Carcerian Stones – Where is this Arofell fella?

We’re continuing the D&D adventure story. Previously, we found our adventurers at the gates of Havenswerd, and the bard declared he’s a criminal in the city. We have Ryan the human DM, Dan playing Toth the goliath warden, James playing Heoriss the eladrin invoker, Ian playing Iofae the eladrin sorcerer, and Klenn playing Phileas the half-elf bard. And now…

Wait, there’s also a puzzle hidden in the story. And now…

*****

Ryan: Havenswerd is a big city. You’ll need some know-how to navigate the streets.
Dan: You’re throwing a skill challenge at us?
Ryan: 3 separate ones, in fact. One for shopping, one for the tavern investigation, and one for our bard reaching his friend.
Dan: But it’s just shopping!
Ryan: *shrugs* It’s a street maze. You’ll have to find the shops first.

Ian: How good are we at Streetwise? I have a 4.
James: I’m at ground zero.
Dan: I’m below ground zero… Negative 1! Never thought Streetwise to be useful…

Ian: Alright, we’ll have to swap then. My brother will still go to the tavern. Dan, you go with him. He might need help. And I’ll go shopping. Do I need a list of what they’re buying first? *looking at Ryan*
Ryan: No. You just need to find a shop first. I’ll let you buy for them then, even if these guys aren’t around.

Dan: Wait a minute. So we’re split into 3 groups with individual skill challenges?
Ryan: That’s right.
Dan: That’s not the way to do it.
Ryan: Well, you’re the one who split the party. Besides, it’s different.
Klenn: I think it’s fun, and saves time. So how do we do this?

Phileas gave the party some directions on how to reach the tavern. Through his friend, he’ll contact the party once he’s safe.

Ryan: Hold on a second. Uh, Klenn, you mind telling me who this trusted friend of yours is?
Klenn: Oh, he’s a thief lord, of some sorts. His name is Logan.
James: *shocked* You’re consorting with scoundrels?
Klenn: Let’s just say my character has… flexible morals.
Dan: *pounding on table* AHAHAHA! That’s a good one!

It was late afternoon, and though there’s still light, Phileas didn’t want to wait outside Havenswerd for night to fall (what with the wolves and all). He moved briskly along the side of the walls and disappeared into the shadows of the residential houses. The rest of the party will be split in 2. Iofae will attempt to navigate the streets to find the shops for purchasing much needed equipment. Toth and Heoriss will go to the tavern, retrieve Phileas’ belongings if they’re still there, and gather clues about the murder.

Ryan: So, which group wants to start first?
Klenn: Me. What am I to do?
Ryan: You’re trying to sneak around to reach your friend, so roll for Stealth first, then for Streetwise.
Klenn: *rolls d20*

Phileas reached his thief lord friend.

Klenn: Yes!
Ian: My turn. Streetwise huh? *rolls d20*

Iofae got lost in the maze of identically-looking streets.

Ian: Sorry guys… Now what?
Ryan: Hmm… Roll for Perception.

But he did notice a man slinking suspiciously into an alley. Iofae, lacking any other direction, decided to follow him. At the end of the alley, there was a door. But the man had disappeared.

Ian: I open the door.
Ryan: It’s locked.
Ian: I’m so glad I took this. I have Thievery. I try to pick the lock.
Ryan: Go ahead.

The locked door opened with a soft click. It was dark inside. Iofae moved in further and was stopped by the feeling of a sharp point propped against his neck. “Move any closer, and I’ll slit you.”

Torches lit up, and Iofae saw the man he was following holding a dagger to his neck. There was a group of men further in. He also saw Phileas among them.

Klenn: I am?
Ryan: Ian unwittingly stumbled into your friend’s hideout.
Ian: Oh cool!
Ryan: And you can get help with the shopping from these new friends. And now we turn to our CSI team here…

Medieval alley
[image by jewhyte]

Toth and Heoriss reached the tavern. They decided to go around to the back, where Phileas jumped off, instead of asking the good lady tavern keeper.

Dan: 2nd floor, right? Ok, I’ll heft you up.
James: I’ve got a better idea.

Heoriss blurred, and reappeared at the 2nd floor.

Dan: Bloody eladrins and their teleportations. *smile* Ok, I’ll climb up.
Ryan: Roll for Athletics.
Dan: *rolls d20* Yes!
Ryan: Now roll for Stealth.
Dan: What? Why?
Ryan: Because you’re trying to be quiet.

Toth managed to climb quietly up to the 2nd floor of the tavern, and entered what used to be Phileas’ room through the open window. The dead body was already removed, and there were signs of cleaning up, though there’s still a reddish stain on the floor.

