Session 75

Posted in Shadows Within on February 1, 2010 by eric22222

30th of Summer’s End

The adventurers make it back to Remnas shortly before nightfall. With the sun at their backs, they walk back to the inn where Murc greets them.

“Oh, good. Everybody’s still alive. So what was this whole outing about, now?”

“Just a fetch quest of sorts,” Epona says. “How’s Mathus doing?”

“He’s out getting some fresh air,” Murc says. “He was a bit under the weather this mornin’, blaming it on falling into a river or something. Probably just needs some rest. Oh, Marlak’s out and about, too. Said he’ll be traveling to Karkin with ya’ll soon.”

“Yeah, well after that last fight, I’m ready for a warm meal and some sleep.  Hopefully, Mathus will be feeling better tomorrow.”

Glod spends some time attempting to translate Coron’s Journal, but makes no progress.

1st of Land’s Blessing

The team spends the day resting off their injuries. Through the night, Glod finally translates some of the journal. He learns that the pages are not in the correct order, however.

2nd of Land’s Blessing

Glod relates his findings to the team that morning. They decide they can’t learn anything without more pages.

“Well, that’s interesting and everything, but not much to go for now,” Kerwyn says.

“It’s going to take some more translating before we have the whole story,” Glod says.

“Though I’m curious as to what a hollow is…” Gante says.

“Nothing pleasant, I’d imagine.”

They head out in to town to go to the diviner’s shop.

“I’m coming, I’m coming. Have patience!” The old man’s familiar voice springs from behind the curtain at the back of the store. A wrinkled face emerges from the curtain, not yet revealing anything below its neck. In quick succession, he eyes each of them. “Hmm, two elves, a gnome, and… wait. Ah! My customers have returned!”

He bursts from behind the curtain, drawing a chair to the table with a flourish. “So how was your journey to the temple, hmm?”

“Filled with danger, deadly traps, the usual,” Epona says.

Glod grumbles under his breath.

“Not deadly enough to stop you, I see. So you still have need of my services, yes?”

“That depends,” Epona says, brandishing the pearl, “on what kind of deal we can make.”

The old man’s eyes widen, trying to mimic the size of the pearl. His mouth is slightly agape as he blinks in surprise.

“It truly is as marvelous as I had heard… Of greater value even than I require for the spell.”

“We were hoping to make change,” Glod says.

Perhaps we could arrange something… What did you have in mind?”

The team discusses the idea of what they could get for the excess value.

“We do have that Soul Stone,” Gante says. “We know theres more than one. Maybe he could help us find the rest?”

“Or maybe he has some goods we could sell for some gold,” Kerwyn says. “Hey, old man, what kind of goods do you have here?”

“Divining’s a service industry, boy. Nothing here but my skills to know that which is not known. Unless you’re interested in this table…”

“But if we had a very special item we needed found, you could locate it?” Gante asks.

“Well, of c-” The man stops midsentence, thinking. He scratches his chin. “Are you talking something nearby to locate? Like a lost set of keys? Or something more unique?”

“More unique,” Glod says.

“Then perhaps so. Perhaps so. It would require some knowledge on the nature of the object, but it could be done.”

“What kind of stuff would you need to know about it, anything specific?” Kerwyn asks.

“How much training in the arcane arts do you have, boy?”

“He has very little, but myself, the gnome, and our friend have a fair amount,” Epona says.

“Then my answer will be meaningless to you, boy. As for the rest: The spells I could use for the locating spells would be different based on what sort of ‘uniqueness’ these objects have. Whereas family heirlooms could be found with one set of spells, enchanted swords could require something completely different.”

Epona turns to Gante. “Bring Marlak. He can explain everything we know about the stones.”

Gante returns minutes later with Marlak.

“Marlak, we believe this gentleman may be able to help us locate other artifacts if we have enough info about them,” Epona says.

“Fantastic,” Marlak says. “What do we need to know?”

“I need to know the divinable potential of these items. In detail.”

“I see. Are the rest of you okay with this?” The team nods. ”Very well. You’ll have no trouble. The objects in question are phylacteries.”

“Ah, very good, very good. This is fortunate, indeed. All I will need to find them is some components, which you have already supplied, and an object of importance to the soul’s original host.”

