Thursday, October 22, 2015

Seven temples of the underworld

Pyramids in Mesoamerica are not solid rock structures meant to be climbed for the purpose of worshiping some god. They're living structures that grew over centuries and have layers upon layers of lesser pyramids within them. There, are as you would have guessed, tunnels within. Unlike their Egyptian counterparts which are said to be built for the purpose of being a tomb, these pyramids were ceremonial and government centers. The complexity of them is outstanding and no pyramid shows this better than the one in Cholula, Puebla.

Allow yourself to travel back in time a few centuries. Your party has traveled through a mountain pass between two huge volcanoes and is finally making good way over the grasslands and sparse forests that populate this valley. You quest the famed Tlachihualtépetl, the hand made mill as it translates from the local language. It is said that below the now abandoned abbey is an ancient temple filled with great riches. You're now seeking to reach this abbey and enter its crypts in search of a passage to the temple rumored to be below. 

It is late in the fall and the winter is coming quickly. Already all around you you see preparations in anticipation to the celebrations of the dead. You pass a local cemetery dressed in the classic yellow of the zempoalxochitl flower, the flower of the dead.

You pass the cemetery paying respect to the passers by and those in ritual around the tombs and quickly turn down the road to the local town. Once there you find your way to the local market, the center of all commercial activity and a sure place to find information and directions to the abbey.

The market is packed with merchants lined one next to the other and selling a multitude of products, from flowers, spices and seeds to fish, cloth, pottery, candies and all types of foods. In the multitude of merchants, guards, soldiers, nobles and slaves you find a few who can give you directions to the abbey you quest for. Being late in the day you decide to stay in town and journey early tomorrow morning. Who knows what spirits may roam the roads this night. It is not a good trecena (13 day week) to be out and today's sign favors the west, an ill fated direction that points to the falling of the sun everyday and the arrival of the gods of darkness. Better to journey on a less ominous evening. You find a local house to stay in and settle down for the night.

The next day you set off early in the morning and within a few hours you arrive at what you expect should be your destination. You meet a local farmer taking care of his zempoalxochitl. You make small conversation on the matter of his flowers and he expresses his delight at the good season and harvest and the proper time of year to have these flowers for the celebration of the dead, he's hopeful that no external ill will come to this land this time. When asked about the abbey he retracts himself from you and his expression changes to a cold look. He insists you should not be going there, that it is an ill fated place and only harm will come to you and to those who you return to after visiting it. He points at the building to his back and bids you not to return through these roads should you bring bad luck and ill to his land.

You thank him for his good advice and mention that you only wish to see the place and not actually enter it. He seems to see clearly through your lies and only says, "Yes, like all those who've come before you. Just for a look. Don't come back this way!", he turns and leaves you to your travel. You walk the short distance covering a small forest and come up to an amazing sight as the road leaves the bush.

The amazing sight of the abbey standing on top of a hill, a hill so large it seems impossible to think there's a temple beneath it. If so, if so, what's the size of this beast?!?! What dwells within it?

The Cholula archaeological complex is a temple built over a millennium. Its construction is estimated to have begun in the second century BC and construction stopped around 1100 AD with the downfall of Teotihuacán. As you can see, compared to the church on top, the temple is beyond huge. It is composed of seven temples built one on top of the other. This lead to the expansion of the base which reaches 450m (1485ft) per side for the 7th and largest temple built on top of the previous six. The overall height is 65m (215ft).

The ceremonial site is a walled behemoth that has various entry points to tunnels that run into its insides. This has the potential of being an incredible dungeon to explore. The site of seven temples built one on top of each other over one thousand years. Rulers, priests, rituals and sacrifices taking place here for the span of a millennium. What type of creatures and spirits have been buried here with the construction of each new temple. What fate awaits those who journey deep into it going back one thousand years in history.

Imagine dark underground passages covered with images and strange writings. What stories do these murals tell? What magic is at work here? What powers and spirits could be released? What was the purpose of building a whole new temple above the current one? When was this done? Does it coincide with some cosmic timing, the beginning of a new era? Did the old temple become so corrupted and fill with ill spirits the priests required a whole new temple for the next era? What evil has been dormant in here for centuries? Just waiting for an unaware party of adventurers to release them.

