Session 72

29th of Summer’s End

Having defeated the band of goblins and bugbears to the south, the adventurers have started back towards Remnas. Along the way, Glod identifies the scroll they found as a Fly spell, and Epona identifies the potion as a Shield of Faith.

“You know, I could use an extra healing potion,” Kerwyn says. “Always best to be prepared. I remember a potion shop in Remnas, I’m going to check it out when we get back.”

Gante nods. “Well, let’s check back with Erelos, first.”

The party arrives in Remnas, finding their way to the inn near the center of town. Murc is kicked back in a chair near the door. He is snoring loudly facing the ceiling. There is no sign of Erelos nor Dima.

Gante walks up to Murc. “Well, as much as I hate to wake a sleeping half-drunk half-orc… Epona, you do it.”

“Me? No way, you do it!”

“How about if Mathus does it?” Glod says with a smile.

Mathus sighs, shaking his head, and walks over to Murc. He knocks on the half-orc’s skull. “Hey, big guy! Rise and shiiine! “

Murc swats at Mathus’s hand, snorting through a half-cough, half-snore as he wakes. “Wha-huh? Oh, mornin’ fellas.”

“Hey Murc, you have any clue where Erelos got off to?”

Murc looks around the otherwise deserted dining room. “Uh, nope.”

“Well, I’m pretty sure if Erelos wants to talk to us, he’ll find us, Kerwyn says. “And it’s evening, by the way.”

“So it is, so it is…”

“How about Dima?” Gante asks.

“Hasn’t been back yet.”

“Back from where?”

“I dunno. He didn’t say. He left just a bit after you, said not to wait up,” Murc says, yawning.

“So about that potion shop,” Kerwyn says, making for the door.

“Ooh, I’m coming,” Glod says.

Gante and Epona tag along as well, and Mathus, too.

***

They walk in to the slightly familiar old building. The musty air is a combination of old library and caustic fumes. The shelves appear mostly emptied, save a few overturned vials. They hear a voice from a back room, hidden by a curtain.

“I’m coming, I’m coming. Have patience!”

A wrinkled face emerges from the curtain, not yet revealing anything below its neck. In quick succession, he eyes each of them.

“Three elves, a thief, and a gnome… Whaddyawant?”

“Well, we came by to see if you had anything for sell,” Kerwyn says. “We wern’t sure, you know, with the goblin attack and everything.”

“So you are… customers!”

He bursts through the curtains, places his hands flat on the counter, and smiles broadly. His glasses hang on the tip of his nose. “And what are you interested in this fine evening?”

“Well, mainly I guess any healing potions you might have. But it looks like your stock may be a little slim.”

“Ha! You would think that, wouldn’t you? Take anything that’s not nailed down! Ha! Ha! Haha ha! I know better than to leave stock in the open! I just happen to keep it all nailed down in the back! If you want healing potions I can get you healing potions.”

“Ha ha ha, I guess you wouldn’t stay in business long if you didn’t.”

“With your kind out? Never! Ha! Ha! HahaHA!”

“Hmm… right. Well, how much do your potions cost?”

“If you’re wanting the healing potions, they’re one hundred pieces of gold. Fix you right up, they will.”

“Well, if you could just hook me up with one, that would be great.”

He walks (backwards) through the curtain. After some rummaging noises, he emerges with a small vial of clear liquid. Kerwyn counts out is gold and takes the potion.

“Hey,” Glod says, “do you have any alchemy equipment? I did some back in my university days, and I’d like to be able to whip some potions up on the go.”

“Ah, fine idea. Some amateur potion brewing always helps get some return customers if things don’t go quite right… Come on into the back and we’ll fix you up.”

Kerwyn heads for the door. “Well, this looks like it could take some time, and I don’t think you guys are going to need me, so I’m going to go walk around town, see how its doing. Meet you guys back at the tavern?” Kerwyn heads outside.

Gante also makes for the door. “I think I will keep an eye on Kerwyn, see you guys later.”

Wandering the town, Gante strikes up a conversation. “So Kerwyn, Got quite a bit of money to spend on those potions, you been keeping a secret stash?”

“What? Psh… no. Just used my other one, and decided it was worth the investment. You know, just in case.”

“Well, we’ve been together through some tough stuff, so I guess you wouldn’t hold out on us.”

