ADVANTAGE
“Back before I discovered Magic: The Gathering, my game of choice was chess. During my lunch period, me and the other chess players at my school would gather in the student lounge and play speed games, and often we'd also play after school. A large part of the fun of playing chess at that level is the trash talking, and one of our favorite topics was advantage. If you could put it in front of the word advantage, we claimed it. As in any game, there was also the advantage itself, but we were normally arguing over who had that one. The most popular type of advantage was of course material advantage, which is the equivalent of Magic's card advantage, but consider these other important claims: Space advantage. Development advantage, and its generalization time advantage, which is not to be confused with the very important clock advantage. Pawn structure advantage. Open file advantage. King safety advantage. Center advantage. There were many more, but you get the idea.
When my old best friend Adam Hulse and I moved from chess to Magic, we didn't debate advantage much anymore. I don't think we even knew the term card advantage, even though for us it should have been a natural thing to talk about and we knew about its implications even if we didn't give it a name. In my section of the Magic community, early players knew card advantage well, almost as well as we do now, but didn't understand concepts like tempo or the mana curve. We also didn't forget to keep asking who was winning the game, but understood without having to say anything that this was much harder to work out in Magic than in a deterministic complete information game like chess.
[…]
Also, remember the following rule that I didn't put into the right words until after I [almost finished writing a treatise on the subject]. It sounds obvious, but people forget it and Justin Gary had to tell me that I had forgotten the correct words to put it in:
Rule of Reflection: Everything in Magic has value equal to the amount it increases your chance to win the game.
If it doesn't make you more likely to win the game, it has no value. If it does, it has value equal to the probability it will make the difference. Once you hear it that's an easy thing to say, but a difficult thing to properly apply. Here begins the quest… for Advantage…”
-- Zvi Mowshowitz, “
Advantage: The Grand Unified Theory
”
***
MTG BACKGROUND
Magic: The Gathering
became the most prominent Collectible Card Game, the blockbuster of its field. Launching in 1993, it was a new type of game that the world hadn’t seen before. Still going very strong 24 years later, MTG has over 16,000 printed cards that are eligible for players to play in a given game.
It’s not surprising that the game was created by a mathematician – Richard Garfield, its creator, had studied computer mathematics as an undergraduate, worked for the very innovative Bell Labs in the 1980’s, and went back to the University of Pennsylvania for graduate studies and received a PhD in combinatorial mathematics in 1993, the same year that Magic: The Gathering was launched to the public and became a rousing success.
In case you’re unfamiliar with how the game works, Magic: The Gathering
is rather simple on the surface: it’s a game where you assemble a deck of 60 cards and play against another player who chooses 60 cards. Each of you begins with 20 life, and draw 7 cards into your initial hand, and then take turns playing. If either of you hits 0 life or runs out of cards to draw, you lose.
The simplest version of the game goes like this – each of the 7 cards you draw does different things. The first card you play is almost always a land, because you can play one land for free each turn.
One land produces one “mana,” which you can spend on casting spells. Every spell has a cost in mana, and then some spells will summon a “permanent” card (a creature, artifact, or long-term enchantment) and sometimes they’ll do something immediately (damage the opponent, allow you to draw more cards, force the opponent to draw cards, destroy one of his permanents, things like that).
The goal is to win – typically by reducing your opponent’s life to zero (the most common way), occasionally by forcing them to run out of cards to draw, and (very rarely) some other eccentric means of winning.
Maybe this will sound like an overreach on my part, but I think Magic: The Gathering
is actually one of the most interesting things ever invented in the United States – and yes, I’m aware that Americans have invented a whole lot of interesting things.
***
WHY STUDY GAMES?
In the past, I’ve pointed to three fields that are almost universally worthy of study for general mental models – athletics, finance, and warfare.
All three of those fields have multiple sides competing within them, so you can see how competition forces each side to improve. Success is relatively easy to observe and measure in each of them: you can see financial returns easily on a graph, you can view the results of battles and wars, you can see the final scores and winning histories of individual athletes and sports teams.