Ian: Blood is notoriously hard to remove…
James: Ok, we search the room for Phileas’ belongings and any clues to the murder.
Ryan: Perception check.
James: *rolls d20* Alright, 20! That’s 29 total.

Heoriss finds a pouch with some money, a flute, and a long sword with some runes on it, hidden away in a corner behind a small cupboard. He also noticed a golden dagger jutting from the ceiling, stuck in a wooden beam.

James: Ok, you’re up.
Dan: Alright. Can I reach the ceiling, or do I have to jump?
Ryan: The ceiling’s low enough for you to reach with a small jump. To simplify things, I’ll just let you pass with the jump.

Toth looked at the golden dagger in his hands. A strange symbol is engraved at the hilt, but both of them didn’t recognise it. They heard someone coming up the stairs, and the voice of a woman saying, “I’ll be right back!”. They decided they’ve gotten what they could find, and left the room in the same manner they came in.

When they were on ground level again, they heard a psst. A shabbily dressed man, a beggar most probably, was looking at them. “Hey. You Toth and Hayoris? Pheeleeus sent me.” They followed the beggar, and reached the thief lord, Logan’s hideout. And the party was reunited.

It’s night time, but somehow, Logan managed to get their stuff bought.

James: We suck. We seriously need some cash. And quick.
Dan: Hear hear.
Ian: There’s not a lot we can buy. Hey, what about this Arofell wizard? We need quests. He seems like the kind of person who gives quests.
Klenn: Yeah. He’s at the Wizards Guild, right? Can we go to this Wizards Guild?
Ryan: So it’s decided? You’re going to Wizards Guild to look for Arofell?
Dan: Yup.
Ryan: You wanna do it at night?
Dan: Oh…

The Wizards Guild

The next morning, the party left to look for the Wizards Guild. Logan got Phileas a disguise, so the half-elf could move around the city.

Dan: Do we need a Streetwise check?
Ryan: *smile* Nope.

Logan also sent one of his underlings to guide the party to the Wizards Guild. It was mid morning by the time they reached the guild. The small guild “office” had a clerk, and the party asked him where could they find Arofell.

“Oh it’s my first day here. Perhaps you could ask the wizards back there. There’s a building behind this one that acts as their labs.”

They went around to the back and saw a 3-storey high building. They counted 1, 2, … 7 doors on each storey. A wizard or two hung around in the courtyard, and apprentices scurried back and forth.

“That nincompoop! I would sooner burn myself to death than to share the same floor as that useless excuse of a wizard!”
“Oh don’t mind him. He doesn’t like Arofell very much, so he moved to the top floor.”

“Who? Arofell? My master sent me to deliver a message to him once. I think his door was odd-numbered.”
“So what’s his floor?” Toth asked. But the apprentice had scurried away.

“Pardon me? You’ll have to speak louder, young man. I can’t hear you.” A wizened face was straining his eyes to look at the party.
“DO YOU KNOW WHERE TO FIND AROFELL?” Heoriss shouted.
“I’ve been on the ground floor for many years, and I’ve never known this Arofell wizard.”

“I only know all the wizards take larger numbers as their door numbers. Well, except for the one at the top floor, who took number 1. He always insult me whenever I pass a message to him, that arrogant, self-important piece of … Uh, you wouldn’t tell anyone about what I just said, would you?”

“Well, I do know the corner rooms of the 2nd floor aren’t taken.”
“How do you know that?” Iofae asked.
“Because, I uhm…” The young man was blushing furiously.
“Ahh, a tryst?” Phileas offered.
The young man blushed even more.
“If I work hard for a few years, I’ll be able to marry her, and get ourselves a house.”

James: Any more clues?
Ryan: That’s it.
Dan: Alright, math genius, this is your kind of thing.
Ian: Hmm… it’s elementary, my dear Watson.

The party deduced the correct room of Arofell, and entered the room. In it, they found piles and piles of paper and books. The candle on the desk had long ceased burning. A large book lay open on the desk, and a man, perhaps in his mid-forties, was snoring on top of it.

“Mr Arofell?” Phileas asked.

to be continued…

*****
P.S. Skill challenges are non-combat encounters. There’s a difficulty class (DC) for the appropriate skill and situation. For example, to pass a DC 16 for Athletics, you need to roll a d20. If the result plus your Athletics score (plus any other modifiers) is equal to or greater than 16, then you pass.