“Of course not. I’ve got no reason to, right?”

“I don’t suppose so, but after that whole painting thing you apparently pulled off behind my back, I just had to ask. Although it is quite funny that you could get away with something that big without me noticing.”

“That little thing… that was just something I picked up along the way. I didn’t pin you as a big art fan, though.”

“Don’t think I didn’t notice that was Dwarven art. You underestimate my appraisal abilities.”

“My, my. I wish you had told me you were a Dwarven art fan. I’ll keep a look out for any good bargains I run across.”

“Just an old hobby of mine. Surely you noticed my friendliness with our Dwarven friends.”

“Oh yeah, I think every tavern we’ve walked into has noticed…”

Back at the shop, the old man continues to pull things off of shelves for Glod.

“You want be able to start without the beakers and flasks, not to mention proper mixing tools. You won’t need any specialized stoppers for amateur work, so that’ll save you some cash for now at least.”

“It might be better start with just the basics, perhaps some vials and common ingredients. Mortar and pestle, that sort of thing.”

“Oh, and you’ll need to have a proper heat source, naturally. Arcane ones just don’t work as well as the real thing. Let’s see, a bit of sulfur, some charcoal, cedar chips, iron shavings… Alright, this should be enough to start you off. Not the whole package mind you, but it’s a start. Total comes to one hundred fifty gold pieces.”

“Sold!”

The old man wraps up the supplies in a combination of canvas and burlap. And make sure all your friends know where you got such a good deal!

“Before we leave…” Epona pulls the ring they found from her pouch. “Sir, do you happen to know who in the city could identify this ring I found?”

“Ah, so you have need of magical identification. There is… a diviner. But he doesn’t work for free! You pay the right price, though, and you’ll get what you need.”

“Where can we find him?”

The old man gives the party directions to an area just one block over. “Just head out, go left, take a left on the main road, another left, and it’s on the left.” The thank the old man and head out into the city, finding the diviner’s place soon enough.

The walls of this old building are covered in long, flowing pieces of cloth. A small table in the center holds a crystal ball. They hear a voice from a back room, hidden by a curtain.

“I’m coming, I’m coming. Have patience!”

A wrinkled face emerges from the curtain, not yet revealing anything below its neck. In quick succession, he eyes each of them.

“Two elves and a gnome… Whaddyawant?”

Jon: Wait, is this the same guy?
GM: Well, I mean there are some similarities… I guess… but no, definitely not. I mean, the other guy had glasses.

“Yes, I was told that you could help me identify this magical ring I found.”

“So you are… customers!”

He bursts through the curtains, places his hands flat on the small table, and smiles broadly. His glasses hang on the tip of his nose.

“You don’t happen to be related to the man who owns the potion shop do you?”

“Ah, so there is a potion shop in town? Intriguing… So you need a magical ring identified! I can perform this service. Or rather, I could if I had the required components.”

“What would that be?” Epona asks.

“I require a pearl of great value.”

“How great, exactly?”

“Very great.”

Glod speaks from the other end of the room. “You wouldn’t happen to know of a pearl shop around here?”

“Ah, but no. I don’t leave the shop much. However, I know of a place to the west…”

“Yes?”

“It is a dangerous area, filled with monsters… traps… perhaps even worse.”

“Sounds exciting.”

“Aw, come on,” Glod says. “Just wear the ring for a while. What’s the worst that could happen?”

Mathus laughs. “The worst? Well, you could just explode, but that might actually be an improvement.”

“Yes, to the west lies the Temple of the Ocean Goddess. They say among the treasures within is a pearl as large as your feathered friend there…”

Quoth lights up at the sound of such a treasure. Glod, however… “Hold up, wait, wait. I’m not having any part with any water temples.”

“Oh, come on Glod,” Epona says. “Where’s your sense of adventure? Sir, can you give us some directions?”

“Head due west from Remnas. Once you reach the coast, travel south. Keep your eyes open and you’ll spot it.”

“Thank you sir. Glod, Mathus, let’s head back to the tavern to meet up with the others.”

***

“…And that’s why I don’t eat calzones anymore,” Gante says, wrapping up a tale.

Murc stares at the paladin with a look of disbelief. “You’re kiddin’ me.”

