### Dice Math III – Summing dice

It’s been a while since the last time (part I and part II). Besides dice pools and linear RNGs, a common way to get a random number is to roll a few dice and sum their results. This results in a curved distribution where some results are more probable than others. For example, rolling 3d6, you can only get result 3 by getting three ones but there are multiple ways of adding to e.g. 7 using numbers between 1 and 6.  Continue reading “Dice Math III – Summing dice”

### Map #9 – Forgotten Libary

Time for another map. This is also my first patreon release!  This time I drew a forgotten library. The building above ground is small and simple and the collection there is mundane and not at all impressive. However, the two dungeon levels hold rare and forbidden books. Unfortunately, the lower dungeon got damaged and the librarian fell to a small cave, died from the fall and now haunts the remains of the library. This could be located as part of ruins of a small city or even in the middle of wilderness.

In game, PCs would have to locate information from the library’s collection, but the librarian should complicate things. Place other – possibly undead – foes in the library to represent previous adventurers who have fallen before the librarians wrath if you wish.

Edit: I forgot to include the gridless version in the original post. Here’s a link to it.

Check out my patreon if you want to access high resolution versions and support me.

### MAP #8 – Hall of the Underking

Initially, I thought that this would be a dwarven ruin, but there isn’t anything in the map to prevent it being built by someone else. A cataclysm in the past cracked the dungeon in half and since that, it has become a nest for monstrous spiders. The spiders will likely stay away from the intruders unless they touch the webs or eggs. If you want, the spider webs could be sticky and slow or halt movement completely. There is a “fake” treasure room that could be mostly empty except for a few trinkets. However, the real vault is hidden behind a secret door. Additionally, there are two rooms for royal guards and at the first sight of any trouble they would have assaulted the throne room to protect the king or whatever noble is in charge of the city.

I think this small dungeon could be inserted into almost any dungeon crawl if you need an encounter with a little added environmental hazard. In DnD terms, lower level adventurers would get the most out of this map.

Here is a link to a version with a grid. Although be warned, the alignment is really poor and the grid itself is quite a patchwork.

I’ve also started a patreon, so check that out, if you want to support my mapmaking efforts. Note, this isn’t yet a “patron map”. Stay tuned for the first patreon post in the next few days!

### Going Patreon

I’ve decided to open a patreon page. See that for more details. There are a few reasons for that. First, I’m currently a graduate student and I could use a little extra income.  Secondly, I’d like to give myself some extra incentive to finalize my maps properly and keep drawing them regularly. First patron map should be going live in the next week or latest at the start of August.

I’ll also keep posting versions of the maps here and nothing will change in that regard, so there will be at least one version of each map I draw posted here. So if you have enjoyed my maps thus far, you can keep doing so for free.

So if you want to chip in or just check what I have written here is the link.

### MAP #7 – Rebel Base

Time to go scifi. This map was actually drawn a while ago, but I only recently scanned and finished it. This could easily fit into a Star Wars game, but honestly any scifi setting should do, even ‘harder’ scifi.

Basic gist of the map is that there is a hidden base (Not extremely well camouflaged but you could imagine it employing stealth technologies to mask signals from their equipment and ships) taking advantage of a small crater in a dense forest. The base has basic facilities for around two dozen people and mostly passive sensor arrays. Even if the name says ‘Rebel base’, there is no reason that the occupants have to be rebels. It could easily be an imperial outpost (in the Star Wars context) or serve whatever group you wish. However the current setup makes more sense for an armed group rather than traders, smugglers or scientists.

### Map – Hidden ruins

Time for a new map. This time, I don’t have much background for the map, but the idea is that the original entrance to these ruins was sealed off, but the ruins were rediscovered (cultists, adventurers, forces of evil or just unlucky miners) later. The map is currently quite empty except for a couple of statues and an altar. Additionally, there is a trap that opens to a pit underneath marked by a dashed line in the room with two statues. As usual, ‘S’ denotes a secret door.

Just in case you need it, here is a version without the grid.

### Map – Desert Base

After a productive week (on the map making front, that is), I have another one ready. This is a small desert base for either bandits or or more benevolent denizens. The actual base consists of a cave on a side of a mountain or a hill and two large rock pillars that have room for lookouts. Each ‘tower’ has multiple arrowslits. The elevation could be  about 20 ft. There is a balcony facing inwards in the other one. Besides the suspension bridges, there isn’t much to see from the outside and the base should be difficult to spot from a distance. The base also has a reliable, but not infinite source of fresh water from a small underground stream.

Since the blood splatters make this map harder to use for practical purposes, here is a link to version without it: No blood and here is a link to a version without the grid (and without the blood).

### Map – Tavern in the Woods

Here’s another hand drawn map of a tavern build on ruins of an old keep. It’s located in remote woods away from the most frequented roads. Usual customers are hunters, smugglers and bandits. There is a strict policy of not asking questions and both the keeper and clientele like to keep disputes away from the tavern. Indeed, rare aggressors usually find themselves facing an unlikely alliance.

The tavern itself has a main room with almost around the clock service. The tower has a couple of rooms offering privacy but most opt for a simple shared accommodation. Besides the main hall, there is a basement. It has a couple of holding cells but most of the time it is used simply for storage or even accommodation.

The fist case is the so called exploding dice, i.e. if a die comes up with the (usually) maximum possible result, then another die is rolled and added to the dice pool. Eg. a player rolls 5 d6s, and gets 1,1,3,6,6. The player then rolls two more d6s, say 2,6. The second six again adds another die which gives 2. Given the target number of 5, the final result is then 3 hits. So how does this affect the probability distribution? Well, I’m glad that you asked! First consider the expected number of hits for each die. With standard dicepool, the probability of getting a hit is p. For the exploding dice, we need to account for the possibility of getting another roll. Let’s call $p_{max}$ the probability of exploding. So first there is a chance of getting a hit. Then there is a  $p_{max}$ chance of getting another roll that gives a hit with probability of p and again there is a probability $p_{max}$ of the additional die exploding and giving another roll with probability p of getting a hit and so on. This can be expressed as $$p + p_{max}\left(p + p_{max}(p + p_{max}(\ldots))\right)$$ This can be expanded as$$p +p \cdot p_{max} + p \cdot p_{max}^{2} + p \cdot p_{max}^{3} + \ldots$$ Continue reading “Dice pools – Addendum”