DxDy dice mechanic | … e.g. D4D6

Math(s) warning: If you are a mathematician the words I use below may well be formally inaccurate, sorry!

Trad-game warning: I can imagine that rolling a die to see how many dice you roll will be an unwelcome idea in some circles – it’s OK, I’m not the D&D police, please feel free to ignore this idea.

I stumbled onto this recently (it may be well known to others) and hopefully I’m not just inadvertently regurgitating something I’ve read elsewhere.

If for example you roll D6D6s (i.e. you roll a D6 to see how many D6s you are going to roll and sum) you get a weird probability profile that has a weird leading spike:

For some strange reason it reminds me of a sleeping triceratops …

It certainly looks nothing like a standard 6D6 roll (flatter and pushed leftwards as well as having the leading spike):

The ‘at least’ number is almost linear for most of the graph as compared to 6D6:

Here’s the idea again, but where some other combinations have been done (again weird leading spike):

Here’s a mismatched pair  D4D10 and D10D4 (spike more pronounced when fewer dice are in the mix – perhaps not too unexpected):

Application in gaming?  I’ve got nothing! But …  perhaps one day it might find a place!

You’d need a probability structure that runs from 1 to the end number, has a leading spike, a flattish mid-section and then tails off as you approach the highest numbers.

OK – with that in mind and shooting from the hip here as I’m typing this up – a new way to roll stats (where we invert the thing to favour high not low numbers):

So compared to 4D6 drop the lowest, 19-D2D8 is more likely to give 17s and 18s.

Here it is again but vs 3D6:

Here’s also 19-D3D5 (no 3’s and the chance of a 14 to 18 is much higher than 4D6 drop the lowest):

I guess I’m not seriously advancing this as a replacement mechanic for rolling stats, but that said, statistically it’s not completely ludicrous (unless I’ve made a mistake) …

Perhaps you can think of a better use case?
No? OK, not to worry!

:O\

– – –

Me on DriveThru; at the moment I’m mainly pimping my procedural:
:: High Seas ‘Hex Crawl’ – In the Heart of the Sea,
:: Wilderness Hex Crawl – In the Heart of the Unknown,
:: Dungeon/network generator – In the Heart of the Delve & Dangerous