Kerwyn laughs as the rest of the group arrives. “Oh, welcome back. What did you guys find out?”

“Well, we found a diviner that could identify the ring, but he would need a valuable pearl. He told us about this Temple of the Ocean Goddess filled with monsters traps and a pearl the size of Quoth.”

Kerwyn smiles. “A big pearl, you say…”

“I figure a little more adventuring can’t hurt before we head back to Marlak. Murc, do you want to join?”

Murc takes a heavy swig of his ale. “I found out that I kinda promised the townsfolk I’d stay here as protection until the wall was built back. Guess I got carried away last night with the whole “bein’ a hero” thing… and the ale.”

“Well, I guess we’d better get some sleep. No doubt this temple is pretty far off.”

30th of Summer’s End

The adventurers descend to the ground floor, smelling fried meat, and possibly eggs.

“Ah, good morning!” A familiar voice greets them.

Gante, a bit surprised, returns the greeting. “Marlak! How are you?”

Also in the dining area is Dima, and one dozen former sailors.

“So I guess that’s where you went off to yesterday, Dima.”

“Yes, with most of the uprising crushed, there was no need for everyone to stay at the Wizard’s Tower. Besides, these men have a come quite a way in their skills with the blade.”

Mathus steps through. “Who’s the geezer?”

Epona responds: “Well, in a very far-removed way, he’s the reason your not dragon food by now.”

“Let’s not get too specific on the details… I don’t want to owe another favor here.”

“Ah, Glod, I nearly forgot.” Marlak reaches into a bag, searching for something. “While at Milo’s tower, I browsed through his library and found a book that could help with the Soul Stone research…”

Marlak hands Glod an old tome. The cover is a deep blue.

“This is the journal of Jens Coron. The information you discovered at the Academy indicated he knew something about the stones, in addition to the notes you found below the tower. The problem, though, is that the notes appear to be… encoded Coron did have a penchant for puzzles, and seems to have made his journal fit his personality.”

“What sort of encoding?” Glod asks.

“I assumed at first a sort of cryptogram, though that seems impossible for more than a few words. My guess is a sort of cipher. I’m sure you can put those sleepless nights to good use on it.”

“Is it magical at all?”

“We found signs of a faint enchantment, though we were unable to determine the effect or even the school of magic.”

“Well,” Kerwyn says, “I guess you guys could spend all day studying it, or we could head out to the temple.”

“Heading out to a temple, eh?”

Glod crosses his arms. “They seem to want to…”

“Yes, we heard about this Temple of the Ocean Goddess from a diviner. We thought we’d do a little celebratory treasure hunting.”

“Best of luck then, and do try to return safely.”

“I have my doubts, but I suppose this lot is pretty good at dealing with trouble.”

“Dima, would you and Murc mind keeping Marlak safe until we return? Your pal Murc has a promise to keep to the townsfolk anyways, so I feel like you will be here a while.”

Dima laughs a bit. “Certainly.”

Session 71

29th of Summer’s End

Having defeated the bugbears and hobgoblins, the party takes a quick rest. Glod’s light spell ends, so he casts a different one that will last them for another hour. Gante decides to search the crate, finding a small flask amid piles of cloth. The adventurers head deeper into the cave, stumbling across a large pit. Mathus stops them before they fall in, and jumps the gap. On the other side, he finds some planks of wood, which he uses to make a bridge for everyone to cross.

Heading around the bend, they hear a goblin warcry. Two bugbears, taking cover behind crates, prepare to attack. More javelins fly in their direction, landing short. Mathus and Gante rush forward to face the battle head on. Kerwyn attempts to line up a shot with his crossbow, but can’t get a good angle past the melee fighters. Gante is hit by a series of magic missles from out of sight.

“Guys, watch it! They’ve got a caster up here!”

Glod uses a grease spell to unbalance the bugbears. Taking advantage of the distraction, Mathus and Gante leap onto the crates and attack with their blades. Each slays his respective opponent. Two hobgoblins rush up to hold the defensive line, while the goblin caster creates a sphere of fire on the party’s side. Glod flees the flames, then returns the favor. The grease catches fire, seperating the party from the goblins. They continue firing spells and projectiles, clearing out most of the room. One goblin caster, who had been crouching behind a treasure chest, flees through a tunnel to escape.

