Trifletraxor said:
Does this favour the lower skilled character? I'm very vell aware that if both characters roll a normal success, the lower skilled have the greatest chance of winning, however, I think the overall chance of who will win the opposed roll is pretty much the way it should be. Or am I wrong?
Well, in terms of 'margin' of success, yeah, you're wrong.
An interesting way to look at this is to set some 'averages', look at the results, and work your way out from these to see what happens.
So, let's say we start out with 50 versus 50 (and let's put crits and fumbles aside for the moment). We can easily see that in this case it doesn't matter whether we choose 'low wins' or 'high wins'. All things are equal. So let's shift things outwards, and go for 'halves' - it always makes sense to double or halve the stats to see if things start to break.
So now let's look at, say, 25 versus 75. Now 'low wins' or 'high wins' DOES make a difference, because we are dealing with ranges of numbers. 25 has 25 possible success results, 75...75. If we pick low wins, 75 has 50 possible successes that would be trumped by any of 25's successes (we're still ignoring crits for now). This would appear to be counter-intuitive, since 75 is evidently a lot more skilled than 25, and should kick its arse much of the time - certainly more than a third of the time (give or take, within the 'success range').
We can counter this with Ru's method -
margin of success; the gap between what you roll and what your skill is. This is cool, but it does involve minus math, even if it does stick to the idea that 'low' is good - after all, we're looking to roll
under our skill.
It can also be countered using the high roll wins method - and, it amounts to the same thing, because you are still talking about the
margin of success. Both systems have the same result, the only difference being, with high wins, you take what you see on the dice as the 'score' - there's no math with the high roll method.
That all makes sense (at least to me) so far. But we're still only dealing with results from 1-100 (00 being read as the ton). If we expand our experimental top-end outwards (might as well double it again), then we'll be looking at 25 versus 150.
I'm going to make a little leap here and say: we already know that halving breaks. And it breaks pretty quickly, too. So we'll go with the 'add the score above 100 to the margin of success' method.
Again, we can see that both 'low wins' and 'high wins' work. Again, the difference is, 'low wins' needs an additional operation.
Now let's throw in the crits and fumbles (because crit trumps a success trumps a fail trumps a fumble). If we take a crit to mean that a LOW roll is even better, because we are looking at 1/10 of your skill rating...then suddenly LOW rolls make all the sense in the world. After all, if I'm complaining about the 'low roll' method needing extra math...how about the math involved with: figuring ten percent of your skill, minusing that from your total skill, and seeing if your roll fits within THAT range. AND, funbles are at the TOP end, so why the *uck would you want to roll high?
You CAN'T stick fumbles at the low end, because then they detract from your crit chance and your overall chance (25 has 25 possible successes...no need to steal from that lot). You COULD spread crit results though, by nominating them as DOUBLEs that are a success (75 would score a crit on 11, 22, 33, etc through to 66). And if you do that, fumbles could still sit happy as-falling-off-a-log at the top end of rolls...(so then it would become....roll HIGH, but not TOO high).
To summarize - roll low AND roll high systems both work statistically (especially if you use the 'add scores above 100 to your result'), and there are ways to deal with each of them.
But, having thought about this a lot, I think I'm going to be trying out high rolls to win. If only because it uses one tiny part less math. And that, for the likes of me, has got to be a good thing at the gaming table!
- Q
PS Halving sucks.
