### 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.

In the last post, I mentioned a few examples of common modifications to the “pure” dice pool mechanic. I’ll cover a couple of them here.

#### Exploding dice

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”

### Dice math – Part II: Dice pools

In part 1, I covered some properties of a linear dice mechanic using d20 system as an example. Another very common mechanic is the dice pool. The basic idea is that the player rolls multiple similar dice and counts the number of dice that have result equal to or greater than a target number. The number of ‘hits’ is then the result of the roll. Games that use it are numerous: Shadowrun, World of Darkness, Burning wheel, Warhammer (the miniature game!). For example, in Shadowrun, the dice are d6s and the target number is five. So rolling 7 dice and getting numbers 2,3,3,5,6,1,4 would result in two hits. Sometimes there are additional complications, like exploding dice, re-rolls or botches. I’ll cover these on a separate post. The next part is going to be a little math heavy.

### Map – A (Small) cultist dungeon

Here’s another map. This one features a small dungeon that local cultists have used as a meeting place for their rituals. It has also two hidden entrances: one via a secret door (marked with an S) and another through a small underground pond. The main chamber opens to a cliff and sometimes sacrifices are made by forcing people to jump of the planks extending over the edge. The cave is often deserted unless a ritual night is at hand. Again, this one would also favor lower level play.

The likely location to find this dungeon would be nearby a small town or a village where most of the villagers take part in a murderous cult in exchange for protection and favors. They could worship either a genuinely powerful entity or a weaker spirit that has, for example, minor healing powers.

### Map – Smuggler’s Den

I recently started making hand-drawn dungeon maps again and here is one for you to use. The map is about a semi-hidden cave that is being used by local smugglers or thieves to gain a clandestine entry into the city. Room 1 has a very small opening to the sea/river (or even a lake, whichever body of water you prefer) to spot both incoming shipments and to get an advance warning on possible hostiles. There den is not often deserted and you can usually find at least a couple of unsavory characters inside.

In DnD 3e/Pathfinder terms this location would best serve levels before 5, since it has limited space and tactical depth for higher level characters.