Consider that such cultures built their pyramids with tiers representing different planes or levels of existence. Like the Chichenitza pyramid to the left, whose nine tiers represented the nine planes of Xibalbá, the Mayan underworld.

It is easy to see how going down a pyramids tier can take you deeper into unknown worlds of existence. Bringing you closer to the demons that dwell these mesoamerican underworlds.

Welcome to the seven temples of the underworld, journey on brave adventurers.

Image sources

Wednesday, October 21, 2015

Got and got not in the past 30 years

Today is back to the future day. What did we get in the last 30 years? Well we certainly did not get the hover board which was the one key item I really wanted to have today! The shoes, well that's still to be seen with so much speculation going around. Will we have self lacing Nike shoes today? Will we have it by years end? What do you think?
What we did get is this. Portable devices is what the movie certainly got wrong. No cell phones, no smart phones, no tablets. Mobile communications and the internet is one thing the movie totally missed out. Yes, there was video conferencing, but on the big living room TV, not on some portable device. So I'm thankful for that because we didn't have to wait until the 23 century to get a portable communication device like the one to the right.
We didn't get this either. Which kinda sucks when you look back and realize we're still using the same energy sources as back then and that little has moved forward in that regard.

We did get the Force awakens instead of yet another Jaws movie. On the downside we also got Jar Jar Binks.

Mixed blessing. Sure flying cars sound awesome until they crash and fall on your roof. No, as much as I'd like to I prefer to pass on the whole flying thing altogether.

Clothing style. Oh thank goodness we didn't. Nuf said.

We got the Kinect. Not exactly mind control, but darn good enough if you ask me. Plus we got 3D TV and video games and online gaming!

We got Google glass which wasn't exactly like the Doc's and it wasn't commercial success either.

But at least we didn't need to wait until the 23rd
century to get this. And although it may not be a commercial success today, it should be noted that not many people use Doc's glasses in the future. So maybe it's a niche market in the movie as it is today.

Tuesday, October 20, 2015

The dungeon within the dungeon

"That can't be; that's inside the room.", a epic quote from aliens that reminds us that there can always be something behind the wall or above the roof that we forget to account for when we dungeon craw. How many times do you put service areas, ducts and tunnels in your dungeon? I know I place way less than I should.

Surely enough I put many "secret passages", because secret passages are cool. Yet aside from being cool and providing a questionable escape benefit, what is their purpose?

Let's take a moment to think about all the cool things that could be in a dungeon that have a purpose aside from being secret and cool.

Vent ducts

Deep dungeon sections need to have direct vents to the outside. Otherwise you're just breathing the rebreathed air of all the creatures between here and the dungeon entrance. And that's allowing for good sanitary practices which are seldom the norm in dungeons. Specially after they've been abandoned and take over by orcs, ogres, goblins, bugbears and the like.

So somewhere, somehow, there has to be a way to connect that room you're in to the outside world. Maybe the tunnel's roof (which you can't see) has vent ducts to the surface.

What about kitchens and cooking areas? How did they original inhabitants feed themselves? Did the guards go up five dungeon levels to eat or did they cook things locally?

Drainage ducts

There has to be a way to drain water from the dungeon. Deep underground water may flow out the walls and there has to be a way to get rid of it. Creatures will also produce liquid waste and will want to get rid of it one way or another. Specially the more intelligent and advanced they are. What mechanisms does your dungeon provide for that? Are there drainage tunnels below the main tunnels? Such a drainage system may connect rooms in an unexpected and very beneficial way.

Water fountains

Water, drinkable water, needs to be provided to the inner parts of the dungeon. Either to drink or to clean up. Where are the living quarter areas? Whoever built the dungeon did it to be manned by some type of creature, human or otherwise, and although they may be inhumane to prisoners they certainly had to have an expectation when it comes to standards of living for the guards and higher ranking staff. Right? How do you provide that if you don't have a nice and reliable source of water. It would be really really really bad to wake up thirsty at night or with a terrible hangover only to realize you have to craw up three dungeon levels for a mug of water.