I’ve recently started to include competitive games
as a potentially fourth category – it fits all the criteria.
Games offer something else, too – they’re a complete system
. Whereas reality is infinitely vast, games offer a set of clean and clear rules to be played by. In business, there’s almost an infinite number of things you can do, and you can do them in a nearly infinite number of variations. The same goes for individual careers, or artistic choices.
But games, at any given time, offer a somewhat limited set of moves. A complex game might have millions of permeations, but that’s still considerably less than infinity, eh?
By honing in on skilled high-level game play, and studying it, we can identify rules and patterns that work and lead to winning. Those patterns – deduced from study of something complete with a fixed ruleset – can then be re-applied profitably to the infinite complexity of life.
***
WHY STUDY MTG?
Lots of games are interesting – Chess and Go are consistently ranked as the two of the most enduring, complex, and interesting games.
But Magic: The Gathering
offers a couple unique advantages over Chess and Go.
As Mowshowitz wrote, “We also didn't forget to keep asking who was winning the game, but understood without having to say anything that
this was much harder to work out in Magic than in a deterministic complete information game like chess.
”
In Magic, you’re up against another player who is trying to defeat you. You do not know all of the cards in his deck or in his hand. You’re playing with incomplete information all the time.
Additionally, part of the genius of Garfield’s game design is that new cards are released regularly, which reshape the playing field and what other players are including in their decks, and how they combine to defeat what has been played most commonly recently.
This is referred to as the “meta-game” – there’s no single “best deck”; the best deck in competitive tournament play is the one that wins most often against collectively all of the other decks being commonly played.
You have to both anticipate and adapt to what others are doing in the meta-game in order to win on a sustained basis.
In Chess, there’s perfect information – you can see all of your pieces and all of your opponent’s pieces. An outside observer can see the board and know everything that all of the players know about the board.
In Magic, the imperfect information – meaning, the cards in hand and deck are hidden – makes for a very interesting game that has some things in common with life. You don’t know what others are thinking and what they’re going to do to respond to you.
You’ll often get choices in Magic to do a little damage to the opponent immediately, or save your damage-dealing in case they get a powerful creature out you need to kill. Sometimes you’ll hold a counterspell – which cancels what the opponent casts – and you need to pick the right spot to use it. If the opponent plays something “pretty good but not amazing,” do you counter it to slow them down or do you hold on to your counter in case they attempt something bigger later?
This leads to a lot of opportunities to train your perception, your pattern recognition, and your moment-by-moment decisionmaking. You need to learn to control your emotions, to make decisions quickly but not rashly, and to process and make dozens of choices throughout the game.
***
LIMIT BREAKS #9: HIDDEN LOGIC
In any game, in any industry, in any aspect of life you want to thrive, it’s key to identify what matters and what does not.
I think Mowshowitz said it well when he said –
“Everything in Magic has value equal to the amount it increases your chance to win the game.”
But often, it’s not clear what wins the game
– especially in more complex areas of life like career, one’s network, and all sorts of infinite choices and decisions we could make.
Often, the very most sophisticated and successful in a field are employing “hidden logic” – they’re seeing derived variables that are not explicitly written down, managing their affairs, and making decisions by them.
If you can identify the hidden logic of situations, the key variables that lead to winning and losing, you’ll thrive to a much higher degree than people who are ignorant of the beautiful hidden and logic that underlies so much of human affairs.
***
MOWSHOWITZ’S EXPLORATION
Zvi Mowshowitz’s
Grand Unified Theory of Advantage
series is worth reading if you’ve got any background in Magic; it probably doesn’t make sense to read if you haven’t played the game (it’s rather technical), but if you have, it’s a gold mine.
In it, he explores and points out the flaws in various types of advantage theories in Magic.
He starts by analyzing different types of “card advantage” – for instance, if I play a single card that forces you to discard three cards randomly, I gained an advantage of two cards on you.
(I played one card from my hand, which is now spent and gone. You discarded three cards, which are now dead and gone. 3-1 = advantage gained of 2.)
