Charters
December 29, 2018
Book of Nihilo
January 17, 2019
Thanks to strenuous testing, math wizards, and number-crunching scripts, Breakaway’s dice system has been tweaked and The Dice devlog is updated. This means a much more balanced spread for players and Charter Authority alike – with a slight advantage on the player’s side at a lower skill level. The below is for all the people who enjoy crunchy statistics.
Here’s the spread of win possibilities for players with the original system – where single tied dice were always given in favor of the player. Notice how players have a spread of 31-91% chance of winning any roll, no matter what? Also, win chances for players can decrease as a skill levels up in some cases. When I first thought up the comparison system, I wanted to give players a small advantage against the CA – especially at lower skill levels.
I didn’t intend for them to have this much of an advantage – and you can imagine my absolute panic when I found out the discrepancies between skill levels. Not only is it incredibly imbalanced, win percentages were heavily fractured between each dice rolled, instead of the overall roll – meaning possibilities were down to per-dice tie, which created very strange blips between tie chance per dice pool and win chance.
I didn’t intend for them to have this much of an advantage – and you can imagine my absolute panic when I found out the discrepancies between skill levels. Not only is it incredibly imbalanced, win percentages were heavily fractured between each dice rolled, instead of the overall roll – meaning possibilities were down to per-dice tie, which created very strange blips between tie chance per dice pool and win chance.
Thankfully, I have some very, very good people who can write scripts for running heavy numbers and possibilities to determine if a system is fair or robust. It was through these scripts that a fairer spread was achieved with two simple changes: a tie between two dice are ignored, and rolls that tie are either settled by a random roll or considered to be a mixed success.
Look at that spread! It still slightly favors the player, which I wanted, and is more balanced across the board. The spread isn't as wide as I thought it would be, but I think that's to be expected in a comparison system.
An interesting blip happens around the 2d6 player line, which theoretically could be where the probability of a tie and its outcome overlap with the win chances of what would otherwise be a normal spread. The nature of the anomaly is uncertain (as it would be in many statistic spread with theoretical outcomes), but I think that’s as close as we’re going to get to a fair system. A 1% chance anomaly isn't as huge an issue as 50% chance for players to win on 2d6 versus 5d6. (I still can't believe it.)
An interesting blip happens around the 2d6 player line, which theoretically could be where the probability of a tie and its outcome overlap with the win chances of what would otherwise be a normal spread. The nature of the anomaly is uncertain (as it would be in many statistic spread with theoretical outcomes), but I think that’s as close as we’re going to get to a fair system. A 1% chance anomaly isn't as huge an issue as 50% chance for players to win on 2d6 versus 5d6. (I still can't believe it.)
Now that the system is balanced, a decision will have to be made on whether tied rolls require the random roll, or if they should be a mixed success. This may come down to personal discretion. Is the roll important to the player, and therefor deserve a better chance at winning, or is the outcome likely to be more interesting if it is a mixed success?
For fun, here’s the graph on the chances for ties. It’s a very pleasing graph to look at, such is its balance. Also, I was surprised to find out how tight the number range was. Turns out even with 5d6 v 5d6, you’re only going to have a 26% chance of tying, where I thought it would be in the upper ranges of 30%. It’s obvious I’m not good at estimation!
A big thank you goes to:
A big thank you goes to:
- Fletcher and Griff, because they’re math gods.
- Adrian, for putting up with math questions until I bothered Fletcher and Griff.