"Foolish people work hard to appear happy. Work hard to be happy." - Lucius Malfoy



The howler arrived early, well before breakfast. It didn't arrive in the Great Hall, of course. Draco had heard Tanaxu's arrival and groggily opened his eyes in time to see the letter, growing red and about to burst. Draco managed to grab the letter and dive into Harry's trunk before it exploded. Harry slept through it, of course, his Quietus slider was always set to high when he slept. Draco preferred to be able to hear his surroundings, even if that disturbed his sleep from time to time. Still, Gregory only caught a few words, which meant that the rest of Slytherin probably hadn't.

Now, heart pounding, Draco sat at his desk writing.

Mother,

We are family, and if not as close as we should be, still I do not wish to plot against you.

I share your concerns about our future, but money sitting in a vault acts as a general's reserve, and like a reserve it must be used at the proper time. I will cease spending "extravagantly" if you aid my search for Severus Snape and assist my investigations. Father swore Snape joined Voldemort, yet he survives. Besides, I fear you are moping. I know it is not my place, but it would serve you well to get out of the house.

Please, for his memory and our future, assist me.

PS What do you know of my Professors? Which may be allies?

"Well, Don't ogres make soup out of people's bones? That would explain the skinning," said Vincent.

Offense started in thirty minutes and most of the class were still brainstorming theories.

Neville shook his head. "I don't think Ogres sneak up on people like that. If they attacked, everyone would know. I'm thinking it's a Tystnaden."

"Hm. That might work," said Hermione. She still stayed in the regular girl's dorm and Lavander Brown had instantly sought out the most famous Gryffindor's advice, since everyone knew that Hermione had read literally dozens of books. Hermione, intrigued, had spent several days reading through the library to see if she could solve this mystery. Seeing that nobody apart from Neville knew what they were discussing, she explained. "The Tystnaded is a creature that obliviates anyone who sees them. So, you see, it may have actually stumbled on the whole group, killed one of them, and then the rest of them forgot."

"Ooh, what do they look like?" said Colin Creevey. He'd attached himself to the group as had several other students. Any spotting of Hermione Granger and Harry Potter drew a crowd, these days.

"Well, obviously nobody knows," sniffed Hermione. She was used to the crowds, but the fact that the first year kept following her around made her wary. Still, she'd gotten used to it enough that she didn't put as much bite into her words as most girls would have.

"They sound dangerous. Tricky," said Harry. He'd also been attracted to the problem but hadn't had nearly as much free time and hadn't even heard of a Tystnaden until now. "If only the people who see them get obliviated, then would probably want to avoid crowds. Others would see the first people getting confused, they'd get wary. Maybe start casting area-effect hexes. If I were a Tystnaden I don't think I'd attack crowds. I'd pick off lone individuals. But the creature did that, or they think it did. So why would the Aurors separate?" Harry looked visibly shaken and spent several hours over the next day planning how to defeat a Tystnaden. The first trick was to recognize you'd been obliviated, and it would help to precommit to what kind of message you'd leave yourself...

The conversation continued while the first years poured out of the lecture hall and Luna Lovegood, hearing strange and possibly mythical creatures named by several students, chimed in. "It's a Yautja," she said, in an air less distracted than she usually used.

"I've never heard of that," said Draco, who had followed behind her.

"Of course," said Luna sweetly. "They are invisible hunters who only attack the strongest victims. Like Aurors, or adventurers. It's their rite of passage."

"That does kind of fit," said Neville.

"So why aren't more people killed by them," asked Hermione. "I mean, if every one of these creatures has to do this?"

"Oh, they rarely hunt on Earth," said Luna. "It's too far away."

Several students laughed and Harry Potter just snorted while the discussion turned to reasonable options.

In Peverell Hospital, Draco walked around examining security when someone called his name.

"So," said one of the Weasley twins, "he's got you doing it too. Any ideas?" The other one was quickly rolling up a scroll of some sort. Draco thought he saw a map, which made sense. He was still getting a feel for the layout. Security seemed impossibly tight, with Aurors guarding entrances and confiscating anything useful (although they'd let him keep a quill and his journal, to take notes). Draco glanced from one to the other.

"Twins raises a possibility. Have you considered using the two of you, one disguised as someone else? Then removing it for the confusion aspect?"

