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Twoo Cents – When to Play Fast and Loose

In marketing class I’ve been learning consumer behavior, which is cool. Psychology is always exciting to me because it gives me a chance at something I can apply to my every day life. Understanding how and why we do and think is very interesting.
The other day we started studying a decision making model called Prospect Theory. It’s really simple but has some big applications for your Magic game. Let me explain.

Here we have value (enjoyment to you, which can be positive or negative) graphed against losses and gains.

Notice:
As gains increase, value from gains decreases. This means we get diminishing returns from gains. $50 million isn’t much better than $25 million. The same is true for losses. -$50 million isn’t much worse than -$25 million.

What are the ramifications of this?

It turns out our evaluation of risk is different depending on whether we’re up or down (from a reference point). Imagine this-

You could have either $25 million or flip a coin for $50 million or $0.

For any of us but the most degenerate gamblers, we are going to take the $25 million every time. We would even take $20 million over the gamble. We want a guarantee of being rich. The extra $25 million would be nice but we don’t need it. Graphically we see that the difference between 0 and 25 is significantly greater than the difference between 25 and 50. This is because we are evaluating risk in the domain of gains. We are risk averse in the domain of gains.

Now imagine you owe LSV $50 million and he is going to break your legs if you don’t come up with it. Your decision is very different in this situation. If you take the sure $25 million you are still $25 million in the hole, which is unimaginably far from where you want to be. If you flip a coin you could get all the way back to $0! What’s the difference between $25 million and $50 million anyway? Not too much. Graphically we see that the difference between $0 and -$25 million is much greater than the difference between -$25 million and -$50 million. We are risk acceptant in the domain of losses.

Daydreaming in the back of class I thought back to a recent Halo 3 session with my friend Victor (if you aren’t familiar with this game, skip this paragraph and the next!). I was in a situation where I was isolated in a corner on narrows and some guy had hit me with his battle rifle twice before I saw him. I couldn’t expect teammates to clean me up in this situation, so how am I going to make the best of this situation? I could try to out BR him, but he’s approximately my skill level so I’m almost guaranteed to lose. I would be guaranteed to get some shots on him, sure, but he would be able to safely recharge. What if I threw a grenade? The guy is my skill level so it’s unlikely that the grenade will hit him, but if it does I will be able to get a BR shot off to save myself before I die. It’s risky, but it was my only chance.

Interestingly, throwing the grenade, while the right play, also has lower expected gains! I can expect to get 1/2 of his health with the BR and maybe 1/3 with grenade, but it’s All or Nothing in this situation. Depending on where I am, I am willing to sacrifice expected gains for more or less risk.

One more quick non-Magic example: if two basketball teams match up and one has a clear advantage, the expected winner should shoot 50% 2 pointers for an expected gain of 1 over 35% 3 pointers for an expected gain of 1.05 because they don’t want to take on a higher risk strategy. Inversely, the worst team is willing to shoot 30% 3 pointers for an expected gain of .9 over 47.5% 2 pointers for an expected gain of .95 because a higher risk strategy is advantageous. The worse the mismatch is the farther we can take this. A bad team might be willing to shoot theoretical 10% 7 pointers for an expected gain of .7. Even if the expected gain is lower, the high risk gives a better chance of winning.

Last and MOST important lesson before moving into Magic examples.

In order to win a game you need to be in the domain of gains when the game ends.

It could be a lot, or it could be by the slimmest of margins. There is no gradient- either you win or you lose. It is binary. This is why I say “It’s All or Nothing”.

Evaluating Risk in the Domain of Losses (playing fast and loose)

First, a definition:

Playing Loose = making risky, high variance plays.

This definition of playing loose doesn’t imply good or bad play. It is simply a style of play. Playing loose could be bad, but let’s talk about times when it is exactly what you need to do to win.

I remember an early lesson of risk evaluation in Onslaught Block draft. In a world where morph was the going rate my brother and I thought Mistform Dreamer and Gustcloak Harrier were THE TOPS. We forced u/w fliers all block, to a lot of success. I remember having around 100 of all the staple commons, regardless of whether that is real or not.

In one particular draft, we got to the third pack in bad shape. Someone upstream must have been u/w. We had no bombs, our curve was miserable, and we barely had any playables. We opened this card:

Decree of Pain

Decree of Pain was (in our opinion) the best card in Scourge. -2/-2 was incredible in a morph filled world and if you ever got to survive to 8 mana… oh boy. This wasn’t the first time we opened this card in pack 3. Previously we had shipped it. Why would we take it? We had a great u/w deck and it didn’t make sense to throw it all away for a chance to play Decree of Pain.