Given that everything you do in Magic requires cards to get going, gaining more “card advantage” on the other player should help you win, no? If they no cards in their hand or on the board, they can’t do anything.
But Zvi notes, it’s no use being “up five cards” if you then hit zero life and die… so he looks at things like tempo and speed – if you’re slowly gaining card advantage on me, but I’m quickly killing you, the game is mine.
Now, here is where I’d like to stop and note – “card advantage” is nowhere in the rules of Magic; neither is tempo or speed. All of these are derived variables, strategic ways of thinking about the game that you’re not mandated to think.
You can think about the game however you want – or even play it without thinking strategically at all.
But nowhere in the rules does it say anything about card advantage or tempo. There’s rules about putting down land, and casting permanent spells and temporary spells, and starting with life totals of 20 and dying when you hit a life total of 0. The interactions in between hitting zero life or zero cards are all derived, strategic thinking.
***
LIFE: OVERRATED
Since many readers here will have never played Magic
, I’ll stop with the technical stuff – it’s gone about as far as it can go – aside from making one last point from Zvi that is extremely counterintuitive and not how people normally think about the game.
From “
Advantage Theory: Putting It All Together
”, emphasis added –
“Life is the resource whose importance varies most in the game.
Cards can be irrelevant, but more often than not they are critical and most of the rest of the time the battle can be viewed as some form of virtual or effective card war. Tempo can be irrelevant, but that is almost always because neither side has any, while mana is the same case in reverse: It becomes meaningless when both sides have too much. Like mana, life points have a critical point: The big difference is between Not Enough Life, Enough Life and Lots 'o Life.
When both players have more than enough life points life often becomes all but irrelevant until something changes that.
One and four life points are very different numbers, but it can be much harder to tell the difference between twenty and twenty-five. It is also common for one player's life total to be moot or almost moot.
This is all true because life doesn't do anything at all until that moment that it does everything. As long as you're alive your life total has no direct impact on the game.
When a player starts getting close to death it has a dramatic effect on the game and so does paying life to get something in exchange, but the primary reason to pay attention to life is that when a player drops to zero life points he is dead and nothing else matters. Being dead does not have any effect on tempo or card advantage (in any form) or anything else. It wins you the game. Nothing more, nothing less. This system allows Magic to grant players an early advantage and not automatically shut the player who falls behind out of the game.”
Sounds logical, right?
Yet, I contend this is extremely counterintuitive.
Your life total in Magic does not matter until hits zero, or is at risk of hitting zero.
This is, again, extremely counterintuitive
– and it actually applies to any game that has binary win/loss conditions with life totals.
The naive understanding of most people who first play the game – mine, too – is that the player who has more life than the other is “winning.” That’s not necessarily true.
In Magic, there’s a lot of ways to get defenses up such that the opponent cannot damage you any more. If you get enough defenses up that it’s not possible for the opponent to do any damage for the rest of the game
, then it doesn’t matter if you had 20 life, 10 life, or 1 life when you finally got all those defenses up.
Life, in Magic, is a binary variable – once it hits zero, you lose. Until it hits zero, it only effects you insofar as you’re worried about taking damage that’ll take you to zero life.
There’s many cards that do exactly 3 damage – lightning bolt, for instance. If you’re facing an opponent carrying only 3-damage cards, then your life total matters in increments of 1+3. If you have 4 life then you can can absorb one lightning bolt and survive, 7 life means you can take two bolts, 10 life means three bolts… and so on.
Thus, dropping from 4 life to 3 life might mean losing on the next turn if your opponent can cast lightning bolt on you, but dropping from 6 life to 4 life might not make a difference.
This, again, is counterintuitive – if your opponent is racing to damage you, and you’re ignoring the damage while racing to get complete defenses up so they can’t damage you, it doesn’t matter if you’re on the brink of death when those full defenses come up – you’ve survived, and presumably they’re now at your mercy.
Okay, this is a slightly eccentric point, no? Let’s look at another example of Hidden Logic in sports, and then we'll generalize it to everyday life.
