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I know that this subject was beaten to death already, but my mathematical self could not stop before I found something similar in result to normal d20 pool resolution, without using as many dice.

Most common alternative, even/odd, compare successes, gives very different results from normal donjon. First it promotes larger pools - there is no way to lose if you have enough more dice. For example, in normal donjon, there is almost 3% chance than 1 dice will win with 20. With even/odd you have next to no chances. 5 versus 10 is 27% in donjon, versus around 6% in even/odd. Second big problem is very big chance for ties, which do not happen in donjon often. Third problem is great number of sucesses for bigger pools - donjon tends to give only few sucesses to winner.

After a lot of testing and tweaking, I think I have came up with system which should give similar results to donjon, using a lot less dice. Of course, it is a bit different - in many cases, it skews number of sucesses by 1 and in certain places, chances of winning for weaker pool is considerably smaller than in donjon - but these are differences like 10% versus 16% or 17% versus 24%. If anybody will be interested, I can give more exact calculations - just tell what dice pool you would like to compare.

System:

Both parties roll at the same time and compare the result. You roll d20 plus extra d20 for every 10 DP you have. You add your DP mod 10 to the result. So, 1DP = 1d20+1, 10DP = 2d20, 19DP = 2d20+9, 21DP = 3d20+1. In case of a tie, person with better DP wins. In case of another tie, make it a real tie, roll again, or just toss a coin - it won't happen so often. Winner gets 1 success plus 1 success for each 5 points he has more than opponent (so 1-4 = 1s, 5-9 = 2s, 10-14=3s, etc).

It might seem reasonable to just roll 1d20 and add DP - but it has bad effect of increasing chance of high number of successes for better pool. It is better to roll, so many dice will average the result. Higher DP should still win - but with fewer successes.


Variation would be to use dice instead of bonus for mod 10 leftovers. This would be something like
1 = +1d1 (or +1d2)
2 = +1d4
3 = +1d6
4 = +1d8
5 = +1d10
6 = +1d12
7 = +2d6
8 = +1d6+1d8
9 = +2d8

It has a main benefit of having everything on table (for +1 or +1d2 I would suggest using some kind of special d6 die, so everybody will recognize it is 1d2 without extra explanations beforehand; even if you will use it as +1d1, roll it with others, as reminder about bonus).

Here we have arrived at Earthdawn system :) - with exception of having +1d20 added at very start for extra randomness. I have not tested this variation - I'm not sure how much it affects the expected number of successes, but I doubt it will make any real difference, given 5 points per success divider.


This does not solve the initiative resolution. I think it is nice as it is - especially if you now have enough spare dice to left ones from rolling initiative on table and put them aside one by one as count goes. If you don't have enough dice, or just want to change another rule, make a bowl with lottery tickets, with numbers - and let everybody pick correct number of them. It would be best to use some kind of plastic or wooden chips - pure paper ones with get dirty and torn in no time. You can number them 1-100 if you don't want ties, or 1-20x5 if you prefer normal resolution. If 100 tokens is not enough for your party, I think it is time to go out for a moment and see the world outside of gaming room...