"Thief's Downfall." They said together. Then they started alternating phrases. "And please / we're experts / First thing we / thought of. We've racked our brains / trying to take advantage / it's hard to see something." One shrugged, slightly ahead of the other turning around. The Aurors watched them carefully. Draco had shown a note from Harry to allow him in (searched, but he could get the benefit of a doubt to bring in items that might normally be confiscated).

"I assume there's an anti-Apparition jinx?"

"Of course," said Fred, or maybe George. A trio of Aurors started to move a patient from his bed into the Healing Room, and Draco heard the splash of the Thief's Downfall.

Draco asked "Do we know if that blocks non-Wizards?"

"Well, I'm not sure," said George or maybe Fred.

They exchanged a look and Fred, Fred?, continued. "We tried to summon the Sorting Hat but it doesn't answer us most of the time."

George, George?, shrugged. "I think it knows when we're actually desperate and testing doesn't count."

"I was actually thinking more of House Elves," Draco said. One of the twins raised an eyebrow and they all huddled together to discuss possible solutions.

In the dungeons near Slytherin.

Harry Potter realized, now that he lived there, that this unused classroom lit with eerie green light didn't belong to the Slytherin dungeons proper. Draco had never let him into the Syltherin Dungeons, the rest of the Slytherins referred to this as the "public" dungeon.

Which made it still convenient to teach lessons to the expanded Bayesian Conspiracy. Draco invited the Silvery Slytherins, so that added Daphne Greengrass and Gregory. (Draco tried to not think of her as Daphne of Greengrass, because he might slip and say it. A Malfoy never insults by accident). Harry Potter had invited Hermione and Neville, for now. For the first two weeks lessons covered material Draco already knew. He'd co-taught, provided examples, translated Muggle concepts into Wizarding terms. But now Draco found himself lost with the rest of the non-Harry Potters.

They'd gotten diverted when Draco stated that the methods didn't help during a fight.

"What do you mean, of course they do" said Harry.

"I'm being imprecise," Draco admitted. "They help at times during a battle, but during lulls. I'm not saying that they are useless. Just limited during an actual battle. Once the spells are flying you don't have time for this."

"The techniques are useful for decision making, and you make decisions all the time during battle."

Draco just cocked his head in question.

"You kind of don't," said Neville. "I mean, you are flying around with Chaotic Leaps, kicking, punching, casting spells, dodging. We spend a lot of time preparing, but during the battle itself we just kind of re-act. I mean, if you imagine a battle where your enemy chats with you for a few hours sure …. but real battles?"

Hermione said "Right. All the decision making is done ahead of time. And it's been really useful, I agree. "

Draco nodded. "Right. I mean, I'm certainly making decisions, but all of these techniques, they cost too much time I just pick something that's good enough. It's not like I'm consciously deciding or weighing trade offs. It feels like I'm not making any decisions at all, during a fight. On the first day, when I got ambushed, it's not like I did anything clever. Either time I got ambushed. I don't feel like I made any decisions, even though I tried. But that's only when the spells fly. Even in a battle, there's lots of time to think about things. Just not then."

Harry considered this for a full minute.

"There's a theory for this, called recognition primed decision making. They interviewed firefighters and soldiers to figure out how they made decisions, and they talked to one fire captain who said he didn't think he'd made a decision in a fire during his entire career. He did, of course, he made lots of decisions. Once, there was a tiny fire in a two-story house. His team goes into the ground floor and uses a muggle Aquamenti to douse the fire, but it doesn't go out. In fact, the fire roars back at them. So the captain orders his men out, and right as they are leaving the floor collapses. It turns out there was a basement and it had been on fire for a long time. The captain attributed getting his men out to his sixth sense."

Harry paused. "But you see, it was really just him subconsciously noticing confusion. Once the interviewer sat down and asked him to explain the situation in detail, explain it to someone who wasn't a fire-fighter, there were all these tiny details he'd noticed. The way the smoke moved, the way the fire reacted. The captain knew it didn't add up, so he did the prudent thing and retreated. Just in time."

"Yes, but the only lesson is to be experienced," Draco said. "Other people, even the novice fire fighters didn't notice the problems. You can't teach that. Our battles give us that experience, and we use the techniques outside of battles, afterwards, to clarify our thoughts. We prepare. The preparation makes us strong. It's not that the techniques are useless, not by any means."

Harry held up his hand, and Draco stopped.

"I agree, but I think I can explain this better. We've covered experimentation and falsifiability, but efficiency matters in the real world too. I agree with your general point. Sometimes you have to make snap decisions, and yes, in those cases you can't do everything perfectly. Unlike the 2-4-6 game, sometimes you don't have the time or ability to make a bunch of predictions and get answers. Sometimes you only have a few chances, or even one chance, like the fire-fighter. I think there are some applicable lessons."

