early game play as if they have it, until you have the trump.

If you follow this maxim consistently – and particularly if other players know you are – you are not playing perfectly.

Let me provide a simple example to illustrate.

You are playing a game of Limited Magic in a generic format. Life totals stand at 20 apiece. Your opponent has a Gray Ogre in play; you have just tapped out to play a Hill Giant with a nice special ability that makes him very valuable – say, when he attacks he gets +1/+1 and first strike. You know that your opponent has Giant Growth in his deck, and you yourself have a Giant Growth in hand.

Your opponent plays a fourth land and attacks. Should you block?

The normal answer would be no. If your opponent has a Giant Growth he will trade a one-mana spell for your four-mana spell and play another threat, gaining considerable tempo advantage. Moreover, your giant is simply more powerful in card quality than a Giant Growth. Much better to take two points of damage, let your opponent tap out (or low) to play a new creature, and then swing back for four when you’ll be in a position to dominate any attempt he makes to block. (Alternately, if you need to hold back and defend, you can do so with untapped mana so you can trump his Giant Growth with your own.)

Now assume that you’re in the second player’s position. Should you attack into the Hill Giant if you don’t have a trick? Of course not…if you do, your Ogre just dies for nothing. So you attack if you have the Giant Growth but hold back if you don’t.

The problem is obvious…this “perfect play” analysis assumes both players have perfect information.

Suppose you as the Hill Giant player never block, since you conclude that an attack implies a Giant Growth. Perfect play for the second player then becomes “attack whether you’ve got the trick or not” because it’s just free damage. (An implicit assumption is that if the second player doesn’t attack he also won’t block the return attack because his own tricks will get trumped.)

In other words, by following the rule – by making the single “correct play” all the time – you are giving your opponent the opportunity to do two extra points of damage to you when their cards aren’t good enough to back it up.

The correct play, in fact, is to block… some of the time!

Let’s get theoretical for a moment – don’t worry, I won’t be long. Suppose you’re playing an infinite series of games with this start. In one out of four games your opponent has the Giant Growth and in the rest he doesn’t. Next, we need a 2 by 2 matrix to judge the cost and benefit of you blocking or not blocking in each situation:

He Has Giant Growth

He doesn’t

You block



You don’t block



Basically if you don’t block you take two damage, which we’re calling a loss of one “unit”. If you do you either kill an Ogre at no cost (gaining a huge advantage worth five units) or you trade your Giant for a Giant Growth, setting you way back on card quality and tempo for a loss of five units.

Let’s start with the “perfect play” scenario in which he attacks if and only if he has the Giant Growth and you never block. One game in four you lost one unit and three games out of four nothing happens, so the outcome for his turn is that you lose 0.25 units. However, he notices that you aren’t blocking so he starts attacking sometimes when he’s empty. The turn improves for him from a gain (your loss) of 0.25 to 0.4 or 0.6 units or even a full unit if he always attacks.

Now if your opponent is always attacking, you should always be blocking! Three times out of four you just kill an Ogre for a gain of five compared to one time in four where you get wrecked and lose five. If he always attacks and you always block, his turn gives you an average gain of 2.5 units!

This problem has a dynamic mathematical equilibrium. The correct frequency of bluff for your opponent is determined by how frequently you choose to block. The correct frequency with which you should block is determined by how often your opponent bluffs. And the equilibrium point that describes the perfect frequency with which you block and your opponent bluffs is determined by the likelihood that he has the card (in the abstract) and the relative cost/benefit of calling a bluff vs. calling when he has the goods.

Of course, in real life you don’t play an infinite series of games. This is important, because if you’re someone who never calls bluffs (or who always calls) your opponent won’t necessarily know this. But don’t assume that your play habits are all that secret. Over the years I’ve learned an awful lot about regular PTQ players in my area and even more about the regulars at my store. Some of them call too often or too infrequently and I’m able to use that against them.