“Looks like there’s another exit to the cave…”

“After that goblin, then!”

Gante calls on his steed and takes after the fleeing goblin. The rest are close behind. When Gante closes in on the caster though, he calms his horse and stops.

Epona yells out to the paladin. “What are you doing? Get him!”

“…I don’t know, that really wouldn’t be civil.”

“Great, the paladin’s gone pacifist on us.”

“I got him, I got him…” Glod casts a trio of magic missles, which bolt across the open field, striking the goblin dead.

Barely in range at that point.

“What was that, paladin?” Mathus walks up to Gante.

“I don’t know, I just felt like he wasn’t all so bad…”

“What?! Sure! He was just out fetching us some tea!”

“He roasted me to a state of well done!” Glod says.

“Hey, at least I caught up to him!”

“I guess it’s alright,” Glod says. “By my guess you just got a face full of enchantment magic.”

Epona catches up to the others. “Let’s head back to town then, shall we? Wait, where’s Kerwyn? Oh, right, treasure.”

“Not just any treasure,” Kerwyn says. “Magic treasure.” He holds up a dagger, ring, and a scroll. “Care to take a look, Glod?”

“Yeah, yeah. Let’s get back to town and I’ll figure it out.”

Session 70

29th of Summer’s End

The moon shines brightly on the open plains of Kendra. Sitting in a large field are five adventurers, resting around a campfire after a long battle. The half-orc and elf clean their weapons. A paladin, cleric, and gnome sit nearby.

The elven man, taking a break from cleaning his sword, stokes the fire. “Was it wise to send the thieves out on their own? Kerwyn and Erelos went out to get that cart at least two hours ago. I understand we can’t carry this thing on our own, but we could have at least sent someone more trustworthy along…”

“Oh, come on, Dima,” the half-orc says. “I trust ‘em. We wouldn’t even ‘a beat ole’ scaly here if they ain’t helped.” Murc pats the remains of a large red dragon.

“What exactly do you plan to do with this beast, anyway?” Dima asks.

“I wouldn’t worry about Kerwyn,” Gante says. “He’s a first-class rogue to be sure, but he wouldn’t think of betraying his companions. As for the dragon, I’m hoping we can use it’s hide for some armor or other useful equipment. At the very least, its head should make a good trophy, and the rest should bring a pretty penny if we find the right buyer.”

“I’m just glad that most of us made it out alive,” Epona says. “We were cutting it close, and I must say Murc, that was quite a feat you pulled standing face to face with that beast.”

“‘S long as I get to take one of its teeth. Tradition, ya see.” Murc, finally done cleaning his axe, rests himself against the dragon. “Anything big enough to eatcha is worth a trophy.”

Dima nods. “Well, I’m sure we can get someone back in Remnas to craft whatever you need. I’m sure they’ll be thrilled to see what we’ve managed to pull off. With that dragon out of the way, they can finally start rebuilding.”

In the distance, the sound of squeaky cart wheels can be heard. Kerwyn and Erelos appear on the road with a pair of horses pulling a cart.

“Anybody order a cart?”

The adventurers work hard to get the dragon into the cart. The creature easily weighs a full ton. After ten minutes of struggling, Glod suggests simply wedging the cart underneath the dragon instead of lifting the dragon on to the cart. A further ten minutes finds the beast nestled snugly on the wooden cart. As an afterthought, Murc tosses the late rider on as well.

“Might as well bring ‘em along.”

Dima finishes hitching the horses back to the cart. They strain to pull the massive load, but have an easier time once it gets moving. “Well, let’s get this to Remnas.”

The midnight hour has passed by the time the capital city of Kendra comes into view. What with the explosions and ensuing chaos from midday, the city is still not settled: makeshift camps are set up outside the walls as many buildings were destroyed. The adventurers begin to enter the large campsite just outside of town, where those displaced from their homes have found refuge.

“Fellows, it has been a pleasure,” Erelos says, skipping a few steps ahead, “but this is where we part ways. Can’t bring too much attention to myself in my line of work.”

“Naturally. So you intend to sneak back to the city unnoticed?”

“On the contrary. I intend to make as much commotion as I can.” He raises his arms and begins shouting to the crowds in the camp. “Attention! Citizens of Remnas, be the first to welcome the heroes of Kendra! Behold those that have slain the dragon!”