Update: I changed the sword of Phileas in the tavern from a magical short sword to a magical long sword. Yes, I know it sounds like innuendo. I just need him to deal a bit more damage, even if it’s all in my mind. … Alright, stop leering. You’re creeping me out…

Know what you are optimising for

Seth Godin gave a math puzzle. I know! I’m shocked too! I’d have to plagiarise a bit, since the puzzle fills more than 50% of his article. I’ll take the minimum that still makes sense. Here it goes:

Let’s say your goal is to reduce gasoline consumption.

And let’s say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment:

  • Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
  • Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)

My first answer was the second scenario. It’s wrong. The first scenario is the better investment. 2 of Seth’s readers had provided their own explanations (see Charlie‘s and Nariman‘s explanations).

Charlie gave a concrete example with calculations. Nariman distilled the question into math symbols. *smile* Both explained the answer excellently. I’m going to borrow on Nariman’s math workings and continue from there. You might want to read both explanations first.

So, following up on Nariman’s math calculations, we have

Let m be number of miles driven by a car…
Let s be the gas consumption (in gallons) for Suburbans (= m/10)
Let p be the gas consumption (in gallons) for Priuses (= m/50)
Let T be the total consumption (in gallons) (= s + p = m/10 + m/50 = 6m/50 = 0.12/m)

Now, Charlie used a “magic number” to start, 1300 miles. We’ll use that. Without loss of generality, we’ll examine only 1 Suburban and 1 Prius (since we’re talking about 50% existence for each).

In the 1st scenario, the total gasoline consumption is
1300/13 + 1300/50
= 100 + 26
= 126 gallons

In the 2nd scenario, the total gasoline consumption is
1300/10 + 1300/100
= 130 + 13
= 143 gallons

So with simple numbers, it’s easy to see that the 1st scenario is better. But can we make the 2nd scenario better? We doubled the mileage of a Prius and it’s still not good enough. How much do we need to improve the mileage before it becomes comparable?

Let h be the mileage such that the 2nd scenario is comparable.
So for the 2nd scenario, it becomes
1300/10 + 1300/h
= 130 + 1300/h

Here’s where it gets interesting. Let h go to infinity. The expression
130 + 1300/h
goes to 130 (because 1300/h goes to zero),
which is still more than 126 (from the 1st scenario).

This means, even if the Prius can travel all the way to Alpha Centauri and back a gazillion times, and then run a bajillion laps on the circumference of the universe, all on just a drop of oil, the 1st scenario is still better!

I don’t know much about cars, but I’d say that’s bad…

The misdirection

I’m guessing your first answer is also that the 2nd scenario is better. The reason why it’s wrong is because we were optimising for the wrong thing. The very first statement is

Let’s say your goal is to reduce gasoline consumption.

We were supposed to minimise gasoline consumption. But when the question came up, the term “mileage” appeared and took centre stage. And subsequently wrangled our minds to forget about what we were trying to do, and coerced us to maximise mileage instead.

We were solving the wrong problem.

Parting thoughts

Improving something that’s fairly good (a 50 miles per gallon Prius) is harder than improving something that’s fairly terrible (a 10 miles per gallon Suburban). Individually speaking, you should go ahead and improve the Prius (it was a 100% improvement!). But taken together, you should be improving the weakest link. In this case, the Suburban.

It’s not about Prius’ efficiency. It’s about Suburban’s inefficiency.

We aren’t just improving one line of transportation. We are improving the entire system of transportation on the planet.

Random thought: the problem of minimising gasoline consumption is not the dual problem of maximising mileage. Go figure.

Carcerian Stones – The Surprise Slip

We’re continuing the D&D adventure story. Previously, our adventurers evaded a large pack of wolves, rested at an abbey, and all had the same dream. We have Ryan the human DM, Dan playing Toth the goliath warden, James playing Heoriss the eladrin invoker, Ian playing Iofae the eladrin sorcerer, and Klenn playing Phileas the half-elf bard. And now…

*****

Ryan: All of you wake up in the morning, all having had the same dream. A monk led each of you to a small dining room to break fast.
Ian: So we know that we all had the same dream?
Ryan: Well, the dream is a strange one. Wouldn’t one of you be likely to talk about it?
James: So who do you think the man in blue robes is?
Ryan: *cough*
James: Oh. Right.

“So who do you think the man in blue robes is?” asked Heoriss.
“Who cares! My master was killed. I have to go back to the cottage.” grunted Toth.
“And we should tell our father about what happened.” said Iofae.

James: Wait, we have a father!?
Ian: Didn’t you read the background story Ryan gave us?
James: Sorry…

“I shall accompany you. We can proceed to Havenswerd after all the necessary affairs had been taken care off.” said Phileas with a musical lilt.

