Great resource, awesome tables!
but I think you got the part about 2d10 being different from 1d100 wrong...
Dice probability statistics are pretty funny like that, actually. If a D50 existed, those would work OK too instead of 2d10s!
Check out the following rolls on anydice.com! The graph output shows the likelihood of 'any roll of the given values will land on that result'.
Dice probability statistics is how I know that the 'average roll on a d6' is 3.5 and that you should take a 3d4 (mean result 7.5) weapon over a 1d12 (mean result 6.5) ! Pays to know these things to help give players a subtle and useful edge over NPCs.
Ah, I see the issue. I suppose I wasn't clear enough in the language. The 2d10 method works best on actually rolled ("offline") dice, because you're using each die as a substitute for the 'tens' and the 'one'.
For instance, I roll a 4 and a 7 on my 2d10. That means I rolled '47'. 8 and 4 -> 84. 3 and 5 -> 35. '00' is 100, '01' is... 01.
I came up with the 2d10 method because most people just don't own a 100-sided die. They're basically a golf-ball anyway and just roll and bounce forever on smooth surfaces. There are 'd100' dice though, where you get a 'tens' d10 (10, 20, 30 [...]) and a 'ones' d10 (1, 2, 3 [...]) but I tried to not rely on folks having a full set of dice. The 'd100' dice is actually the same roll we're simulating with two d10s anyway, by virtue of the fact we're still rolling two dice.
Yet, digitally, if you ask some dice rollers for a 'd100' it will roll a literal 'd100' rather than the '2d10 with one tens die and one ones die', which 'unskews' the table. You can just tell whatever dice roller 'gimme 2d50' if it allows for custom dice though and it will output the correct sorts of results.
There is no actual difference between rolling a 'd100' or rolling '2d10 with one tens die and one ones die', this goes for any dice, digital or real.
There IS a difference between rolling 1d12 vs 2d6, vs 3d4. This is because there are multiple ways to roll some results when using more that one die. Craps is a dice game built around '7' being the most common roll on 2d6.
Once you use a d10 for the tens place and a d10 for the ones place, this property no longer applies; there is only one combination of dice rolls that result in each number 1-100.
2d50 WOULD give the kind of center-skewed result you are describing, but of course then you couldn't roll a '1'!
>There is no actual difference between rolling a 'd100' or rolling '2d10 with one tens die and one ones die', this goes for any dice, digital or real.
I suppose I was taught incorrectly then. My understanding is that according to dice probability statistics all dice 'bend to their combined median' in results when multiple same-sided dice are introduced and that the probability curve becomes more a sin-wave the more dice are introduced but is only ever 'flat' when rolling a singular die. The median for a d100 is 50, where the medians for two d10s would be '5 and 5', which would leave me expecting 50s (and more specifically 55s) more often and for the 2d10s to skew very slightly towards the higher end of the table of possible results vs the much more neutrally weighted d100.
Any case, as goes 2d50: that's accounted for in my tables as in every table you don't get a different result when you roll a 1 versus a 2; I tried to keep it method agnostic so that it didn't matter what method was used.
I would caveat that with digital dice rollers, some use neutrally-weighted tables that treat every possible result of the given set of dice as equally likely, which would 'unbias' the dice. (Also some don't use particularly high quality RNGs -- but that's a separate matter entirely haha)
You are not wrong that dice ‘bend to their combined median’ when rolling multiple dice and adding them together! But with percentile dice, we are not adding the results, so the combined median model does not apply.
The reason they do that is that there are different results in terms of which dice rolled which number which get bundled together. If you're not bundling any numbers together - and 2d10 as a d100 doesn't do that - you don't see the effect. Using a 2 d10s as an example there are 100 distinct results. 2d10 ranges from 2-20, for a total of 19 different results, with those near 11 much more common than others. The only way to get a 2 is to roll a 11 (an 11 in a d100), whereas to get an 11 you can roll 1,10; 2,9; 3,8; 4,7; 5,6; 6,5; 7,4; 8,3; 9,2; 10,1 . That's 10 different results, but it's also ten different numbers when using the dice to simulate a d100, so you don't get that weighting.
Sorry to reopen an old thread, but it looks like 2d50 is *exactly* what you're going for, with more likely results in the middle (near 50). I programmed a d50 in Sophie's Dice (also available through Itch) and rolled up some NPCs for tomorrow's game; this is a fantastic resource!
That's awesome! It's great to hear all this stuff is helping folks out. Oh, also, if you didn't see it there's a companion app available so that you don't have to break out the dice (digital or otherwise) and can get results straight from the table. I just launched it yesterday and, though it's still an early version, it's got everything but the villain plans and pre-rolled NPCs in it. No definitions or long-form explanations in it yet that the book provides but it should help if you're doing prep-work and want stuff done in a hurry.
Best of luck with your game!