This time was different. Our draft was a nightmare trainwreck. We were way over in the domain of losses and we had to get back up above par. It was time to gamble. By taking Decree of Pain we were throwing away two packs of a color. This wasn’t much, but Onslaught wasn’t too friendly with splashing BB and how many black cards could we expect to pick up in one pack? It was a gamble that could potentially put us even deeper in the hole, but there was no way another dry u/w pack was going to win us the draft. Deep in the hole? Let’s gamble!

Now let’s take a look at a classic situation.

Do we attack here? It’s a simple question with a complicated answer. The answer sometimes has to do with our opponent’s historical behavior. Usually it has to do with our matchup, our cards in hand to theirs, our cards in deck to theirs.

Imagine that it’s game 3. The first game our opponent played such hits as Mind Control and Frost Titan. Obviously he has Foresees and all the other good blue commons. In the second game our opponent double mulliganed and missed his third land drop, and we still BARELY squeaked it out. Our deck has a Giant Growth and a Lightning Bolt but struggles hard against an Azure Drake.

And here we are, on the doorstep of victory or defeat. Do we attack and bluff? Do we sit back and wait? If we attack and he takes it we just got in 2 damage. That damage might be important. But if we attack and he blocks we lose our Runeclaw Bear, which is worth a lot more than the 2 damage we are gambling for. So why would we attack here?

We are not expected to win this game. The longer the game goes, the greater the chance of getting buried under Foresees, Mind Controls, and Frost Titans. Those are cards we can’t expect to beat. We are way over in the domain of losses. If we gamble and squeak in a few extra damage here or there we might have a chance of winning a close game before he is able to take control. I want to attack here, with the knowledge that my opponent might snap block. I am willing to make a lower expected gains play just because it’s risky.

What can I expect my opponent to do here? In his mind, he is winning. Maybe he will trade an Azure drake for a Giant Growth. Maybe he should. Maybe he thinks he is so far ahead and he NEEDS the Azure Drake. Maybe since he is in the domain of gains he doesn’t want to gamble. And his lead starts to erode. He is willing to make a lower expected gains play just because it is low risk.

In winning a game of Magic it is okay sometimes to let your lead erode. All that matters is being in the lead when the game ends. See how and when the game is going to end and play accordingly.

Evaluating Risk in the Domain of Gains (playing tight)

Playing Tight = Making low risk, low variance plays with relatively known results.

This definition of playing loose doesn’t imply playing well- it is only a style. There are times where playing tight will lose you the game. Let’s talk about situations where playing tight is exactly what you need to be doing.

In Pro Tour Kyoto, Nassif and LSV clashed in the top 8.

Check out the whole game or just the play starting at 2:30.

Nassif’s play is on of my favorite plays of all time (admittedly it wouldn’t be if it hadn’t worked). How could he let that Ajani Goldmane resolve? There was a chance that Ajani Goldmane would win the game by itself, and it almost did. Expending his Negate would put Nassif in a situation where he could probably only lose to a land + head games this turn.

Nassif decided he could beat an Ajani. It made the game a lot harder, but he could beat it. Could he beat an improbable Head Games this turn? No, he couldn’t. In this situation Nassif made a lower expected gains play with low risk and relatively known outcome. Winning Magic isn’t about maximizing gains- it’s just about making sure your value is positive when the game ends.

Did Luis have the land and the Head Games? It doesn’t matter. The evaluation of the play was solid, regardless of the result.

Consider another classic situation:

Day of Judgment

You are an aggro deck and you are going to kill your opponent the next turn for sure if you play this creature, but they might have a wrath. What do you do? Do you play it safe, or do you risk losing with no recovery? You might overextend, or you might underextend.

The answer has to do with whether we are winning or losing. If we are in a dominant board position without playing the creature, we might play around the wrath. We might not even know they have a wrath, but sometimes we are so far ahead we have the luxury of playing around cards we don’t even know of. In other circumstances we might empty our hand to a deck that we know plays 8 wraths. Our risk aversion or acceptance is completely contextual with where we stand on the domain of gains or losses.

What does this mean for the rest of us? Simple. When we’re ahead, we’ll play it safe. Let’s not make big, risky plays, even if they can put us even farther ahead. Let’s be careful, and if our lead erodes a little bit, so be it. Our lead has to erode completely for us to lose the game, so let’s evaluate decisions accordingly.