Dan: I can practically hear the thee’s and thou’s spilling out of your mouth…
Klenn: *smile*
Ryan: It is at this point that I have to give you these. *hands out a slip of paper to each of them* Note that you can tell the others as much, or as little about the information as you want.
Dan: *reading his slip* Now you tell me there’s cool stuff at the cottage…
James and Ian: We’re the babies in the dream?!?!
Klenn: Aw man, this is tough… you’re giving me a hard part to play…

Dan: Ok, it’s decided. We’ll go back to the cottage, then to the village to say good bye to the twin’s father. Then we proceed to that big town.
Ian: It’s Havenswerd.
Dan: Whatever. Do we get any treasures yet? I wanna buy stuff. Wait, will there be battles back to the cottage and the village?
Ryan: *shrugs* Who knows? It’s broad daylight though. You might wanna hurry before night falls…

The party bids farewell to the monks. That is, Phileas bids farewell on behalf of the party. Then all of them left for Mathea’s cottage. Travelling on the road made the journey easier and faster. When they arrived at the wrecked cottage, they found…

Dan: Cool! A magic axe! Anything else?
Ryan: I’m trying to pace the adventure… Aren’t you supposed to be crying over the loss of your master or something?

At the village, the twins found their father and told him about the night’s adventure. For some reason, the old eladrin wasn’t surprised. He told them of the strange evening some 20 years ago when 2 monks appeared with both of them at his door. The eladrin went to his room and gave them…

James: Money! We’ll split between the 2 of us *gesturing to Ian*
Dan: Hey no fair!
Ian: You got a magic item. Besides, I think Ryan has more planned for all of us. We just have to fight a bunch more wolves and skeletons to get them. You’re awfully quiet. *looking at Klenn*
Klenn: This *waving his slip* is giving me problems.
Ian: What does it say?
Klenn: You’ll find out soon. I’m preparing the backstory for it now.
Ian: Secrets? Well, I’ve got something from the slip that’s secret too.
James: Mine says that blue dude is Corellon. And that’s where my powers come from.
Ryan: Aaannnd it’s about late afternoon. What do you want to do now?

The party ran like heck (their words) towards the abbey. They asked for the hospitality of the monks again. Iofae asked the head monk if they knew of the babies sent to the village Jorv. The head monk nodded, “That’s all I know. My god tells me just what I needed. You’ll have to find out more yourself.”.

“My condolences to you for the loss of Mathea. He was a good man.” said the head monk.
“Do you know anything about the creature that attacked him?” asked Toth.
“From your description, I can only say it’s a foul beast, probably from another realm. I’ve never known anything like it. Perhaps Arofell can tell you more.”
“Where can I find this Arofell fella?”
“Havenswerd, at the Wizards Guild.”

Dan: Alright, people, we’re going to Havenswerd.
James: First thing in the morning. I’m not going out there with wolves prowling in the night.

The next morning, the party left for Havenswerd. This time, all of them thanked the monks for their hospitality. The skies were blue, the air was fresh, and no hint of danger exists. Soon, they arrived at the gates of Havenswerd.

Klenn: Uh, guys…

“I have something I need to tell you.” said Phileas. “I’m sort of a criminal in Havenswerd.”

James: What?!?
Dan: Seriously?

“It’s a bit of a misunderstanding, of course. I was performing at a tavern, and after my performance, I went back to my room, and lo and behold, there was a dead man on the floor!”

“It was also most unfortunate that the tavern keeper came up to ask if I needed anything. And she saw the unmoving person lying down, a bloody patch on the white of his shirt.”

“It was also most unfortunate that the dead man was the son of a wealthy merchant prince in the city.”

Ian: Your slip of paper has so many details?
Klenn: I made them up. I was only told I was accused of something, and I’m free to decide whether I was rightfully or wrongfully accused. I’m innocent of course *smile*. I was also told I’m free to come up with whatever accusations and circumstances that led to the situation.
Ryan: That was beyond whatever I could imagine. I was thinking maybe some minor theft or something.

“Now what do we do? Do you know the murderer?” asked Toth.

“No. And I intend to find out. I fled the scene, after the good lady screamed bloody ‘Murderer! Murderer!’ all the way down to the tavern common place. I heard shouting from below, and knew I didn’t have much time. I leapt out of the window, jumped down onto the pavement, and ran. I heard footsteps behind me and increased my pace.”

“Just when I was running out of alleys to duck into, a tall man dressed in blue robes, beckoned me in his direction. He didn’t have any weapons on him, and seemed harmless. He pointed behind him and just said, ‘That way! There’s a rope ladder and you can climb it to get over the wall and out of the city. Quick!'”