“Hmm, any ideas, Marlak?”

“Well, the objects required in such an instance are generally unique, themselves. An object of extreme importance to the person.”

“Do we even know the original host?” Gante asks.

“Hold up,” Glod says. “I think I still have that library book.” Glod reaches into his back and pulls out a worn tome labelled “Greater Artifacts.”

Precious little information has been collected on these artifacts. There is no exact findings as to how many there are in all, though at least six have been found and verified. Experts estimate there may be more, with some studies concluding hundreds may exist. The history of these artifacts is uncertain. It is known that they were made in the same time period, though evidence only proves they were made no more than one year apart. Each bears an icon across the front. The stones seem to have a certain amount of self-awareness; the reason behind this is still unknown. Known owners of soul stones are hesitant to part with them, making further exploration of their magical properties difficult.

“What kind of research are we taking, Marlak?” Gante asks.

“Figuring out whose soul we’re trying to locate, and what we can use that was important to them.”

“And how would we find that?”

“Research, Gante. Lots of research.”

“Would our trip to visit Sir Hanan help?”

“It certainly wouldn’t hurt.”

“Well, I guess that’s our best plan,” Kerwyn says. “Go find the dead guy and let Marlak research.”

“Alright, sir,” Epona says. “After we get the ring identified, we’ll come back a few days to see the rest of our deal through.”

“Very good. I will begin the spell,” he says, taking the pearl. “It will be ready in one hour.”

“Oh,” Epona says, “before I forget, what is your name?”

“Well, you passed it on the way in. It’s written on the sign, right next to ‘master diviner.’”

“Ah, thank you.” On the way out, they pass the sign: BELORIN MILLSTONE: MASTER DIVINER. “I wanted to make sure I can find him if he tries to pull a fast one on us.”

***

“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. He steps forward through the curtain. Epona hands him the ring. “Very good. Let’s see what secrets lurk beyond this ring, what hidden knowledge awaits us…” Dramatically, he holds the ring up, and his empty hand to his head. He closes his eyes and begins chanting, most likely not required for the spell. “Let ignorance fade and knowledge rise, blindness give way to opened eyes… Yes, it is so clear, it… hm.” He opens his eyes, a bit surprised. “Well. I’m not sure you’ll care for this news…”

“I don’t like the sound of that.”

“The good news is it isn’t cursed in the traditional way of thinking of cursed items. It’s a curse known as intermittent functioning. Specifically, the requirement variety of unreliability. You see… THIS (holding the ring up dramatically again) is a ring of invisibility! However, it will only function when no one else is looking at you.”

“What.”

“I’m quite certain. Go ahead, everyone turn around, let her see for herself.” Millstone hands Epona the ring. The team obliges, turning their eyes. Epona looks at her hand.

“It works!”

“Really?” Gante turns around.

“…You idiot.”

Glod turns around. “You know, we could use this to tell when someone’s watching us…”

“That’s… that’s actually really clever.”

“Though passing wildlife could throw it off. We may even be able to get it fixed up. But more importantly, who would even bother making such a ring?!”

“Thanks, master diviner, we will hopefully be back by in the next few weeks or so.”

They head back into town. Gante goes to help with rebuilding, offering aid where he can. Epona gives her help as well. Kerwyn wanders the city streets, and Glod continues attempting to translate the journal. Throughout the day, he deciphers a few more pages:

How I Winged a Water Temple

Posted in Dungeoneering on January 19, 2010 by eric22222

The last two sessions we played centered around the “Temple of the Ocean Goddess,” AKA the obligatory water temple. I came up with a few puzzles I wanted to do, a few battles I wanted to run, but was otherwise unprepared. So how did I manage to turn a few ideas into this?

Pictured: every gamer's nightmare

The answer: an extensive knowledge of video game tropes and clichés.

While sitting down to plan season two of our campaign, I wanted to make sure I did something for each player. Without getting into too much detail, I based it off of which of our past adventures they liked most (note to players: GMs love feedback!).

Jon (playing both our paladin and cleric) really liked the mountain shrine from session 10. I remember drawing it up and lamenting how terribly video game-like it felt. The party had to get a pair of objects acting as keys, one from the top floor and one from the bottom, then face off against a boss. Yet that was apparently his favorite? Okay, what if I go all out for this one?

