### Dice Probabilities for Tabletop RPGs

Posted:

**Tue Feb 01, 2011 5:11 pm UTC**I'm playing a tabletop RPG called world of darkness. It uses a d10 system (10 sided die) to make choices.

Many rolls are 'DC 8'. This means that rolls of 8 and above are considered successes. 1 is considered a botch, and removes a success. This leaves a 'die' of [-1, 0, 0, 0, 0, 0, 0, 1, 1, 1]. (an '8' success isn't worth any more than a '9' success, and a '2' failure isn't worse than a '7' failure)

Also, if you get negative successes, you 'botch' the entire thing. The number of negative successes doesn't matter, just that you botched it.

I made a py script (spoiled below) to go through all possible die rolls and add up the number of successes you got, trying to make probability tables based on the number of dice you rolled. (if you roll 9 dice, you have a >75% chance of getting at least one success, and the median number of successes you get is 2).

I generated a chart based on this (the .pdf), but it doesn't seem intuitive for some reason. the .xlsx that I generated the chart in is attached as well.

Here is the code that I used to generate the numbers for the .xlsx: (DO NOT RUN FOR MORE THAN ~>6 DIE unless you want to spend several minutes waiting for your computer to respond)

tl;dr I ran the numbers, and they don't look right, did i do something wrong or are my intuitions wrong?

EDIT: The reason my 'intuitions are wrong' is because, well... if I roll 9 dice, each with a 30% success rate... I only get two successes on 'average' (median)? That doesn't seem right.

Many rolls are 'DC 8'. This means that rolls of 8 and above are considered successes. 1 is considered a botch, and removes a success. This leaves a 'die' of [-1, 0, 0, 0, 0, 0, 0, 1, 1, 1]. (an '8' success isn't worth any more than a '9' success, and a '2' failure isn't worse than a '7' failure)

Also, if you get negative successes, you 'botch' the entire thing. The number of negative successes doesn't matter, just that you botched it.

I made a py script (spoiled below) to go through all possible die rolls and add up the number of successes you got, trying to make probability tables based on the number of dice you rolled. (if you roll 9 dice, you have a >75% chance of getting at least one success, and the median number of successes you get is 2).

I generated a chart based on this (the .pdf), but it doesn't seem intuitive for some reason. the .xlsx that I generated the chart in is attached as well.

Here is the code that I used to generate the numbers for the .xlsx: (DO NOT RUN FOR MORE THAN ~>6 DIE unless you want to spend several minutes waiting for your computer to respond)

**Spoiler:**

tl;dr I ran the numbers, and they don't look right, did i do something wrong or are my intuitions wrong?

EDIT: The reason my 'intuitions are wrong' is because, well... if I roll 9 dice, each with a 30% success rate... I only get two successes on 'average' (median)? That doesn't seem right.