***
RUN EXPECTANCY VS WIN EXPECTANCY IN BASEBALL
The American sport of baseball is an interesting one – there’s no “clock”; the game doesn’t end by time passing.
Instead, the game is measured by “innings” – basically, it’s one “turn” of play – and each inning, your team gets 3 “outs” before the inning ends.
There’s nine innings; so, each team gets 27 outs total before the game ends.
To score in baseball, you need to get one of your team – a batter – around four bases that they can advance through. If a player gets around all four bases, you score one “run” – basically, a point.
Whoever has the most runs at the end of the game, wins.
To get around the bases, you need to hit a ball that the defense controls with a wooden bat.
Now, the game is interesting because you can try to hit the ball as hard as you can, or you can try to hit the ball just a little bit in order to move a player already on one of the bases forwards.
A common situation in baseball is where the first player up hits the ball hard, and gets to second base – halfway to scoring.
Early in the game, you should keep playing normally – by having everyone on your team swing as hard as they can, some of the will make a bad play and get out, whereas others will hit the ball hard and get to first base, second base, or hit a home run (hitting the ball all the way out of the field of play, scoring everyone on a base and the person who hit it).
Again, early in the game, you don’t do anything differently if the first player hits a double and gets to second base.
But as soon as it’s the 9th inning, everything changes. The 9th is the last inning, so if you’re losing at the end of the 9th, the game is over and you lose.
So if you’re losing 4-3 in the 9th and final inning, and your first guy gets to second base, you probably want to have your next player hit a “sacrifice” where they make an out on person to get the guy to third base. Then, even a weakly hit ball on the next play scores the player, ties the game, and you can survive to keep playing extra innings.
In baseball, this is a difference between two hidden variables – run expectancy
and win expectancy
.
Briefly, every situation in baseball has a certain “run expectancy” associated with it – how many runs you’ll be expected to score in that situation. There’s a whole lot of statisticians that calculate this sort of thing and are intrigued with it. (I self-taught myself statistics from baseball, incidentally.)
When you’ve got a player on second base and no outs, you’ll (mathematically, on average)
score 1.228 runs
.
If you sacrifice bunt the man over to third base, you’ll score on average 0.980 runs.
That is, by trading one out to move the player forward one base, you’ll decrease your average amount scored by 1.228 - 0.980 = .248 runs.
Early in the game, before the final outcome looks close to settling, you’re better off just maximizing runs – you don’t know how many the other team will score, so your best bet is maximizing the amount you score.
But if the game is about to end in the 9th inning, average runs
don’t matter – you lose if you don’t score one more.
By sacrificing the guy over to third base, you increase the chances of at least one run scoring
at the expense of the average.
You can then map the “chances of winning” with each situation – win expectancy – and calculate whether it’s worth playing to tie the game or playing for a higher average runs for a chance to win at the expense of losing immediately.
Hidden logic.
But okay, let’s step outside of math and games and apply this to life.
***
NEGOTIATIONS AND WIN CONDITIONS
When I lead a negotiation, the first thing I’ll do with my side is define our “win conditions” into three categories –
Need
Want
Nice-to-have
Negotiations are complicated, and there’s often a mix of things you absolutely need to have happen to make a deal good, things you very strongly want to have happen to make it a good deal, and a variety of little nice-to-haves that aren’t as important.
My rules go like this –
Need: you get every single item here or you walk away. Place items into this category very sparingly, and never budge an inch or indicate any flexibility on them. By definition, you need
these and will walk and if they’re not met.
Want: these are what you’re negotiating over. Almost everything important goes here. If there’s any way to make a deal happen, at all, without a condition, it goes here.
Niceties: you make a list of all the little bonus things, and handle them last.
My definition of a good negotiation is one where you get all of your needs (obviously, or you’d walk) and most of your wants. The nice-to-haves are good to keep in mind but less important.
One of the most common mistakes I see people make in negotiations is to not define their win conditions well – they define a lot of things as “must-haves” but then they trade them away. They don’t know what their bottom line or walkaway point is, and they often crumble in the heat of things.