This applies to the best players. For a loooong time I had a positive record against Dave Humpherys, despite the fact that he is a much better Magic player than I am. The reason was simple – Dave was too reluctant to call. Whether it was confidence that he could outplay me and win provided he didn’t get wrecked or whether he simply assumed I must have a good trick, Dave would consistently let me steal points of life away from him and over time those life points added up to game wins.

Another thing you don’t have in real life is a perfect measure of how likely your opponent is to have a trick and what the relative payoffs are. No matter… you simply have to estimate – from your perspective and from your opponent’s.

In theory, yours and your opponent’s perspectives should be the same. Anything that increases your chance to win the game from 50% to 55% worsened your opponent’s chances from 50% to 45%. This is a zero-sum game. But your opponent may not make the same assessment.

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I’ve written about this example before, but it’s such a perfect illustration of when not to bluff that I’m going to use it again. I was playing Josh Smith, a very strong player, in Masques Limited. On the draw, I led with Groundskeeper and a turn 2 Vine Trellis, ready to bring out the four-drops in my hand. Josh laid a Blaster Mage on turn 3 and on my turn I failed to draw a third land.

As I looked at the situation it was clear to me that Josh’s Blaster Mage was a major threat, since once I failed to play a land he would blow up my Wall and I would need two more lands before I could even begin to play out my hand. Meanwhile, the prospect of my Groundskeeper returning excess lands that my spellshapers were pitching was extremely remote. So, with Josh tapped out, I estimated the risk of a wrong call as being very high and swung with my Groundskeeper, figuring the right play for Josh was to take the point of damage.

Josh, of course, blocked.

From his perspective, the risk/reward scenario was quite different. If I played a trick that required mana, he was trading Blaster Mage for a good trick and quite possibly my entire turn. If I had a free spell like Invigorate he would eventually have to trade a creature for it, so best to get it out of my hand.

Josh didn’t know that I had missed a land drop, had no play for the turn and rated his Blaster Mage as such a fearsome threat. As he looked at what would happen if he didn’t block, he envisioned taking a point and then me playing land and a four-mana spell. At that point he wouldn’t be able to afford the tempo of blowing up my Wall on his turn when I might still have more land and no longer need the acceleration. So from his perspective, the Blaster Mage was just an Ogre with a marginal ability.

If you think your opponent may misevaluate the risk/reward of calling a potential bluff that should figure strongly into your decision of whether to bluff. In the example above, Josh didn’t realize how powerful his Blaster Mage was, so he was much more likely to call than if he’d known that I had no third land and no three-mana creature. That should have kept me from bluffing. The same can happen in reverse, too. If your hand is triple Lava Spike and your opponent saw two Kodama’s Might but no Spikes in game one, he may think that taking a couple of points isn’t so big and the risk of losing a creature is high, whereas you know that the real danger is that he’s dipping close to burn range.

So let’s sum up. What are the main objective points to consider when considering bluffing or whether to call a potential bluff?

Risk/reward from both perspectives.

If you’re at 20 life and have just dropped Visara against mono-G and your opponent attacks you with a Hill Giant you pretty much don’t block. Since untapping with Visara in play will pretty much win you the game and no trick will put you low enough, the risk/reward is unfavorable for calling even if you know your opponent will bluff every single time he doesn’t have a pump spell.

In a recent MTGO draft, my opponent tapped out to play Horobi against me and I had no way to target creatures. We were both at high life totals and my only creature in play was a Cruel Deceiver, while he had another creature out. I peeked at the top card of my deck and attacked… and he blocked with Horobi! I’m a polite guy, so I said, “Nice call” as my Deceiver died and all I could do was play a new creature. (I could have simply said “go” but I knew I had almost nothing in my deck that would target Horobi so I had to hope that he didn’t have any ongoing targeting effects, either.) He untapped, targeted my guy with something, played a Kabuto Moth, and I conceded a few turns later.

