Good morning gamers,
In our last post on dueling math, we talked about how to make a spreadsheet that computes your probabilities of winning a fight, given two sets of combatants. We talked about how to scale the number of dice being used - and even applying certain dueling penalties to your models. When we got to increasing your dueling rolls (usually with Might, could be with other rules), we decided to call it quits and start a new post. That's where we're picking up today.
Part 5: Handling Dueling Penalties and Boosts Better
It turns out that computing boosted dueling rolls requires re-thinking the way we've done the previous computations, since we can now have numbers going both up and down (and, of course, the reductions and boosts can be totally different). We also know that penalties are applied before Might is spent, so nothing can get below a 1 - and nothing can be higher than a 6. We know that reasonably we shouldn't see more than a -2 penalty applied to dueling rolls AND we shouldn't see more than a +5 applied to boosting rolls (to boost a 1 to a 6), so let's assume that (from a configuration perspective) this is what we need the tool to do.
To begin with, let's take as our case study a duel between Angbor the Fearless (who gets a -1 penalty when he doesn't roll a 6) and a Morannon Orc Captain with shield. To compute Angbor's dueling probabilities, we will be setting up an extra set of numbers near the box that pre-computes the dueling penalties and boosts we're willing to make:
On the right side of the 6x6 grid, we have greyed-out numbers that apply the penalties and bonuses that we specify in our configuration section for the vertical character. You'll see something similar below the 6x6 grid for the horizontal character. These tell us what value we would ROLL in order to get the final result on the left-hand side (so Angbor's value for "1" on the left shows a "2" on the right side because the 2 will be degraded to a 1 with his broadsword). Similarly, he has no value for a 5 - any 5s will become 4s and any 6s will remain 6s.
The greyed out cells work as follows: =<original_value> - <dueling_penalty> - <boosting_bonus>. If you're thinking, "Wait, why am I subtracting a negative number and subtracting a positive number? I want my negative number to make my number go down and my positive number to make my number go up, right?" Well, yes . . . that's actually what we're doing, but it's not intuitive. Let's look at an example to make it a little clearer.
Suppose you suffer a -1 penalty from a two-handed weapon. Assuming you don't have Might to boost your dueling roll, you will end up with a 3 whenever you would have rolled a 4. In our system, to figure out how often you get a result of a 3 as your final value, you want the grey number to become a 4 in the line that the 3 is displayed in. Since the penalty is listed as a negative value, we need to subtract the negative from our original value in order for it to get increased properly.
Similarly, if you boost your dueling roll by +1 (usually with Might), all rolls of 2 will become a 3 after you boost it. So if we're trying to figure out how often we get an end result of 3, we would want the grey number to become 2 (which, again, involves subtraction).
Two of the greyed-out cells do special things: the one in the "5" slot has to check to see if both the dueling penalty box is set to preserving 6s AND no Might is being used to boost - when this is the case, it returns 0 (since you will never have a situation where you end up with a 5 high). In all other cases, it works just like all the other cells. Similarly, the cell in the "6" slot has to check to see if the dueling penalty box is set to preserving 6s - if so, it's set to 6. Otherwise, we use the exact same formula that we used in the previous boxes (original score - penalties - boosts).
Okay, so let's assume that we now have the right values being calculated so we know what our expected values are supposed to be. How do we translate these new values into our 6x6 grid? Well, we update our cells on the left and top sides of the grid - here's how . . .