Quick and Dirty:
Either it changes everything (x)or rolling dice becomes a torture, but the propabilites are like the original. If you hack dice and use some coins.
The more detailed answer(s):
After a crash course through the die system (I barely got all the details, but enough to get most basics), I had to observe, that it heavily relies on the different dice being used to achieve high sums. Trying to simulate any of the dice (d4, d6, d8 and d10) just with d6 and modifiers to that rolls is a mess:
a d4 can be easily simulated with d6: simply take 1d6 and reroll any 5 or 6 (or fill out the eyes with something so you got 2 blank sides). Simple enough, this even shows a perfect 1/4 for each number.
a d6 is a d6 is a d6. Nothing needed to change here. 1/6th probability.
Up to here: no problems. But now we get the troublesome two dice: d8 and d10:
a d10 can somewhat reliably be simulated with 2d6-2, however instead of a flat and even distribution now the result is a curved distribution, as you can see easily see on anydice - and there is a slight chance to create a result of 0 which is not useable at all.
the most problematic die is the d8. To simulate a d8, one might use the simulated d4 again (remember: 5&6=0), but again one gets a curved distribution. Using some calculation in the head, this is even an assymetric distribution: 16% of the cases are 00 and have to be rerolled, the other numbers show up as listed below (no guarantee though, I was unable to simulate it on anydice)
- 5% for 1, 8% for 2 ; 11% for 3; 14% for 4 ; 12% for 5; 9% for 6; 6% for 7; 3% for 8
Hacking Dice part 1: the d4/d6 combo die
So, we might instead of simulating dice start to manipulate a few dice to get better results. So, let's start make a few sets of special d6, best in different colors (like a red, black and white one), that can simulate d4, still be used as standard d6 and will make the checking of other rolls (see below) easier. I suggest to manipulate the d6 in the following way with a pen and some tip-ex/colored filler:
- 1 = 1
- 2 = V (a Roman 5!)
- 3 = 2
- 4 = 3
- 5 = X (read as a 6 when using it as D6)
- 6 = 4
Now, the die has numbers 1-4 circling around it and the V and X on exactly opposite sides.
- d4 now is a bit different, but even easier than simulated: either it shows the right number, or a 'striked' side. When it is a striked side, check the side closest to you for the result. No reroll needed.
We can use the hacked d4 to simulate the other dice, but that is not perfect, so I just skim over it:
- d10 is a bit easier than the calculation above now. Roll 2 hacked d6: 1-4 is as given, V is 5, X is 0. it's the same curve as the 2d6-2, the calculation is just incorporated to the die now. Reroll any XX
- d8 done with 2 hacked d4 - read the side numbers for a V, and assume 0 for X. The curve shifts somewhat, and I havn't yet done the math how, but it should be mostly in a stable way, avoiding several 00 results for all but the 11% XX - much better than the 33% before!
Hacking Dice part 2: adding coins
But there are even better variants to simulate the needed dice, by taking not dice but coins to add to the result. Most easily, one might come to the idea of just adding some coin tosses to a standard die, but that is not perfect, as the d8 example shows:
Hacking Dice part 3: perfect d8 and d10
Now, but we are onto something here... How about using the coin as an offset to decide if you rolled the "high" or the "low" end of the die.
With this the d8 can be easily simulated by taking an "offset" of 4:
- 1d4 + 1 coin*4: read the die just as a d4, offsetting that by 4 when the coin flip is won. so 1-4 on the failed coin, and 5-8 on winning.
The same holds true for the d10, just now the offset is 5:
- 1d5+ 1 coin*5: it's a d5, reading V as 5, X as reroll. And then offset the die by 5 if needed: fail the coin and it is 1-5, win for 6-10
The d8 and d10 'substitute pools' might make the scanning for the right numbers harder:
- you'd have to take different colors of dice for the different substitute set.
- You have to keep track which substitute die is a d8 or d10 in each roll.
- When just simulating dice (you will get more centered results for that!) does flat out the probabilites quite a lot and give much more "centralised" results for the larger dice - the median numbers of those d8 and d10 getting substitutes come up much more often than the extremes (save for the 00 on the d8 in variant 1).
- This means, that once you get large dice you get extremely unlikely a very low number (which the system avoids in itself anyway), but you likewise have only a very slim chance of gaining an extremely high number. It is a mess.
However there are the ways to simulate the dice without messing up the probabilities, you just need a pack of coins and the hacked dice. To make the resolution faster, best paint one side of the coins in the same color to the die they belong to. Also, you might just roll each die one after another to keep better tabs on which die you just rolled, detting them aside on cards labeled with d4, d6, d8 and d10.
With those problems (unless you use the variants with coins), there is also a solution that was suggested by Reibello in the chat when we discussed the probabilities:
If you want to keep the system as it is, it might be a better solution to take playing card sets for each of the dice
To do so, you would just need to grab a poker set and choose one suit for each die, use ace for the 1 and then make stacks till 4, 6, 8 or 10, putting the other cards away. It does clearly save you the trouble of calculating with offsets, manipulating dice and furthermore, manipulating the results after the "die roll" is pretty easy, but mixing the cards and pulling one has a different feeling to it than rolling dice - and if there is a crafty cardplayer at the table, he might even use fake shuffling methods to manipulate the "rolls".
As a last way out, you could rewrite all those tables/wall of textes to only include results between 2 and 12 and deal with the bell curved distributions you will get, but... that the work you need to put into rewriting the system is much larger than just hacking some dice or using substitute pools.
Thanks & Gratitude
I kindly thank Reibello for helping me with understanding the dice system and discussing the math with me - and for pointing out that while the simulation does indeed kind of work, keeping track of those dice pools would make it a hellish task to roll anything save for d4 and d6 (where you still will have to use at least 2 colors to keep them apart).
Also, I want to thank nitsua60 for helping figuring out the d4/d8/d10 simulation methods with less rerolling and in the end giving me the input that was used to make the hacked dice parts possible.