"Consider Chocolate Frogs. They come with those Famous Witch and Wizard trading cards, right? Well, they appear to be randomly distributed. I couldn't afford real chocolate frogs, and it would distract us to have them, so I just made a pretend set of trading cards. I'd been saving this for another lesson, but I think it applies. Suppose you want to complete your set of trading cards. If you could predict which card was in which box, you'd just have to buy one box to complete your set, instead of trade. And you only have enough money to buy so many frogs before you run out of money or your parents ground you for eating too much chocolate."

Harry had been mumbling a few words here and there, and finally pulled a pack of Muggle cards from his pouch and set them on the table. "Rather than guess the exact person on each card, we'll just guess if it's a Witch or Wizard. Here, I'll deal a few cards out."

Harry flipped over the top cards of the deck and placed them on the table. Draco got a Wizard, Daphne got a Wizard, Gregory got a Witch, as did Hermione. Neville got a Wizard and then Harry flipped up another card and placed a Wizard in front of himself. Harry picked up the next card and looked at Draco. "Let's play a game, at your turn you guess the gender whoever gets the most cards correct gets an actual Chocolate Frog."

"Witch," said Draco. "We've never seen more than two in a row," he added. Harry flipped over the card and put it down in front of Draco. It was a Wizard.

"Don't feel bad. You made a prediction and you were wrong, but you stated a rule that could be falsified. You performed an experiment. Incidentally, that reminds me of the Better's Oath. We aren't betting, but we are playing a game for stakes, which is similar. I happen to like betting because it forces you to think clearly about how probable something is. Anyway, part of the Better's Oath is 'When I win a bet, I will not shame my opponent, for a betting loser has far more honor than the mass of men who live by loose and idle talk.' So it would be wrong of us to shame Draco, he had an idea, he tested it. He's learned something."

Harry held out the next card, still face down, in front of Daphne. "Witch. I don't know, it just seems like we've had a lot of Wizards." The card was a witch. Harry started to hand it to her, then just put it down and put a pebble on it.

"That way we can still see the pattern. I'll mark the correct cards. Winner still gets a frog. Since we're talking about fast decision making, you have to think fast."

Gregory guessed Wizard correctly, Hermione incorrectly called a Witch, Neville guessed Witch and got one. Harry flipped up a wizard in front of himself without guessing, then pulled out a card for Draco.

"Wizard."

Harry held the card still. "You don't have a theory?" Draco just shrugged so Harry flipped up the card, it was a wizard. They played a few more rounds, faster this time, then Harry set aside the deck and said. "OK, we have a moment to retreat. Now we can apply the theories. So, what do we know. You can see the pattern that's there. Look at what you see."

Hermione started. "There are 30 cards out, and 19 of them are wizards, which seems like yet another bias against Witches. I know, these are famous ones and there are more famous wizards than witches, but it still goes that way."

Draco said "We've had up to five wizards in a row, starting with Neville's fourth card and working around. We've only had three witches in a row."

Gregory had been doing some counting. "After a witch, we had 7 wizards and 4 witches. I'm not sure that means anything."

Neville started to bring up Arithmancy, but Harry cut him off. "The lesson has nothing to do with that. Well, not with Wizarding Arithmancy, math is involved. But I promise it doesn't have anything to do with magical numbers. Well, I suppose it could, but since I don't know much about it it's not my intent."

Harry let them discuss the patterns for four more minutes. "Does anyone have any theories or ideas?"

Nobody did. Actually, Gregory proposed a rather elegant theory, but Neville found a counterexample in the second round. Gregory thought about this and modified his theory, and Harry pointed out that this additional complexity should weigh against him believing his theory, but that didn't mean it was wrong. But nobody else had any ideas.

"OK," said Harry, "Now we're back to an actual battle. I'm going to deal out the rest of the cards. Three left for each person. Draco?"

By this point Draco had given up. The pattern was too complex for him to see. He picked Wizard the next three cards, and was right twice. After another minute, the deck was exhausted and Draco was tied with Neville and Daphne.

"I should have made more cards, a tie was too likely. When I thought of this I figured we'd have fewer people. Anyway, we've got enough information to prove my point. Gregory's theory was proven wrong soon after he amended it, so there's that."