As he speaks, the people crowd around the group and the cart. At first dozens, but by the time they reach the gate, they have a parade of hundreds, some leading the way, others trailing behind. Erelos disappears into the masses as musicians join the throng. They start a well-known celebratory tune and begin parading the dragon through the city streets.

“Well look at that,” Glod says. “Bards doing something useful.”

***

The morning light creeps into a large inn room in Remnas. Murc, feeling the sun in his eyes, rolls over and snores exceptionally loudly. Dima jerks up at the sudden noise and looks around. Cupping his face in one hand, he inhales deeply.

Murc sits up. “Does anybody remember last night? I kind of lost track of events once they broke out the ale…”

“Well, we paladins don’t dabble in that stuff, but I don’t think you want to know what all you were up to.”

Dima staggers to his feet. “I for one think it’d be best to just forget it then. For now, some breakfast may be in order.”

Murc looks out the window. “Lunch, I’d say.”

Kerwyn grabs his gear. “Whatever you want to call it, I’m starving. Let’s get something to eat.”

“So much for a quiet morning,” Glod says, shutting his spellbook.

“I don’t think we’ll have quiet for a while,” Gante says, descending the stairs. “We’re famous now.”

At a table near the door, the adventurers see Erelos speaking with a gruff-looking elf.

“…but you’ll have as much time as you want to discuess that. Ah, here are the triumphant heroes now.”

The elf eyes the group, paying particular attention to Glod.

Epona greets them. “Nice to see you’re doing well, Erelos. Who’s this you have with you?”

“Allow me to introduce… well, I hesitate to say “your hierling…”

The elf scoffs.

“Your actions last night in the goblins’ base earned you a new companion. This is Mathus D’Luc, a ranger from the northern woods. Mathus here will be leading you to the south, assuming you are in fit enough condition. A large force was seen fleeing the city yesterday afternoon, and I would think it best if they were crushed now before they became a problem.”

Mathus rolls his eyes. “Glorious day, I get to help you track them down.”

“I get the feeling you aren’t too thrilled,” Epona says.

“I could honestly care less. I am, however, obligated to assist you.”

“What do you mean ‘obligated,’” Epona asks. “Just because we rescued you from the goblins doesn’t mean you have to help us…”

“‘Rescued?’ I suppose I should thank you lot for that, but I’m not sure I want to. Thanks to your heroics, I’m bound by that ridiculous oath to assist you.”

“I’m not sure what you mean,” Gante says.

“It isn’t important. All you need to know is that I have to assist you. Either for a full year or until I repay the debt I owe. In this case a life. So. Lucky me.”

“Erelos, how big a force are we talking?” Glod asks.

“According to my sources, no more than two dozen, but probably a well-armed group if they escaped the choas of the city.”

Glod catches Mathus’s stare. “What? You have a problem with gnomes?”

“Not at all; they’re delicious.”

Glod stares up at the elf. “Well… have a problem with wizards?” Mathus rolls his eyes. “Yeah, well, keep it that way. What say we get going, everyone? Murc?”

“I’ma be treating this headache, fellas. Besta luck to you, though. Dima?”

“I actually have other business to attend to. I should be back by this evening.”

Mathus heads out the door. “Let’s go, come on!”

Epona and Glod wait with Mathus for the others. “Look on the bright side, you might save our lives today and be done with it.”

“If only…”

“Just don’t try and get us in trouble so you can save us.”

“What? You don’t want to play damsel-in-distress?”

Epona glares at Mathus. She lowers her voice slightly. “I think you’ll be the one in distress if that happens.”

The others join the group and begin traveling south.

***

“So how far do you think they’ve gotten?” Gante asks.

Mathus shrugs. “Does it matter? If you lot were any slower, they could stand still and we’d never find ‘em. Their pace isn’t very quick. They’re probably looking for somewhere to hide. I’d tell you how far they are by the scent, but one of you stinks so bad I can’t smell anything else.”

The sound of running water is heard ahead. Mathus points to a tree over a stream.

“What about it?” Epona asks.

“It was cut down by the goblins. Who’s up for a quick balancing act?”

