Reply To: Dice, Probability, and Simulation

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Alright, to be perfectly honest, it looked like a really interesting article, so I posted it here to take a better look at it later! It’s going to take some time to do that.

First and foremost, you need to be aware of the fact that the article is full of “math poop,” which is a technical term. I take a long time combing through my own original material because making sense of the shite is pretty challenging. I’m long past calling myself any semblance of intelligent, but it still hurts to be called retarded – unless the person calling names is me. :p

…So, when you see “variance,” it is not in the common English word context. It’s in the math context, which can be just as bad as evil-robot-lawyer-speak if you don’t know what’s going on. I actually still don’t know what’s going on, but I intend to get it sorted out by no later than this weekend.

One thing you can start with is the first set of graphs the blogger puts out. The middle one is indeed the normal distribution output of 3d6, which is a cumulative dice. Because this is the most readily read graph (it makes sense when you look at it), we can dissect what all the axes are on the graph, and therefore see what they are on the other graphs as well:

1. The bottom, horizontal axis is the die output, or in this case, sum. 3d6 ranges in values from 3 to 18 for a total of 16 outputs. Likewise, the D100 (kind of but not exactly a cumulative dice) graph to the left ranges from 1 to 100, and the non-cumulative d6 chart to the right is a bit different: it counts the number of d6’s used for a given roll.

2. The vertical axis notes the probability of getting a given roll. 3d6 definitely spikes in the middle, because on average your rolls will sum to those numbers, regardless of how the sum is achieved (I suppose you could design a game in which the manner of getting the sum would be important, but why (or maybe, why not)?). Ideally, you have a 1% chance of rolling any one number with a D100, but I don’t buy it when you’re using crappy dice like D10s. However, note that the D100 graph is a constant flat line, which is what any other single dice would be as well in ideal circumstances. The non-cumulative d6 chart for Shadowrun on the right is again different, as it’s noting the probability of scoring with a 5 or 6 with any one die. The curve for that chart drops off not because you’re less likely to succeed with more dice, but because you’re less likely to succeed with all of the dice at once. The Shadowrun graph is going to be what is most similar to Codex in this case.

3. All of the graphs have an added pair of numbers on them, which I believe are the variance and standard deviation. These are important numbers apparently, but I still don’t know what significant they hold for real human beings. I will get back to you on that matter in time…