That was a horrible block. It worked, but gained him virtually nothing. Obviously I have nothing in my hand that can target his creatures or I’d have used it before attacking. That means he is about to win the game on Horobi’s back. Obviously I will attack if the top card of my deck is a land, so even if he assumes I’ll bluff 100% of the time there is roughly a 40% chance that he’s making a wrong call and the penalty for that is much worse than what he gains by killing my Deceiver for free. Barring some “tell” that made him 98% sure that I was bluffing, it was a bad call.

Risk/reward is a dynamic measure. If your opponent’s life is low enough, the risk of letting an attacker through may be worse than blocking and finding out that you have the trick. As we’ve already discussed, if your trick will eat up your whole turn’s worth of mana, it may not be so bad to fall for it. Similarly, in some matchups a good trick is worth more than a good creature. Your opponent may decide that blocking isn’t so bad even if you have it, simply to get it out of your hand so he doesn’t have to keep playing around it.

The player you’re trying to bluff, or considering calling.

It is an axiom in poker that you never bluff a bad player, a heavy winner or a heavy loser. Putting aside the winner/loser aspect, it is a fundamental truth that bad players will call bluffs far more often than they should. This is good for you because it means they are also blocking when they shouldn’t be, but it should also be borne in mind when considering a bluff.

At Grand Prix: Chicago I sent Hana Kami into Osyp’s Gibbering Kami on turn four with four mana up. Osyp had no spirits in the graveyard, so if he blocked and I had a trick he would simply be losing a 2/2 flyer and the chance to soulshift later. In Team Sealed the cardpools are deep enough that Kodama’s Might is a pretty likely bet, and I’d shown him Serpent Skin in a previous game.

Osyp was a good enough player not to block. The potential gain was modest relative to the cost if I had a trick, the downside to not blocking was just one point of damage, and there were two likely common tricks I could have so the odds I was bluffing was relatively small. If I was playing someone I didn’t know, I probably wouldn’t have swung, since a lot of players would just block there… and I happened to have nothing.

Another factor to consider is how good your opponent thinks you are. In my experience, people who think you’re much better or much worse than they are are less likely to call. People who think you’re much better often fall into the mental trap of “taking your word for it” and assuming you’ve always got a hand full of power cards. I know some players who are more likely to chump block a Hill Giant with an Ogre than block the other way around.

Even better is the person who considers him or herself much better than you, because they have two mental barriers to jump before they call. First, they have the psychological barrier of not wanting to walk into your trick. Second, they probably assume that they will beat you unless something drastic happens – like walking into a combat trick. Finally, even if they jump over those hurdles they may simply not think that you’re a good enough player to bluff them!


Many years ago I read a poker book that gave a perfect illustration of how to think about odds when bluffing might be involved. The game was draw poker, and the author kept a four-flush in a pot against a player who only went in with good hands, but who could be relied on to call them to the end. The author made his flush, and when the other player bet, he made a very large raise. The other player called and his set lost to the flush, at which point he said, “The odds against you making that flush were 4 to 1.” The author pointed out that given his bet, the other player should have realized that the odds were 100% that he had made his hand.

The player with the set was looking at the wrong odds. The question wasn’t, “What is the likelihood that he makes his flush?” but “In what percentage of cases in which he makes a big raise has he made his flush?” Since the author knew that his opponent would call the big raise, he would make it if and only if he made his flush, folding the rest of the time.

In first example, we assumed a 25% chance that the player had Giant Growth. But that certainly doesn’t mean that there’s a 25% chance he has it if he attacks. Suppose he will bluff one time in three that he doesn’t have the Giant Growth. That means that there is a 50% chance that he has it when he attacks. 25% of the time he has it and attacks, 25% of the time he doesn’t but attacks anyway, and 50% of the time he doesn’t and doesn’t attack. If he never bluffs that means there is a 100% chance that he has it given that he is attacking.

When you’re considering a bluff, you have to think about how likely it is your opponent will think you’ve got the goods. Have you shown him good combat tricks in a previous game? Is he someone who prefers not to risk getting nailed by a bad call? Is the trick you’re representing common?

