Posts

Showing posts with the label math

Tunnels & Trolls task resolution benchmarking

Image
Tunnels & Trolls has the first universal task resolution procedure in gaming. It's called the saving throw, after the D&D procedure. The Judge is expected to apply the results of this procedure to the fiction in a totally organic fashion. This is radical stuff! The procedure is quite simple: roll 2d6+stat, against a target number of 15+(5*difficulty). A roll of doubles on the 2d6 "explodes"; add another 2d6 and repeat this step. If the total of the 2d6 roll(s) is/are 4 or less, the task fails. Succeed or fail, the player gets (roll+stat)*difficulty experience points. I need a hard modelling surface to apply a "pick your own difficulty" procedure like this. I want to know what the odds are for a normal person to succeed at a given task. That way I can set the task's difficulty level irrespective of the player's actual stats. To that end, I simulated 200k dice rolls and counted them up. (Credit to Vivit Elric for doing the actual programming; I han...

The game gets harder

Image
Some controversy in the Table-Time discord server. When you play old-school D&D, does the game get harder as you progress? Do you need to do more adventuring for the same reward? Is that good, or bad? I don't intend to answer the evaluative questions here. But I can definitively answer the purely quantitative question: the game gets harder, and you do need to do more adventuring for the same reward. Let's assume you have a party of 6 thieves at level X. They each need about 1500 * 2^(X - 2) points to progress to the next level. They collect all their XP from treasure rooms in dungeons. These treasure rooms are generated using the procedures in the 1974 D&D publication. How many treasure rooms do they need to get to the next level? Treasure rooms per level up by level   Between 6 and 400, my math says, and the number goes up as you level up. Here's the same data in number form, with a bit more context.   Note that these values are really swingy at low levels. Most o...

Body, injury, size, monsters, benchmarking

Image
Famously, your ability/competence doesn't decrease as you lose HP. Lots of games have tried to model injuries and death at low/zero HP; here's my shot at it. We'll add a new stat to people and monsters, Injury Points, or IP, scaled to their size. System assumptions HP doesn't represent physical durability or martial fitness directly; it represents protagonism in a genre that privileges those things. Thus as we increase in HP (via leveling) we normally improve our attack bonus, but we also improve our ability to ignore various harms and annoyances. If I've got high HP, it'll take me ages to starve to death, not because I have secret caloric reserves, but because, holy mackerel, when was the last time you read a good pulp fantasy novel where the hero starved to death? Similarly, I'll last for ages in combat, taking many more hits than a normal man, and it's not because I'm more physically durable, but because I am a hero, and heroes don't die in pi...