Commonly, people in negotiations place too many things in the “Need” bucket – if there’s any way
to get the deal done without a condition being met, it’s a “Want.” And again, I consider a successful negotiation one in which you’re getting almost all of your Wants.
Now, there’s no explicit rule that you need to set win conditions in a negotiation – it’s entirely hidden logic; something for you to analyze, detect, and strategize through on your side. And yet, knowing the hidden and underlying logic of a negotiation lets you make very simple lists of objectives to navigate through to ensure you get the best possible deal.
***
THRESHOLD OF INTRODUCTIONS
Finally, let’s turn to something that’s incredibly abstract and intangible – the kind of thing most people don’t apply logic to and never think about.
Will someone introduce you to someone else they know?
Introductions are one of the most powerful ways to meet people. If you’re introduced by someone a person trusts and admires, you’re on very solid ground to start getting to know them.
I realized, some years ago, that there’s three thresholds you can be at when asking a person for an introduction –
1. They won’t introduce you for any reason.
2. They’ll only introduce you for a very relevant and specific reason.
3. They’ll introduce you to just about anyone you ask them to.
At threshold #1, you’re untrusted, or have bad manners, or wouldn’t represent the introducer well.
At threshold #2, you’re alright – if you’re looking for an accountant and they know an accountant, they’ll introduce you for that reason.
The magic is at threshold #3 – if someone trusts you to an incredible degree, knows you’ll always represent them well in any situation, and knows you’re universally a worthwhile person for anyone they know to get to know as well, then they’ll be willing to make many introductions for you to anyone they meet.
Using this very simple (and hidden) logic, you can evaluate where you’re at with anyone you know. The magic, again, is getting to threshold #3, where a person trusts you enough to introduce you to anyone they know. I met Jesse Sussman last year at GiveGetWin Summer Camp II at UChicago, where he was a standout performer. Since then, he’s raised over $10,000 for charity at GiveGetWin, and been an incredibly enjoyable person to work with, carrying forth brilliant insights along with a rare humility for his talent level, and just genuinely being an upbeat, hardworking, great guy to know and be around.
I’ll introduce him to basically anyone at this point if he asks.
In your own life, once you have even just three to five well-connected people who feel the same way about you, you’re basically set – from there, you can start to get to know just about anyone you’d want to know for your projects, career, and life.
Again, this is a hidden logic
behind introductions – you can quickly ask yourself if someone would introduce you to people they know, and under what circumstances. It’s easy to test, too – you just ask to be introduced.
There’s of course little confounding factors – maybe the person you asked to be introduced to is busy, or the person you asked for an introduction doesn’t know they as well as you thought they did – but in general, I’ve found these three simple thresholds to be a very easy way to understand getting to know people and assessing where you’re at.
From there, it’s easy enough to analyze what you need to do differently if you’re below that third magical threshold – manners? Credibility? Attitude? Building a few deeper relationships instead of more shallower ones? It lends itself well to analysis and improvement.
***
CONCLUSION
You should ever and always ask, “What matters here?”
In any situation that’s competitive, you should ask, “What really leads to winning and losing?”
In non-competitive aspects of life, you should ask, “Where am I now, and where do I want to be?”
Often, we run on vague feelings and intuitions, but never use analysis, logic, and strategy to clarify what really leads to outcomes. Thus, effort is diffused and results are erratic.
You can learn about discerning underlying logic by reading memoirs of people who were successful, and technical manuals by experts in their field. In different types of business, repeat purchase rate, churn/attrition rate, or referral rate might be a key piece of hidden logic to optimize your business around.
In competitive endeavors, you want to put a cohesive strategy around which (often hidden) variables are going to lead to success.
This rabbit hole, I fear it runs deep and that even these now we have barely scratched the surface, but burn this into your mind –
Always ask, “What matters here? What leads to winning and losing?”
Discern those variables – they’re often not explicitly stated, but when you unearth the hidden logic of situations, it’s beautiful to behold.