Dice & Probabilities

More game design stuff for you. I've been spending a few hours of my holiday rolling dice.

Not, I hasten to add, actually playing a game. God forbid. But just sitting with my dice roller app and my favourite spreadsheet software tapping in numbers and I've ended up with this work in progress:

Glorious, isn't it?

So this was sparked by my playtesting a range of different options for destroying enemy targets in Midnight Dark, which include making P an active stat but only as a secondary effect.

The idea was that for every 5 damage in a single hit that an element suffered it would lose one point of Presence. If Presence reached zero, the element would be destroyed outright.

For P1 elements, this seemed fair enough. But I wondered how easy it would be to take out a P2 element or even a P3 in a single shot.

Way back when I first started writing Horizon Wars, I did a lot of maths in a notebook I still have on a shelf, somewhere. This was all based on probabilities and d12s and whilst none of it was conclusive, it all added up to the Horizon Wars dice system being a pretty good idea. But the system has evolved, since then, with Lucky 12s acquiring a bit more work to do. So I wondered how it influenced the maths.

Now, I've always considered myself pretty good at working out probabilities, but this time I had to confess myself defeated. I could work out no way to write a formula into which I could just plug the values of <target number> and <number of dice rolled> to get a clear idea of how many successes would result, taking into account the ability to cluster dice results to reach the target and for clusters including a d12 to render an additional success.

I know that the best solution would be to write a programme - probably in Python - but my Python programming skills are... extremely rudimentary (no, really rudimentary). I know some far, far better programmers, so I'm going to ask them for some help. But in the mean time, the easiest solution it just to roll a lot of dice and make notes of the results. The more dice I roll, the closer I get to a good picture of the probabilities.

The downside is that I have to roll a lot of dice for every combination of target and number of dice to get an accurate picture and the Horizon Wars system unquestionably throws up some curve balls. Not, I hasten to add, game breaking ones, but curve balls nevertheless.

I'll be unpicking those in due course, but one conclusion I've reached is that getting 5 hits in a single shot is a good threshold, but making it cumulative so that you need 10 hits in a single shot to reduce P by -2 feels like it's disproportionately improbable. So my thinking is that it might end up something like:

5 hits in a single shot = -1 P

7 hits in a single shot = -2 P

9 hits in a single shot = -3 P