## Updating Probability of Damage Rolls#

Probability of damage rolls was the first interactive tutorial I wrote on redblobgames.com. I was just starting to learn how to make diagrams with d3.js and SVG. On that page I also used Bret Victor's Tangle library.

I structured the page in "textbook style", because that's what I was used to. I started with the simplest thing (rolling one die) and worked progressively towards more complicated things (multiple dice, min/max of rolls, discarding rolls, and critical hits). For each scenario, I presented the idea, the code, and then a histogram of the values you'd get from that code.

One of my goals was to structure all of my pages so that I'd first give you the solution you were looking for, and then give you an idea that would change the way you thought about the problem. For the damage rolls page, the problem you're trying to solve is how to set up the rules for the dice so that you get a distribution of values that you like. You fiddle with the rules, look at the distribution, fiddle with the rules again, look at the distribution, and keep fiddling until you get the distribution you want. The big idea was that you should start with a distribution, and then work backwards towards the code. That way you don't have to keep fiddling with parameters.

When I wrote the page, I was just learning how to make diagrams. The level of diagrams on that page took plenty of effort, and I decided not to implement the "work backwards" diagram: letting someone draw a distribution, and then generating corresponding code. It was more complicated than the others and I thought it'd take too much time.

Since then I've gotten better at making diagrams. I decided to attempt the two interactive diagrams I had wanted for that page but hadn't implemented. The first is making the existing non-interactive diagram in section 3 interactive. It shows an arbitrary distribution:

I wanted to make the distribution editable. You should be able to drag the bars up and down to change their size. To do that, I added a mouse drag handler to the bars. Using the `x` position of the drag, I calculated which column you are over, and set the bar height to the `y` position of the drag. However, that wasn't enough, because if you made the bar very short, you can no longer get the mouse over it to drag it back up. I added a white <rect> underneath the bars and put the same drag handler on there. That way all the mouse events would be captured. There are probably some things I could do with SVG's `pointer-events` CSS property without making the rectangle white, but making it white was the easiest thing to do.

Looking back on it, this diagram was fairly easy to implement. It only took an hour. However I think it would've taken far longer back when I originally wrote the page. I barely understood D3, I didn't understand d3 mouse drag, I didn't understand SVG events, and I had been thinking I needed separate drag handles on each bar instead of the much simpler drawing UI pattern. Looking back on that code, I can see how much I've learned since then.

After the first diagram, I showed the code for a four-valued distribution, and then explained how to generalize it to work for any size. That's where the page ended. I added a diagram here to show that it works for any size. I wanted to let you draw any distribution you wanted, and show the code for it:

The "code" is actually a table. It's an array of values, which you pass to a function `roll()` that I previously gave.

With this diagram, the narrative of the page is complete. First I take you from random number code to random number distributions, for lots of different variants of code. Then I say that you should be choosing distributions first instead of choosing code first. Then I let you draw the distribution you want and show the corresponding code. I'm pretty happy with the way section 3 looks now.

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