What does this mean for the rest of us? Simple. When we’re ahead, we’ll play it safe. Let’s not make big, risky plays, even if they can put us even farther ahead. Let’s be careful, and if our lead erodes a little bit, so be it. Our lead has to erode completely for us to lose the game, so let’s evaluate decisions accordingly.

Don’t play scared!

You need the proper mindset in order to win Magic tournaments. If you’re on pace to lose, you can’t be scared of losing. It’s tempting to play scared, play safe, and lose a game you didn’t want to lose but knew you were going to lose. Screw that, this game is winnable! We need this, this, and this to happen, and our opponent to make this mistake, but it’s an out right? LET’S GO! It’s a long shot, but it gives us a small chance to win. We’re giving up a guaranteed chance to barely lose though… well, our friends are going to ask if we won or lost, and they’re not going to want to hear the story. We could explain how we barely lost- that is tempting. No, either we win or we lose here. There are no shades of grey, so let’s go big!

Don’t be afraid of giving up some of your lead!

You remember that game. That game where we were so far ahead that there was no way to lose. We just played our cards how we felt. We can’t lose anyway. We have our last removal spell to kill their only creature so we might as well use it. We might as well use our only counterspell to counter the last card in their hand. And then the next turn it happens. They draw the card, they play it, and we can’t believe what just happened. We might not even remember what we did before. We might focus on how lucky they were to draw it. No, next time, we’re not going to use our last removal spell if it’s possible to beat that creature. We’re not going to use our last counterspell if it’s possible to beat that spell. Maybe we’re giving up some of our lead, but we can afford to give up a little bit of our lead in order to never give up the entirety of our lead.

When you’re playing, try to find out whether you’re on pace to win the game. The answer could change everything.

BONUS: Help make Magic awesome!

Magic is AWESOME! If it wasn’t I wouldn’t be writing about it. I wouldn’t be thinking about it. I wouldn’t be playing it. It wouldn’t have taken me to Europe. It wouldn’t have introduced me to some incredible people. It wouldn’t have given me a writing career. It wouldn’t have given me a sense of work ethic by rewarding my hard work. It wouldn’t. It wouldn’t have taught me that I can do anything, so long as I work harder than anyone else. It wouldn’t have raised my self-esteem. It wouldn’t have centered it and given me perspective. It wouldn’t have given me the stability to help others. It wouldn’t have given me a platform to do it. It wouldn’t have given me an endlessly wide road of possibilities. I wouldn’t be writing to you right now. But it is. Magic is AWESOME!

If you’re in the closet about it, get over it. If you’re not proud of yourself, cut it out. I’m sorry. I understand and I want to be patient with you. But you’re doing a disservice to the community. And maybe you don’t owe the community. But you’re doing a disservice to yourself and you owe it to yourself. This game is not weird or negative, but when you hide it or are ashamed it suddenly is.

Why would you hide the fact that you play basketball from your friends? You wouldn’t. Why would you hide anything that is AWESOME and you LOVE to do from your friends? You wouldn’t. When you are hiding or ashamed of Magic you are sub-communicating that it is something to hide and be ashamed of, and the game is not yours to do this with. When this happens you are hurting the image of the game, you are hurting the community, and you are hurting yourself. Do you want to help make Magic awesome? Of course! Start off by telling EVERYONE how much you love this game. Do it for the game. Do it for all the people you’ve met through Magic. Do it for yourself.

If someone asks you what Magic is you don’t need to explain why it’s cool. You don’t need to explain where you’ve gone, who you’ve met, what you’ve done. You don’t need to prove it. It’s not what you say but how you say it. People respond to your emotions. You are explaining because when emotions don’t work we try to make a rational case. We don’t need to make a rational case. Proudly declaring that Magic is awesome is enough of an answer to that question.

If they want more, they can ask, and they’ll be lucky to find out. Lucky to play. Lucky to see the things you’ve seen. Lucky to have the thoughts you’ve had. Lucky to meet the people you’ve met. They will be very lucky.

If you ask me what basketball is I am not going to launch into an explanation. I am not going to be ready to defend it. I am going to say with a sly smile that “it’s a game” and let them build the story in their own head.

Start off by telling your friends that Magic is awesome. Tell your family that Magic is awesome. Tell everyone on Facebook that Magic is awesome. Tell a stranger that Magic is awesome. It’s simple.

Come from the mental frame that Magic is AWESOME, because it is. Otherwise you wouldn’t still be here ;D.

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