The adventurers walk carefully across the log, arriving safely at the other side. Gante, the last to cross, stumbles in his heavy armor and splashes into the water.

Mathus roars with laughter. “Bwah ha ha!” Gante, struggling against the current, falls beneath the surface. Mathus drops his laugh. “Oh, for the love of… Anyone got some rope?”

Glod grabs his rope. Mathus grabs one end and jumps into the water. With the others holding on, they manage to pull Gante back to shore. Gante coughs up water, and is back on his feet after a minute’s rest. “Well Mathus, it seems you’ve repaid your debt to me…”

“Too bad then that I owe all of you. Let’s keep going.”

After another two hours of traveling, the adventurers arive outside a small cave hidden in the brush. “Is this it?” Glod asks.

“Yeah, shortcake, this is the place.”

“Hmph. Well, maybe I can get some more intelligent conversation over here,” Glod says, searching the area near the cave. “Here we go.” Glod leans near a small hole in the ground. “Anybody home?”

A small rabbit peeks through the hole. “Whoa! Who are you! Who said that, which you are, and are who?”

“Rabbit, have you seen any goblins passing by here? Any bipeds going into the big burrow?”

“Goblins! Ferocious things, gnarled creatures! Gobbling, gobbling goblins!”

“Counting may be too much to ask, but how many?”

“Moving in next door! Making such a ruckus. Many many, so many not seen, as I hid myself!”

“Wise rabbit, then. Anything else? Or was it only goblins?”

“No no, but no! They were goblins, but not goblins. Heavy steps, thudding steps…”

“Thank you, you’ve been very helpful. Good day to you rabbit.”

The rabbit disappears into its burrow, murmuring to itself. “Good to day it can be…”

“This is utterly ridiculous,” Mathus says. “So who’s going in first?”

“Kerwyn, you all set?”

“Yeah, but I could use some light…”

“I’ve got it covered,” Glod says, casting a spell. Magical orbs of light appear and illuminate the cave mouth. “After you.”

The first chamber is small, completely empty save for one empty chair. Kerwyn stops the group. “You hear that? They’re ready for us up ahead.”

“Well, I’d hate to keep them waiting.”

They turn the corner into a long, carvernous corridor. There is a goblin shout from the other end, then a volley of javelins. Glod moves his lights farther ahead to illuminate the source. Two hulking bugbears and a pair of hobgoblins stand behind stacked crates, prepared to strike again. Kerwyn rushes forward to attack over the boxes while Epona casts sound burst behind their fortification. Mathus pulls out his bow, but can’t get a clear shot from the back. Glod casts magic missiles into the fray.

The creatures are overwhelmed by the superior force of the party. Kerwyn takes a moment to rest after being injured. “Not exactly a warm welcome…”

Shadows Within to make a comeback?

Entirely possible!

When Adam skipped town head for grad school, his GURPS game was abandoned. We completely disbanded our weekly meet-ups for a while. Recently, we all downloaded Dungeons & Dragons Online, a free MMORPG, to play with the computer as DM. However, the system-choking graphics have motivated me to get to work on a second season of Shadows Within, with 40% more preparation! No expected timetable yet, but the announcement will go out when we start. Shortly afterwards, session updates will resume. Expect plenty of closure, and plenty more McGuffins.

A Mathematical Analysis of Exploding Dice

With a normal die roll, the result is either 1, 2, 3, 4, 5, or 6. This will later be generalized to N-sided dice, but for now, the standard six-sided variety will suffice. Some games use a system called “exploding dice.” With this system, rolling the maximum value on a die allows the roller to roll the die again and add the new result to the previous one. There is usually no limit on the number of rerolls.

For example, a player rolls a six. He rerolls the die, which lands on six once again. Once more, he rolls, but this time gets a two. His final result for this roll is effectively fourteen, even though the die has only six faces .

Put simply, expected value is what the average result for an experiment would be if were tried an infinite number of times. For example, if a coin flip was worth one point if heads lands and two points for tails, the expected value would be 1.5 since heads and tails are equally likely.

To compute expected value, the sum of each possibility times its respective chance is taken. For the coin flip example, this would be . That is, a 50% chance of 1 point plus a 50% chance of 2 points.

So the problem to be tackled here today is this: how does the expected value of an exploding die differ from its standard expected value?