"So, what was it?" asked Neville. "What was the pattern?"

"Oh, it was random. Just like I said it appeared. I made the cards with the right ratios and then shuffled them up before I got here. About 70% of the cards are Wizards and 30% are Witches, which seems to be the actual ratio the Chocolate Frog company uses, because there are more famous Wizards than Witches, Hermione, which may or may not be unfair but that's how it is."

"So, you rigged it," said Gregory. "There's no lesson."

"No, there are lots of lessons. The first lesson is that people are really good at finding patterns where none exist, and then convincing themselves to ignore other evidence. We're trained to see patterns, we see faces in clouds. More importantly the cost for being wrong is usually much much lower than the cost for not seeing a pattern. If you saw a stick and thought it was a snake and jumped up, the worst that would happen is that people would laugh at you. But if you didn't see a snake that was there, you could get killed. So that's why we jump at shadows. Seeing a pattern that isn't there is called Pareidolia, by the way. As for the second lesson. Daphne, why did you bet Wizard, Witch, Wizard for your last three rounds?"

"Well, not knowing it was random, I just tried to make sure that I guessed two wizards to one witch. That was the closest thing we had to a pattern."

Harry nodded and then turned to Neville.

"Same idea. By the last round I had six wizards and only one witch, so I called witch and got it."

"And you, Draco?"

"I didn't see a pattern, so I just called Wizard each time."

"Why wizard?"

"There were more wizards."

"Draco was moderately unlucky, actually. There were more wizards than witches, so when Daphe and Neville actually called Witch one of the final rounds, that should have cost them. If we'd kept playing long enough, Draco would win as long as he kept calling Wizard. If you kept calling Witch one-third of the time, you'd slowly lose out, even though Witches are one-third of the cards. But in the short term, you can get lucky. The funny thing is, if you tell people that the cards are heavily slanted towards Wizards, like Hermione pointed out, people still try to guess Witch every now and then, which is silly. If you don't know the pattern, it may as well be random, so why are you trying to predict something you can't possible know?"

"That still sounds like you cheated for this game," said Daphne.

"Look, imagine Voldemort chasing you. From experience you know that people who go down into the dungeons get away ten times out of one hundred and the people who go into towers survive five times out of one hundred. If you had time to do a full scientific study, you could figure out why or how that was."

"Sadly, Voldemort does not agree to help you, he just wants you dead. But your first goal is to survive Voldemort … or win the game you are playing. So, head to the dungeons. If you have to make a decision right away make the best decision you can with the information you have. If you want to make a prediction, you can tell yourself the hypothesis and what you expect to happen in your head. But make the best bet to survive or win the Chocolate Frog. Like Draco did. In the short term, you could get unlucky, but it's the best you can do, until you come up with a better hypothesis."

"So," said Draco, "You do agree that you have to at least recognize that a situation is weird, then you take your best shot or retreat to figure it out? And that preparation will allow you to make good, even great decisions in most situations, when you don't have time to sort things out."

"I said as much," said Harry. "Look, my methods aren't perfect. They are a tool. They don't guarantee you'll be right they just help you be …. less wrong. The point is to examine your experiences, and use those tools. Sometimes the best you can do is instinct, but instinct is also a trap."

That lead to a long discussion about various modes of thinking, and Harry said that the real issue, which they didn't have time for, was on hypothesis generation, and they'd discuss it at the next meeting. Later that night Draco, sucking the last bits of chocolate from his hand, opened his diary to the final page.

Author's Note – The Better's Oath was formed by Bryan Caplan, the full version can be found at EconLog.

Recognition Primed Decision Making was in fact studied in the 80s, but I have no idea how Harry Potter got that information. We'll assume his father subscribes to journals. My example and many notes are taken from "Sources of Power: How People Make Decisions" by Gary Klein. I had the pleasure of meeting Doctor Klein a decade ago, although we did not discuss his research.

The experiment that Harry performs (guessing cards) is actually published in '96. A. Tversky and W. Edwards (1966). "Information versus reward in binary choice." Journal of Experimental Psychology, 71, 680-683. See also Y. Schul and R. Mayo 2003, "Searching for certainty in an uncertain world." In Journal of Behavioral Decision Making, 16:2, 93-106. (I found a reference to it on E.Y.'s site)

Tversky also collaborated with Daniel Kahneman, whose book "Thinking: Fast and Slow" served as a partial inspiration for the chapter. T:F&S discusses many of the same biases as listed in HPMOR.