“I gave my pursuers the slip and escaped. And I decided to find some place quiet. And journeyed to Jorv. And now, I’m back.”

Dan: Stop grinning, Ryan.
Ian: That was amazing.
James: Now what?

“I never found out who that man in blue robes was. But from our dreams, I’m guessing they’re the same person. That happened a few nights ago. I’d like to ask you to help me get my belongings back from the tavern, and perhaps gain some clues to the mystery. I have a friend in Havenswerd that I trust. I will stay at his place.”

Dan: Ok, I’ll go shopping. You two *pointing at the twins* help our bard here get his stuff back. And you *pointing at Klenn*, … *laugh*

to be continued…

*****
P.S. Corellon is the god of magic, music and the arts in Dungeons & Dragons 4th Edition.

Chaotic arrangement of books and shelves

Pile of old books
[image by bunhill]

Rands wrote an article describing his love of books. (No, Rands isn’t his real name, and I respect his privacy if he chooses to use a handle.) He talked about the Amazon Kindle, and he also mentioned that he still liked to hold a physical book when he reads. Same here.

I’m going to answer the 3 phases of his book stalking process:

Phase 1: Where are they?

They are everywhere. Alright, only in the living room and my room. Of course I managed to find a couple of books hiding in a kitchen cabinet…

I don’t really have matching bookshelves to hold my books. It’s a cabinet here, a glass shelf there. The majority of my material possessions are books, so they sort of have a life of their own in my house. My father even built a bookshelf for me because he couldn’t stand some of the books just being stacked on the floor…

Phase 2: How are they arranged?

I think the only rule is: put the book(s) where there’s a space. This also means books are vertically and horizontally placed. Sometimes the shelf is too high, and the vertically placed books have some extra space above them, but not enough to place more books vertically. But I can lay books on their side on top of the existing books. Shove, shove, shove…

I’d make a terrible librarian… It goes with my messy nature

Phase 3: And what do you read?

I love fantasy fiction by David Eddings and Terry Brooks. There’s a couple of others, such as the Death Gate Novels by Margaret Weis and Tracy Hickman, and the science fiction ones by Michael Crichton.

There are also comic books, on the legendary kung fu master Chen Min, or Q in Detective Dan’s school or the Kindaichi chronicles.

I also have some books on business, self-help, and marketing. These are the non-technical books to complement the math and programming textbooks lurking… somewhere in those shelves…

And currently, the Dungeons and Dragons books command my attention. The fact that there are people who want to play tabletop RPGs with me helps with my interest.

Last thoughts

I think for an electronic version of books to be appealing to me, it has to be very “futuristic”. I don’t want to swipe from one end of the screen to the other to “flip” a page. I want to see a page being flipped, even if it’s holographically produced.

I don’t want to select a book from a list of titles on the screen. I want to see books in front of me, again holographically produced, for me to pick and choose.

It’s not just the book content I’m after. It’s the whole experience of reading.

Carcerian Stones – The one with blue robes

We’re continuing the D&D adventure story. Previously, the party found themselves surrounded by skeletons. We have Ryan the human DM, Dan playing Toth the goliath warden, James playing Heoriss the eladrin invoker, Ian playing Iofae the eladrin sorcerer, and Klenn playing Phileas the half-elf bard. And now…

*****

Clanking softly, a skeleton clad in chainmail closed in on Toth, slashing with its sword. Another skeleton swung its sword on Phileas, while its brethren rained arrows on Heoriss and Iofae.

“Feel the light!” shouted Heoriss. The air blurred around him, and he vanished… into the midst of the archer skeletons. A column of pure white light burst from Heoriss. As the light enveloped the skeletons, lightning was already dancing on Iofae’s hands. 3 of the archers fell as dust, and Iofae pointed at the remaining archer. Lightning danced from his hands to the archer, disintegrating it, and danced again to the skeleton attacking Phileas.

Phileas moved around to shield Iofae, and swiped at the skeleton’s neck, dislodging its skull in the process.

Dan: How come I always get the hard ones?
James: Because you’re the defender. Now go defend us!

Toth swung his greataxe at the chainmail skeleton, staggering it. The skeleton seemed unaffected by the blow, and swung its sword upwards at Toth and nicked his arm. A beam of light, a crackling of lightning, and a well-timed sword thrust, and the skeleton collapsed.