The first step will be to find a pattern. Here is a quick comparison of values and their respective probabilities:

x, Pr(x)
1, 1/6
2, 1/6
3, 1/6
4, 1/6
5, 1/6
7, 1/36
8, 1/36
9, 1/36
10, 1/36
11, 1/36
13, 1/216
14, 1/216
…

So how can these be put into an elegant formula? First of all, a simple sum of products will be used:

The factors preceeding each sum are powers of six, so they can be consolidated into a nested sum:

Each sum, such as , is equal to the average value times the number of elements. The number of elements remains a constant 5, but the average value is increased by 6 for each subsequent sum, beginning with a value of 3. The formula can now be rewritten like so:

Simplifying some of the products, the formula can be rewritten once again:

Now an obvious pattern begins to develop. By expanding these nested products, the pattern becomes even more clear:

Six is factored out of all terms:

This new formula can be rewritten in sumation notation:

For each term added, our error will be reduced by a factor of 6, so just a few terms will return a very accurate result:

N, sum to N
0, 2.5
1, 3.75
2, 4.0972222
3, 4.178240741
4, 4.194058642
5, 4.197595165

The sum is swiftly approaching exactly 4.2, but what is the relation of that value to a six-sided die’s normally expected value?

Adding the exploding modifier to a six-sided die changes its expected value by a factor of . That is, the ratio of the number of sides on the die to the number of sides that do not “explode.”

I have performed the same calculations on four and eight-sided dice to compare results, and the forumla holds.

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 .

Interestingly enough, this formala holds for a hypothetical one-sided die. Heuristically, since the highest number will always be rolled, the total will constantly increase, returning an infinite result. Mathematically, the expected value of 1 will increase by a factor of , which approaches positive infinity from positive values.

Silk Road – More Details

Alright, now for a little more in-depth look at the new campaign.

The Characters

Ecthelren: played by Will. This isn’t too much of a shift from Will’s rogue Kerwyn in our D&D campaign. He’s monetarily minded, keeping a close eye on the party’s funds. His main responsibility is to add to the illusion that we really are just a bunch of travelling merchants. Of course, he has no reservations about making some money on the side along the way.

Edrick Dorban: played by Eric (me). Since I was in charge of the last campaign, this is my first time on the other side of the GM screen. Edrick is a practically minded scholar with a penchant for gadgets. He’s an avid hunter, so he’s not completely useless in combat. Adam decided my character can spend time during the trip upgrading his crossbow, making him more of an asset if things get rough.

Chewba Ka: played by Jon. This is very different from Jon’s paladin Gante. Though his new character is still a more combat-oriented one, Jon is playing as a Grond, a hairy creature that can’t speak the common language besides a few broken phrases. Essentially, he’s Chewbaaca. Hence the character name.

Cato Peppi: played by John (this is going to get confusing). John was brought in to our gaming circle by Adam. His character is probably what keeps most of the intra-party communication going, as he’s easily the most fleshed out character; John is probably the only one of us with any decent role-playing abilities. So, his slow-witted farmer character has quite a bit of personality, in addition to unusual quirks.

The World

Adam has done a great job of creating his campaign world. He already knew plenty about Roman society, so he has the benefit of being able to pretty much duplicate that. What’s more, he’s set up a nice map for us using the Google Maps API. Check it out here, or the regular image below.

Silk Road – Introduction

I’m doing what I can to keep updating sans computer, even if it means copying and pasting directly from Adam’s campaign opening lines.

The Domiran Empire occupies a large swath of land around the Straits of Armara in the middle of the Centralian Sea. Several other smaller tribes and city states also cluster around the coast of the sea and its islands. Rumors of magic and strange beings abound, but skeptical minds find scarce evidence for either in the lands near the Sea. The use of iron, writing, and animal power are widespread among more civilized groups.

The current Emperor, Aral V, is a good ruler: strong, honest, and intelligent. He has contacted various resourceful people and has now gathered them in his throne room.

“You have been gathered here today because the Empire has a problem, and you may be able to help me solve it. You all know of the Silk road, which leads from the western provinces off deep into the continent. We trade for silk, spices, and other exotic goods along this road, and as a whole send nearly 50 million sesterces a year back down the road in return.