In the example with Osyp above, I had shown him one common trick that would make blocking bad for him and there was another common trick that would arguably make it worse. That meant that it was quite reasonable that I would have a good trick.

The next level is trickier because it comes down to figuring out how likely someone is to bluff in a given situation. The irony here is that this inevitably runs counter to other aspects of analysis, like risk/reward. If blocking is tremendously risky for you, I’m more likely to bluff because of that.

The Donald has got your trump right here.


There’s nothing worse than attacking into a bigger creature, being blocked, using your pump spell and having your opponent respond with Terror. Bluffing into untapped mana is extremely dangerous, since you need your opponent to buy into the bluff and to be out of trumps.

The good news is that the likelihood of trumps makes your bluffs much less likely to be called when your opponent is tapped out. If you’ve got a Terror in your hand, you’re not going to walk into a Giant Growth. You’ll take a hit and bide your time for a turn or two until you can block with 1B up, knowing you’re probably in control of the situation. This can put you in a powerful situation when you read your opponent as having a trump and are able to engineer (or simply happen to arrive at) a situation in which that trump can’t be played.

At the risk of trying to get way too much mileage out of a single point of damage against Osyp, the fact that he was UB definitely helped me decide to bluff. I had to assume that he was packing removal and/or bounce and that he wanted to use that to trump my tricks. That made it all the more sensible for him to take a point of damage rather than risk falling behind on the board (e.g. to Kodama’s Might followed by me playing a three-drop) in which case he’d have to tap out again and would have to face another attack without mana for tricks.

Implied information.

Suppose you are in a situation where you would attack if you had a combat trick or removal spell, but you don’t have one. Your decision over whether to bluff has to take into account the fact that your opponent may gain knowledge of your hand by your decision.

Let’s say you hold back. If your opponent is smart and paying attention, she now knows that you don’t have the trick. (In fact, any time your opponent doesn’t attack you should ask yourself whether there are any cards you can conclude aren’t in her hand.) That may allow her to take risks or otherwise make better plays than she could without that information. Of course, if you bluff and she calls she’ll have the same knowledge with even greater certainty. But if your bluff is successful you’ll often find that she’s playing around a trick you don’t have, not just that turn but on subsequent turns. I’ve had more than one match where my opponent “read” me for having Giant Growth and subsequently made all sorts of bad plays.

The point is that the relative payoff for bluffing and not bluffing don’t just involve actual cards – they involve the information your opponent can use to make decisions.

Final Thought: the Metabluff

Every now and then you can really mess with a good player by playing in a way that makes it seem like you don’t have a card you actually do. In his analysis of his loss to Bruce Cowley in a team PTQ, Mike noted that Bruce had given away information by playing Samurai of the Pale Curtain before attacking, “In any case, if he had had a trick, Bruce wouldn’t have deliberately discouraged the double block with a pre-combat Samurai.”

The reasoning is basically sound, and goes back to the idea of implied information. With the Samurai out, a double-block by Mike becomes less attractive, since he won’t be able to Soulshift his guys back later. Thus, if Bruce has a trick (and wants Mike to double-block) he wouldn’t play the Samurai before attacking.

One can quibble with the logic – for example, Bruce might simply want to eliminate later soulshift – but there is a more elegant point here. Bruce could have been bluffing the absence of a trick to make Mike more likely to block – given Mike’s well-known ability to outthink himself. (Similarly, if Bruce didn’t have a trick but thought there was a good chance Mike wouldn’t block, it could have been smart to attack first and play the Samurai afterwards, “confirming” that he had a trick and had been hoping Mike would block.)

From now on, play Samurai of the Pale Curtain before combat any time you want Mike to think you don’t have a trick. Or that you do. Regardless of your hand, the fact that Mike has read this article and knows you’re messing with him guarantees you’ll be in his head. And Mike, being Mike, has at least a 90% chance of ending his Vizzini monologue with the incorrect glass of wine.

Hugs ’til next time,