The giant form of Mathea flew out from the cottage door, and he hit the ground with a groan. The wolf creature stood at the door, black drops of blood dripping. Mathea pointed at it, and vines burst from the ground to wrap around the creature’s feet. It howled, and black tendrils wrapped around Mathea, slowly engulfing him, and he disappeared. The creature stood still, staring at the party for a while. Then it lifted its maw and howled again, and it too disappeared in tendrils of black.

“Mathea!” Toth knelt at where the great goliath laid before he disappeared. The baying of wolves sounded in the distance. “We have to move now. I don’t think the creature’s done with us yet.” Phileas placed his hands on Toth’s shoulders.

“We can’t go back to the village.” Heoriss looked at Iofae. “The creature already found us there.”

“You came from Havenswerd, didn’t you?” Iofae asked Phileas. “We can go there.”

“And there’s an abbey along the way. We can seek shelter there for the night. Come on, Toth!”

The party moved quickly, staying in the trees to avoid detection, but close to the road. The road was clear, but they didn’t want to try outrunning the wolves on flat ground without any cover. Several times, shadowy forms sprinted ahead of them. The howling was getting louder.

“Why aren’t they attacking?” panted Phileas.
“They’re waiting for the entire pack!” Toth shouted. “Keep running!”

“Get away from my brother!” Heoriss blasted lightning at a vicious canine closing in.
“And get away from mine too!” Iofae cracked lightning at another wolf behind them.

“There’s the abbey! On the road!” Phileas sprinted left, and the rest followed.

4 figures shot out from the edge of the forest, running straight for a simple structured building across a well-travelled road. As they did, a swarm of wolves emerged from the forest as well, barking and howling. Toth reached the other side of the road, turned around and hefted his greataxe. The others fled past him.

Ian: Wait, what are you doing?
Dan: Role playing. *winked at Ryan*
James: Cool, a last stand! I’m in.
Dan: Besides, Ryan’s not gonna let us die like this. Something’s gonna happen. I wanna see what it is.
Ryan: *sigh* Busted… Not giving it to you so easily though.

A particularly savage wolf lunged at Toth. Another snapped at Iofae. “To battle!” as Phileas struck back. Toth rammed his attacker towards the other wolf, and it burst into flame as Iofae backed away.

“What did I tell you about keeping away from my brother?” Heoriss flew shards of solid light towards the wolves. One of the wolves howled in pain as the flames consumed it. The other continued to snap at Toth. Toth brought his greataxe down on the wolf and fell it. As another 3 wolves entered the fray.

Dan: Any time now…
Ryan: *laughing* ok, fine…

A sonorous hymn was heard. A group of 5 humans, dressed in plain white robes, moved towards the party, their voices slow and steady. The advancing wolves had stopped in their tracks, swaying gently in the grasp of the song. “Come with me,” said the closest of them.

Dan: That was some “You shall not pass” moment…
Klenn: I say we take it. I’m all out of powers.

“The wolves will be of no further trouble to you. For now, simply rest.” And he showed them into the abbey, and provided rooms for them to sleep.

Ian: That was tough. I was about to use my daily power.
James: Yeah, me too.
Ian: Thing is, I don’t know what mine’ll do. It’s random.
Ryan: Well, I’m not quite done yet.
James and Ian: WHAT!
Ryan: Nothing to worry about. It’s story time.

That night, all of them had the same dream. It was the abbey, the same one they’re staying at. The sky darkened, and the grass field around the abbey blurred, and tall trees of bright green stood around the abbey. The leaves swayed wildly as they’re buffeted by the wind. Above the abbey, the clouds opened up and shimmering waters floated. Upside down.

A tall man emerged from among the trees, his blue robes staying still without so much as a ruffle. As he marvelled at the scene, a small part of the shimmering waters closed up, and a dark vortex swirled, threatening to suck everything up.

A black orb dropped from the vortex onto the ground, and a creature with four legs stood. It looked curiously at the tall man, and then it loped away. His eyebrows creased ever so slightly. Then he looked around him one more time, and held his hands out in front of him.

Misty particles floated between his hands, formed by a trickle of the glowing water above. Leaves flying in the wind formed a circular wall around the man. The light in his hands grew brighter and brighter. And then it was gone.

And the man held two babies in his arms. His eyebrows creased ever so slightly again. “Odd.” he said.

to be continued… here.

Exploding dice

My Dungeon Master (DM) was worried. The fights were getting a bit lengthy, or as they say, “grindy”. There were 2 ways to speed things up. One, to make it easier to hit. The other, was to make any hits more damaging.