“And yet I know nothing of the lands where this money is going, and nothing about the origin of these spices and silk. The writings of historians give reliable, reasonable sounding reports out to the port city of Tarpa in the land of the Gratians, but after that they trail off into traveler’s tales of headless men, singing trees, and giant birds.

“I want information. Reliable, first hand information on the entire road from here until wherever it goes. I want to know where the Empire’s money is going, what the secret of silk is, and anything else useful, or even just interesting. Accomplish this task and you will all receive titles and fertile land in one of the new provinces.

“Since you are traveling the silk road, I suggest you disguise yourself as merchants. It might be unwise to let the eastern lands learn that the Empire is looking their way. Provisions from the Imperial storehouses will be made available to you, and a cipher book for encoding reports. Send them back down the road with instructions to hand them to the garrison at Pemra. The master of provisions in the antechamber will take you to your supplies.”

No updates for a bit

The laptop is once again out of commision. Posts will resume next week, after which I should have my new computer.

A whole new world

As I mentioned earlier, Adam’s campaign is up next. We’ve already been playing it for a few weeks, learning this strange and foriegn GURPS. We also have one new player who’s been adding some much needed dynamics to an otherwise boring team.

One of the things that annoyed me about my campaign was that the players went through the game without much inter-character interaction. I mean, I’m glad they acted as a team, but there was always a ridiculous level of caution applied to keep the party together (even going so far as to tie themselves together with rope).

This new campaign is proving much more interesting. The characters, who I’ll introduce soon enough, took a more believable amount of time to gain each other’s trust. Their varied backgrounds make for interesting clashes of culture.

The world is a Roman-esque Iron Age setting. The main characters are called together to explore the silk road to the east at the emperor’s request. It’s an intellignce gathering mission, mainly. I’ll go into more detail later, but for now, here’s a quick summary of the PCs:

• Edrick Dorban – scholarly tinkerer
• Ecthelren -  fast-talking merchant
• Chewba Ka -  Grond soldier
• Cato Peppi -  dirt-poor farmer

Shortly after session 69

“Well, that’s it. The dragon’s dead.” The GM flips over the small piece of cardboard in the center of the paper grid.

“About time,” Jon says. “We can make armor out of it or something, right?”

“Oh, definitely.”

“Good. I think my paladin deserves some reward after all that.”

Adam picks up the gnome miniature from one corner of the table. “I wouldn’t mind a cape made from its wings, really. That’d be worth some kind of fire protection, maybe.”

The GM leans back in his chair. “Yeah… I guess we’ll work something out for that.”

“I was still hoping for a treasure hoard,” Will says.

“Heh, is there anything else is a rouge thinks about?”

Notes are jotted as experience points are tallied. “If you don’t mind me asking, what was Murc at, HP-wise?”

“Heh, you guys are gonna love this,” the GM says, looking up from a page of hastily jotted notes. “The poor half-orc’s down to exactly one.”

“Well, I for one am glad he made it through.”

“Yeah, Murc’s pretty surprised he’s alive. He holds his arm up and says ‘we did it? We did it!’” the GM mimes the barbarian’s actions as he describes them.

“So why does Murc have to sound so Texan, anyway?”

“There’s only so many voices I can make…”

“So what about Melrain?”

“Oh yeah… forgot about him…”

***

The players file out from the apartment.

“See you guys tomorrow.”

“Yep.”

“Later.”

The GM and the Roommate are left with empty soda cans and half-eaten bags of chips. The GM nods. “That’s the first campaign I’ve ever run to some sort of actual ending.”

“You went easy on them, didn’t you?”

“What? No! Maybe. A bit.” The GM begins clearing off the table.

“You should’ve killed ‘em off. That’d be a great ending.”

“No, that’s like, an X-Men 3 ending.”

“So what are you going to do with your Sunday nights now?”

“For the next couple weeks… I dunno. Video games? We’ll probably just all hang out until Adam’s ready to start his campaign. He’s going to run a GURPS game set in a Roman tech level.”

“‘GURPS?’”

“Don’t worry about it. I’m sure you’ll learn about it once we get going. In fact, you could join in as a player if you want…”

“Oh, no. You’re not dragging me into your geeky culture.” There’s a short silence in the room, broken by the air conditioner whirring to life. “You really should’ve just killed ‘em off.”