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Showing posts with the label math

On Conga Lines and Triggering Traps

     When exploring a dungeon, one of the ever present dangers is the potential existence of traps. One interesting bit of Old School Wisdom that I have discovered is that traps normally have a 2-in-6 or 1/3 chance of going off whenever someone passes by the trigger.      I personally think that this is a very neat feature, but it raises the question of determining who gets affected by a trap. One person? Just roll a d6 and look at the numbers. But what about when you have a long line of explorers? It isn't uncommon for adventuring parties to bring along lots of help or befriended monsters, so the number of people passing by a trap might be quite large indeed. Slowing down play to roll a d6 for every creature passing the trigger is inefficient, so I started looking into alternatives.     Due to quirks of probability, while the first person in line will have a 1/3 chance of triggering a trap, the person behind them will only trigger the trap when ...

On Expected Uses of Usage Dice

     I do have a page on useful RPG mechanics, ideas, and concepts on this blog and one of the concepts in there that of Dice Chain and Usage Dice. The central idea is this: Roll a die and if you roll at or below a specific number you drop down the chain. It gives a nice element of random chance to how many uses of something you get and makes tracking items like Arrows or Chalk very easy.     However, it can be very unclear how many uses you would expect  to get when you buy a Ud6 or Ud8 item. I have just gotten done doing some math, specifically using Markov Chains, and I believe my math holds up. Thus I have been able to produce this very handy chart: Usage Die Expected Uses Ud4 2 Ud6 5 Ud8 9 Ud10 14 Ud12 20     Now, that chart is certainly handy and can easily be recreated by noticing that each die adds 1/2 of its size to the number of expected use...

Movement Speeds and Dungeoneering

    Unfortunately, OSR has a bit of a problem in its dungeoneering rules. As Delta points out in this blog post , the source material for OD&D (Chainmail) used 1 minute turns in 1:1 combat, but a mistake was made moving things over to the new game giving us the 10 minute turn. The two most notable issues this causes is that spells last significantly longer than they were balanced for and that adventurers explore dungeons incredibly slowly (120 ft per 10 minutes is about 0.14 mph).     The naive solution to this is to simply revert back to using 1 minute turns as should have been done originally. While this does solve both of the main problems of the 10 minute turn, it also has the unfortunate side effect of entirely breaking the dungeoneering rules which heavily rely on a 10 minute turn. After all, it would be a little strange to be checking for encounters every 3 minutes and resting for 1 minute out of every 6. Never mind the horrors that result if you were atte...

The Properties of Hexes and Mapping

    One of the most common tools people will come across in tabletop RPGs are hex maps. They divide a map into a number of hexagonal sections to ease measuring distances, plotting trips, and filling in new areas. Obviously, this comes with limitations that a plain map does not have and can sometimes pull people out of the fiction that they play in, but hex maps have their uses, even if only for the DM.     The problem with hex maps is that it is normally important to have several maps at different scales, such as one for nearby areas, one for the kingdom, and maybe a world map. Obviously all of these levels need to agree with each-other, but what scales to put them at is a pertinent question.     Unfortunately, it is one that does not have any single satisfactory answer. Still, I will be working to discover what I believe are the best sets of mapping scales for use in the general OSR space.  For those not interested in reading the article and my reason...

Thinking about Mechanics: Attack Rolls

       Wow, it has been quite a bit since my last post. My new schedule is pretty hectic and the posts I really want to make are going to take more time than I seem to have, so instead I will write this apparently simple post instead.      I recently came across a post on Delta's D&D Hotspot  that I found very interesting. I will quickly summarize the post for anyone who doesn't feel like reading it (I recommend reading it). In short, the formula OD&D uses for determining if someone hits someone else in combat can be written as: d20 roll + mods >= 20 - level - AC      From there, this can be trivially rearranged for a variety of different systems, including what 5e D&D uses: d20 + level/bonus + mods >= (20 - AC)      In this schema level is replaced with your appropriate bonuses and AC is the hidden THAC0 AC that still sort of underlies the system. (20-AC) is how you convert that THAC0 AC to be the m...