Exploding die
[image by heizfrosch]

So my DM used the exploding dice concept. Basically, for any damage die roll, if you roll the maximum, you get to roll that die one more time. In theory, you could keep rolling dice till the penguins flew. Oh wait a minute…

Common sense says that, the more dice you get to roll, the higher chance of you rolling an exploded die. Thus 4 six-sided dice (hence denoted by the short form 4d6) is better than 2 12-sided dice, even though their totals are the same.

I think there’s also a probability result that says the more samples you get, the closer to the mean you’ll be. Thus 4d6 is “safer” than 2d12, because an average of 14 from 4d6 is better than a 2 from seriously flawed rolls of 2d12.

[corrected average value of 4d6 from 12 to 14. Thanks to ugasoft for pointing it out.]

Anyway, I’ve played with my group using this exploding dice concept for some time now. From personal experience, it speeds up combat somewhat erratically. What I mean is, one game battle could drag for some time, while another has us taking the monsters down quickly. I’m playing a character that deals more dice rolls than others, yet I don’t seem to roll exploding dice often. Just roll a critical, a 20 on a d20 (does maximum damage, no need for die rolls). Much faster that way.

Anyway, I wanted to do some mathematical analysis on this exploding dice concept. You can probably tell from the above that I probably know very little about probability. Well, I hated statistics in university.

I was trying to come up with some lame math formula, then I had the brilliant idea of searching on the Internet. And I found Eric, who did an actual math analysis of exploding dice. Much better than my feeble attempt. I almost wanted to tear up all my calculations in shame. His conclusion:

For any N-sided die numbered 1 to N with all sides equally likely, the exploding modifier will increase the die’s expected value by a factor of N/(N-1)

Reading his article, some faint memory came back to me. Expected value, huh? So the expected value of a d6 is
(1+2+3+4+5+6) / 6 = 3.5

And the expected value of a d12 is
(1+2+3+4+5+6+7+8+9+10+11+12) / 12 = 6.5

So the expected value of 4d6 is 4 * 3.5 = 14,
and the expected value of 2d12 is 2 * 6.5 = 13

Even without Eric’s conclusion, we can see 4d6 is better than 2d12, but let’s finish the calculations. Expected value after explosion for 4d6 is 14 * 6/5 = 16.8, and expected value after explosion for 2d12 is 13 * 12/11 = 14.18…

The takeaway? If you have to choose between 3d6 and 2d10, go for the 3d6, even though 18 (3 * 6) is less than 20 (2 * 10). You’re more likely to roll more stable higher results. Knowing this does nothing for my unlucky rolls of 1’s though…

Carcerian Stones – A Dungeons and Dragons adventure story

I’m going to try something new here, at the blog. I’m going to write an adventure story, based on the Dungeons & Dragons world. It will be fantasy fiction (to encourage creative thinking on my part), mixed with daring moves, devious puzzles (once I can think of some, like in the Mind Trap series), and out-of-character conversations (if you play D&D, you know what I’m talking about).

In case you don’t know, Dungeons & Dragons is a tabletop role playing game, played with dice, pencil and paper (usually, but you can go high-tech), battlefield maps (square grid paper, or full-scale miniatures). I’ve played a few sessions now, and with my history of reading fantasy novels (David Eddings, Terry Brooks), D&D is like a no-brainer. Which makes writing about it, a no-brainer too.

I have a different format in mind though. It’ll probably be faster to understand if you read, instead of me explaining to you. So, here we go…

*****

Ryan: Hey guys, I have a new campaign idea I want to try out. But I need the 2 of you to play fixed characters to move the story…
James and Ian: No problem!
James: I was getting tired of thinking up new characters anyway.
Ryan: Thanks.
Dan: So, what are the twins *pointing at James and Ian* playing?
Ryan: A pair of eladrin twins, 1 a sorcerer, the other an invoker.
Ian: Ain’t that a coincidence…

*****

Ryan: So are you interested in playing?
Klenn: Sure. I’ve never played before though.
Ryan: That’s fine. The others and I will help you. How does a bard work for you?
Klenn: I’m ok with it. *pause* Uh, do I actually have to sing?
Ryan: *laughs* Not if you don’t want to.

*****

Dan: Ok, I want to be a goliath warden.
Ryan: That’s new.
Dan: I’ve never played that before. We have a new story, so I might as well try something new. Will that fit into our campaign?
Ryan: It will fit perfectly.
Dan: Who’s the new guy again?
Ryan: Klenn. Please try not to scare him off. Ian picked up the rules quickly, but you kept giving him *air quote* “advice” *air quote*.