It can get cold in a dungeon (it can also get hot). Some parts may actually be very cold and damp while others warm due to geothermal activity. Does the dungeon have Roman style floors to heat the room and turn the wizard's study into a more comfortable area to spend long winter days in?

What about baths? I'm sure the great overlord of the dungeon must have enjoyed a warm bath in a pool inside the dungeon. If I spent a fortune making my dungeon I'd at least add the basic comforts of life.

As you can see from the images the heating system can be considerably more complex and interesting to explore than the dungeon itself. Now that the dungeon has been abandoned, what lives in the pool? Has it made its lair out of the boiler area? What dwells in the crawlspace below the floor? Is the floor sturdy enough to hold a fully armored party or will some tiles collapse dropping party members into the hands of whatever lives down there now.

Service ducts

So you think they walked the manticore into the dungeon like this? And you actually think it went in on its own free will? Lead by a chain and all?

I'm quite confident it was more like this.

And this.

That spells a great deal of staff and service tunnels to bring those cages in. Because I'm quite certain that thing isn't going to take the right turn down that 10' tunnel very well.

So the dungeon will surely have big service tunnels leading to the surface through which creatures can be brought into the wizard's rooms, labs and even a coliseum. It's very probable that the passages being explored by the party members now are but a fraction of the whole. Below these narrow passages is a wide set of tunnels providing water, air, heat, and passage in and out for all that is required by the dungeon owner.

Now what do these tunnels look like? Are they small and only exploitable after using a spell to make a party member small? Are they big enough to craw through? Can someone kneel or walk around half standing up? Will a small character class like a dwarf or halfling fit comfortably? Or are they huge, capable of letting a wagon through it? Who built this and to what specifications?

So, try connecting all your dungeon levels and rooms with all that is required to provide a sustainable living environment and see it come to life with a complexity that will amaze even the most experienced dungeon crawler.

Clear and present danger

Let's defuse a nuke! Succeed and you're a hero and the story goes on, fail and you TPK and cherry top the pie by royally fucking up a whole city. Roll!

Tension, thrill, anticipation, dice and narrative control are many times hard to reconcile. Sometimes dice give too high an odd for failure. This makes it hard to keep control of the story. It may simply be too much risk to take a certain action. Would you roll on a 5% chance of failure when failure means a city gets leveled? On 1% odds? Even a 1 on a percentile die may be too much. On the other hand dropping the odds to zero takes the whole thrill out of the game. What is the point in rolling then?

Even when working with everyday tasks like killing a goblin, it might be interesting to have a absurdly unexpected outcome. A moment when the goblin rolls incredibly well or you roll incredibly bad or maybe the goblin's wife throws a pan at you and scores a one time perfect hit to your head. Who knows, the point is to introduce something that surprises the players, but not to introduce it so often that it seems the dice and not you are in control of the game.

Looking at this from the angle of dice probability distribution I see two key elements that we need:

  • Strong central values
  • Long tails with many very improbable odds
This way your character should be performing consistently well if the task at hand falls within the character's expertise or consistently bad if it does not. The dice should allow very few failures when the character is good and very few successes when the character is bad at something.

Lets take a look at fudge dice with a plus and with a minus modifier. The odds should look something like this (with good rolls falling above 0):

Good characters should have good odds of succeeding most of the time with a few odd events going wrong. On the other hand bad characters should be expected to fail unless they get lucky. The problem here comes around when good characters are too good or bad characters are just crippled as hell. Since the probability curve is caped at -4 and 4 there is no way to roll below 0 if the character enjoys a +5 modifier. Yes, we can consider a roll outcome of 1 to be a very mild good outcome, but there really is no room for failure. On the other hand a character that suffers a -5 to roll will never get above 0. We might consider the -1 outcome to be a very mild failure, but the truth is the character does not succeed. We fall into what John Wick mentioned in this article as "Yes, but roll dice". A means by which the GM drops the blame of saying "No" onto the dice. "I'm not saying no. (Just making it impossible for you to roll 0 or better)."

Now let us consider the following distribution curves. They have strong central values, but also very long tails. Characters will generally fall within those values, but they're not totally bound within them. There are small odds of amazing success or outstanding failure. These curves can be achieved with exploding dice and you can clearly imagine the excitement on the table as the values begin to pile up into and amazing success! That OMG moment when you see the dice totally in your favor and the GM's face when the high penalties get overwhelmed by your outstanding roll.

