Pseudobot - Math and Graphs; How Fair is the Random Stat Generator?

So, last week, and the week before I worked on a tool to randomly generate character attributes in a way that the results would all have the same point values. At first, the algorithm assumed a character would have no decreased attributes and secondary characteristics, which was not satisfying to me, so I adjusted it so that the character could have minimum values based on some numbers I extrapolated from various GURPS sources as the bare minimum ok amount for a character. I think this was a good improvement. However, after making a naive implementation of the algorithm that gave each attribute or secondary characteristic an equal chance of occurring, on a whim, I decided to generate several thousand characters to see what the expected outcomes would be like. The result was that certain things apparently had certain unfair advantages in selecting them that made it so that certain attributes had noticeably lower or higher averages, thus began a complicated process of trying to make the algorithm as balanced as possible.

Math: Encumbrance - Lifting ST or Dodge and Move?

So, I made a spreadsheet to calculate the costs of either

1. Buying enough ST/Lifting ST to go down to the desired encumbrance level
2. Buying enough Move/Dodge/Speed to ignore the penalties.

Altogether, the results are a little disappointingly boring, but there are a few interesting things to learn from the chart, let's take a look.

Math: Luck as Critical Failure Insurance

Ah, pithy quotes on a kitschy poster.

Yesterday, I graphed the value of luck, and someone asked me what might be the value of luck if it were solely used for "Critical Failure Insurance" as in, only saved for critical failures to make sure we don't have them. So today, a slight variant on yesterday's post, what is the value of Luck if used in this limited context?

Math: What's Luck Got To Do With It?

It's physical, only logical

For some reason, figuring out an easy way to graph this has eluded me for a while, but then I decided to just write a little loop to go through the numbers. Originally, I was going to run through all 216 * 216 * 216 = 10,077,696 combinations together, but that was a little slow, so I used a fun little memoization technique to reduce it to 16 * 16 * 16 = 4,096 combinations, which is a lot more manageable, friends! Let's investigate these numbers further then.

Math: How To Not Die - Spending Points on HT or HP

First good search result for:
"too many hit points"

So, I was doing some thinking, and an idea occurred to me to graph the relative values of HT versus HP to get a kinda picture of whether one is worth more attention or not when trying to create a character that doesn't die. I don't think the graphs are especially surprising, but hey, graphs is graphs, and who doesn't like looking at numbers turned into lines and/or analyzing if I'm taking a game a bit too seriously?

Math: Incremental Improvement from Raising a Skill by One Level

PDF in blue, using the axis on the left
CDF in orange, using the axis on the right.

I was thinking about something last night about the way we generally present the bell curve for a roll of 3d6 as a way to distinguish it from the flatline of a single d20. We then take that probability density function and integrate to get the cumulative density function, or the graph that shows our success of rolling "x or under." These visualizations, I think, are useful, and they aren't wrong, but I don't think the information it conveys to a player in helping making strategic decisions about spending points is showing the whole picture, so I made a new graph that shows different information.

Alternative Mechanics: Alternative Distributions

Interact with results

Yesterday, I looked at changing the spread of values in GURPS by using differently shaped dice. Today, I'll look at different distributions along the series of integers 3:18.