I decided to have a full, multi-story dungeon ready. About two floors in, I hit a wall. I brought in some puzzles from DDO, but didn’t even know what would go behind them. However, I was able to fall back on my favorite thing to add to dungeons: history.

I had decided the temple was built by merfolk, invaded by sahuagin, then abandoned when a hag moved in. From there, I was able to add flavor to every room, hinting at a deeper story, but never fully revealing it. Adam was able to figure out why there was an urn full of money in one room; it was really nice to see they weren’t just passing through and taking everything not nailed down.

The party spent plenty of time on the puzzles, so I was able to decide what was behind the door before they finished. I used some simple rules that I’ve learned from (mostly Zelda) video games:

  1. The boss’s lair is inaccessible without a certain number of items acting as keys. This forces players to explore the entire dungeon and overcome specific challenges to claim the items.
  2. The boss’s lair should be encountered less than halfway through the dungeon. The party has to come back through to previous areas. This makes the dungeon feel more like one big area rather than several small, separate ones.
  3. A single room that acts as a sort of hub is easily identifiable as such. It should make itself known, saying “look at me, the dungeon centers around me!” Think of any Ocarina of Time dungeon.
  4. Players should know when the boss is coming up. In this dungeon, I used the classic “Megaman hall.”

Session 74

Posted in Shadows Within on January 12, 2010 by eric22222

The team continues solving the riddles of the temple of the Ocean Goddess. Read more »

Session 73

Posted in Shadows Within on January 5, 2010 by eric22222

In hopes of finding a large pearl, the team heads to the temple of the Ocean Goddess. Read more »

Session 72

Posted in Shadows Within on December 15, 2009 by eric22222

Back in Remnas, the party stocks up on supplies and gets a lead on some treasure. Read more »

Session 71

Posted in Shadows Within on December 9, 2009 by eric22222

In the goblins’ cave, the team stays on guard. Read more »

Session 70

Posted in Shadows Within on December 2, 2009 by eric22222

After defeating the dragon, the adventurers are treated to a hero’s welcome back in Remnas. Read more »

Shadows Within to make a comeback?

Posted in Announcements on October 22, 2009 by eric22222

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

Posted in Math on June 14, 2009 by eric22222

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 (6+6+2 = 14) .

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 0.5 \times 1+0.5 \times 2 . 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:

\frac{1}{6} \times (1+ \ldots +5) + \frac{1}{36} \times (7+\ldots+11) + \frac{1}{216}(13+\ldots +17) + \ldots

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

\frac{1}{6} (1+2+3+4+5+ \frac{1}{6} (7+8+9+10+11+ \frac{1}{6} ( \ldots )))

Each sum, such as 1+2+3+4+5 , 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:

\frac{1}{6} (3 \times 5 + \frac{1}{6} ((3+6) \times 5 + \frac{1}{6} ( (3+12) \times 5 + \frac{1}{6}( \ldots ))))

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

\frac{1}{6} (15 + \frac{1}{6} (15 + 5 \times 6 \times 1 + \frac{1}{6} (15 + 5 \times 6 \times 2 + \frac{1}{6} ( \ldots ) )))

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

\frac{15 + 30 \times 0}{6^1} + \frac{15 + 30 \times 1}{6^2} + \frac{15 + 30 \times 2}{6^3} +\ldots

Six is factored out of all terms:

\frac{2.5 + 5 \times 0}{6^0} + \frac{2.5 + 5 \times 1}{6^1} + \frac{2.5 + 5 \times 2}{6^2} +\ldots

This new formula can be rewritten in sumation notation:

\displaystyle\sum_{N=0}^\infty \frac{2.5 + 5 \times N}{6^N}

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?

3.5x = 4.2

x = \frac{4.2}{3.5} = \frac{6}{5}

Adding the exploding modifier to a six-sided die changes its expected value by a factor of \frac{6}{5} . 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 \frac{N}{N-1} .

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 \frac{1}{0} , which approaches positive infinity from positive values.

Silk Road – More Details

Posted in Silk Road on May 25, 2009 by eric22222

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.

silkroad-map