So back to defusing the nuke. A task so risky that failure means leveling a whole town. How do you roll and how much is "acceptable failure"? Is the dice mechanism you're using allowing too high an odds for failure? Can it be reduced? And if so to which value? Is this value for failure too low now? And if so what is the thrill of rolling?

This brings me to the topic I addressed in a previous post about the value of the unexpected and how to recreate this in games using dice. With normal bounded die rolls you simply can't. We tend to see dice as random elements in the game because we don't know what value will come up, but we do know. We know a 3d6 will fall between 3 and 18. There is no magic in it and certainly no great unexpected value. As John Wick mentions, bounded dice allow for "Yes, but roll dice" to be a cover-up for simply saying "No". You can't unexpectedly beat the GM with a 3d6 because the GM knows what the limit is and can adjust accordingly. You can't unexpectedly beat the min-max player with a 3d6 because the player has tuned the character in such a way that there is no way such a bounded die roll can defeat the character.

On the other hand unbounded die rolls allow you to break away from such a limitation. They introduce the concept of the highly unexpected into the game. There is always a clear and present danger that something can go against "one's plans". Even the most successful character has a small chance of failing and the most unskilled character a chance of succeeding. More important than these extreme situations is the fact that such improbable rolls can happen in everyday rolls. Every once in a while, maybe once per session, you can roll an outstanding roll when fighting our buddy the goblin and you get to narrate something awesome in what would have otherwise been an off the mill encounter. So maybe the goblin's wife does score an amazing hit with the frying pan that knocks you out and turns what should have been an otherwise trivial retrieval of the key into a journey into the tunnels below the goblin's house. And this to me is what great stories are made out of, incredible turn of events that shock everyone on the table, GM included.

Tuesday, October 13, 2015

Exploding dice on low values

Why do exploding dice seldom explode on low values? We're all used to d10s exploding on 10 and so forth. Question is, why don't they explode on 1s? More so, what's the value of them exploding on 1s, 2s, 3s, etc.? You get the idea, exploding on low values.

On the up side it makes a lot of sense to have a d10 explode on a 10 and keep exploding on and on. It really fuels the player's emotions and adds to the excitement. On the down side it keeps the players with the low values. You roll a 1 and a 10 you get to roll the 10 again, but you're stuck with the one. You might turn that 10 into a ten again, but I'm quite confident you'll get some lower value 9 out of 10 times.

Now, what happens when when what we roll again are low values? Lets say I rolled a 10 and a 1. I get to roll the one again. Obviously it can't get any worse and can only get better, right? I might get a 10 or a 2, either way it's better than keeping the one and I already had a 10.

Of course it requires me to roll low to get another roll. So I can inch myself up to higher valued rolls by adding 1 at a time. This of course doesn't sound as exciting as leaping across values at a rate of ten points at a time. A d10 that explodes on a 10 adds 10 for every time it does explode, whereas a d10 that explodes adds 1 for every time it does explode. So to add 10 points I'd have to make it explode 10 times. A rather uncommon feat I may add.

So it begins to become clear why exploding dice don't tend to explode on low values. It's slow and boring to get a bonus from them. Unless of course the value required to explode increases with level.

Let us imagine a game with five skill levels: unskilled, experienced, expert, master and legendary. Characters who are unskilled at something roll without exploding dice, experienced characters' dice explode on a 1, expert dice explode on a 2, master on a 3 and legendary on a 4. Now lets imagine that all skill rolls are made with 3d10 (you know to have a nice bell curve). While an unskilled character might get a 3 a legendary character can never get less than 15 (3x5) since any 4 or lower value would trigger another roll.

I ran a small program with low exploding 3d6 on anydice and got the following graph. I used d6 to keep the numbers small and the graphs from scrolling sideways. The behavior is nevertheless very similar with d10.

The four curves on the right are the rolls for 3d6 exploding dice for the master (black, explode on 1,2,3, or 4), expert (orange, explode on 1,2, or 3), experienced (cyan, explode on 1 or 2) and novice (green, explode on 1). It is clear to see how the curves move right as skill increases. The dice mechanism prevents skilled characters from rolling too low, which is something we'd expect out of a skilled character, right?