*****

Ryan: I’ll be railroading the story once in a while. I know all of you are excited to start playing, so I’ll fast forward some of the storyline to get to the action. I’ll fill you in with the background story as and when I have an opportunity. Basically, worry about the “why” later, like “why is my character doing this?”.

I’ll start by telling you about the night that seemed normal but not quite. You, James or *refer to some notes* Heoriss, was about to fall asleep when you hear “Quick! Run!” in your mind. Long story short, Heoriss felt a very strong need to heed the warning. Because Heoriss saw a dark figure prowling around the village, matching the description of a large wolfish creature “emanating pure evil”. Or so the folks at the tavern were discussing, spilling ale as they gesticulated wildly. Iofae, Heoriss’ younger brother heard him packing, and wanted to go along.

Cutting things short, while the 2 were fleeing, the travelling bard who arrived a few days ago, followed them.

Dan: Wait, that’s a lot of railroading… and why would the bard follow them?
Klenn: I’m a bard. It’s in my nature to sing about great adventures. A pair of eladrins sneaking off in the middle of the night smells thickly of trouble and great tales.
Ryan: Thank you, Klenn.
Dan: So, what were you doing in the middle of the night?
Klenn: I’m somewhat of a troublesome fella, don’t you know?
Dan: *laughing, turns to Ryan* Where did you find this guy?

Ryan: *smiles* I’m glad you approve. Oh this works out just fine. And after a brief exchange, the bard
Klenn: Phileas.
Ryan: the bard Phileas suggested looking for Mathea to seek help.
James: Who’s that?
Ryan: Mathea is a respected caretaker of the forest near the village. Toth, played by Dan, is Mathea’s student.
Dan: Oh, so I have a mentor. Hey, we’re finally connected!

Ryan: Yes. The 3 of them finally reached the cottage where Mathea and Toth lived. Mathea invited them in, heard the story, didn’t quite believe it.

Then he froze. The candle on the table snuffed out, and the room went dark. The forest was quiet. Moonlight shone through the open window. A growl came from the corner of the room *grrrr* and a midnight-black paw stepped into the pool of moonlight by the window. A rattle sounded from somewhere in the room… and please roll initiative.

Dan: WHAT!!??
James: *claps hands*
Ian: That, was awesome.
Klenn: Indeed.
Ryan: Thank you. I needed to get all of you together. And quickly arriving at the fighting part *glancing at Dan*.
Dan: *surprise fading* I thought you wanted more role playing in our games?
Ryan: I do. Besides, we have Klenn here.
James: Why’s that?
Ryan: *looking at Klenn* Tell them what you studied in university.
Klenn: Uhm, I did theatrical studies.
Dan: Holy smokes!
Ryan: If we role played the story beginning, it might take a while before we meet Toth. So I had to handwave quite a bit. Alright, let’s start the action.

*****

A bright flash of light erupted from the window. An orb of brilliance surrounded a wolf-like creature as Mathea struck it. The room was temporarily illuminated and Heoriss saw 2 lumbering skeletons surrounding Iofae. As the light faded, the creature slashed at Mathea, and the room was dark once more.

Dan: Wah, this is hard. Why’d you plunge everything into darkness?
James: Hey I have something that might help!
Ian: And push him here!
James: Why… oh!

Heoriss’ hands started to glow, and he pointed them at the nearest skeleton. A beam of light as bright as the sun shot out. The skeleton gave a silent cry as the light enveloped it, and was pinned against the table. Iofae backed away, his hands already weaving designs in the air, and sparks burst into flame around that skeleton. With a twitch of his fingers, a spark jumped onto the candle on the table, lighting up the room.

Ian: It worked!
James: High five.
Ryan: Good thinking.
Klenn: Is it my turn now? Uh, how about this?

Phileas charged towards the hapless skeleton, humming and brandishing his short sword, and plunged the sharp point into the skeleton’s mouth. He gave a twist, and the skeleton disintegrated and fell apart.

Dan: One more to go. This battle smells fishy… Something’s up.

Toth raised his greataxe and charged at the other skeleton. He raised the weapon high and brought it down. At the last moment, he twisted the handle and brought the flat of the axe on the skeleton’s head. A shower of bone exploded from the force of the blow, and the skeleton went down.

It grew cold. Chill air swirled furiously around Mathea. Shards of ice were forming in the air, then coalesced when Mathea punched the creature. Ignoring the ice constricting it, the creature lunged towards Toth.

“Out of here!” Mathea roared. The front door burst open, and strong cold air blew all of them out. The cottage went dark. A growl. Then a howl of pain. And outside, the party found themselves surrounded by more skeletons.

Dan: I knew it! Ryan, you’re wicked.

to be continued… here.