The four curves to the left are opposing die rolls using the four skill levels against an expert. As you can see the yellow curve is slightly to the right of zero. This indicates the expected advantage a master should have over an expert. The blue curve is centered on zero and represents the odds of an expert vs an expert. The other two curves (red and pink) land to the left of zero, showing the advantage experts have over the two lower skill levels. Opposing die rolls would tend to fall below zero in a clear disadvantage to the lesser skilled characters.

So low value exploding dice may not be as exciting as high value exploding dice, but they sure make for a nice and simple skill mechanism that is easy to understand and implement in the game. Thoughts?

You can see the actual script for the low exploding d6 by following this link.

In contrast to the low exploding d6 you can see the high exploding d6 here. These explode on values >=6, >=5 and >=4.

As you can see the curve moves a bit towards the right as the skill increases, but they all start at 3. Meaning that no matter how skilled a character is the odds for a low value are the same as any lesser skilled character.

High exploding d6 script

Monday, October 12, 2015

The value of the unexpected

Some game have die rolls that represent really terrible or really awesome outcomes, you know, the dreaded 1 or desired 20. Usually these values are at the extreme end of the game's dice distribution curve, be that a 1 on a d20 a 3 with 3d6 a -4 with four fudge dice, six 10s with four exploding d10s, etc. Yet these values have very different odds of occurring. This begs the question of how much should we grant the unexpected in terms of odds of occurring.

Let us take a moment to look at really infinitesimal odds of something happening and the value of such out comes in games. Is it valuable to consider a die roll that occurs 0.1% or 0.01% of the time as a significant outcome? Does it make sense to create a rule around a roll outcome that occurs once in 1000 rolls or once in 10000 rolls?

While it may initially seem ludicrous to contemplate such small odds as significant, personally I believe it does make sense, more so if the odds are adjusted by skill. Lets imagine for a moment that the most experienced character has 0.1% odds of rolling a crit, but the crit odds get doubled by every step down in skill. The next skill level has a 0.2% odds of a crit, the next  0.4%, the next 0.8%, the next 1.6%, the next 3.2% and the next 6.4%. Six skill levels have taken the possibility of a crit form nearly impossible to a bit over a 1 on a d20. What about the progression starting an one in then thousand (0.01%)? Starting level 0.01%, 1 below 0.02%, 2 below 0.04%, 3 below 0.08% (we're awfully close to 0.1% now, not far to go to 5%), 4 below 0.16%, 5 below 0.36%, 6 below 0.72%, 7 below 1.44%, 8 below 2.88%, 9 below 5.76%. That's only 9 skill level drops before the odds reach 5%+ once again. Dividing the odds of the unexpected by 10, from 0.1% to 0.01% only added 3 levels required to bring them back to awfully probable.

This of course can be written in more human readable terms in the following way. A 1st level character has a 5% odds of a crit and the odds get halved for each level. Thus a 10th level character will have whereabouts of a 0.01% odds of a crit. Something more reasonable because it really sucks to be super good at something and then drop the ball on a 1.

Next issue of course is actually rolling such awfully low odds. These are rolls that we simply can't achieve straight out on a d20 or even d100. Although some games do have a roll again to confirm which give a 0.25% with a double 1 on a d20 and a 0.01% on a double 1 on a d100.

Now what about exploding dice? Well certainly rolling 8 tens with 4 exploding dice is very small odds indeed, but achievable. Certainly way more achievable than rolling 8 ones with 4 exploding dice, the probability of this being exactly 0. That is unless you explode low dice values, but that is the topic of another blog post.

So rolling for the unexpected can certainly add a plot twist to your story. Take the whole adventure down a very different and interesting path, but it presents two challenges. One is actually rolling such low odds and the second is rolling them "easily" and in accordance with character level progression. It makes sense that a 5th level character has lesser odds of a crit than a lowly 1st level one, but how do we adjust this? More so, how do we adjust this easily if at all? A bit more into dice mechanics in the next post in which we try to defuse a nuke.