I found the error in my Excel workbook for this. The table above is the corrected version. Everything sums to 100% properly now. Yay!
For many years I have had interest in implementing an opposed-die roll dice progression mechanic in a game. Many years ago Cory Ring and I wrote a small set of rules for the HMGS MidSouth Dispatch (newsletter) that featured such a mechanic. The problem is that there isn’t enough variance between a d4 and a d12 and then there is the big gap between d12 and d20. The gap can be filled with two dice, but then you don’t get the same uniform distribution of results than a single die achieves.
Recently, I found a company (http://ift.tt/1FMHWjz) that sells d14, d16, d18, d22, and d24. I wrote to them, and they were able to sell me 10 of each such that each type of die was a unique color. Since these are uncommon shapes I wanted to be able to say, “roll the blue one and always mean the d14 — or whatever shape was blue. They arrived recently, and I have begun to think about how to employ them.
The basic notion is that abilities would have a base die as a part point. Modifiers would then change the die rolled. The attacker and defender would each roll a die, with the higher roll winning. I have also thought it might be interesting if the difference in the rolls somehow indicated the level of success. For instance if the attacker’s roll is three times the defender’s that might indicate some sort of critical hit.
On a recent flight for work, I began to wonder about the probabilities of winning under these types of rules. One of the reasons that this die progression approach appeals to me is that someone rolling a d4 COULD defeat someone rolling a d24. But what is that probability? So out came Excel. The table below shows the chance of the attacker (rolling the dice along the left of the table) defeating a defender (rolling the dice across the top of the table).
So, if an attacker roll d4 and the defender rolled d24, the attacker would have just a 6% of winning. Note that the attacker must roll higher than the defender to get a hit, so ties go to the defender. On the other hand, if the attacker rolled d24 and the defender rolled d4, the attacker would have a 905 chance of winning. Again, ties go to the defender.
Looking at this chart, I was pretty happy with the way the probabilities laid out. Then I stated wondering why things weren’t summing to 100%. For instance, why was P(Victory, d4 vs. d24) + P(Victory, d24 vs. d4) not equal to 1? Then Duncan made a comment that helped me figure it out. It’s those ties. Since some rolls are losses for both d4 vs. d24 and d24 vs. d4 those were the missing percentages.
The table (above) shows the probabilities of ties that are always failures. For a d4 vs. anything, there are 4 rolls that are always ties: 1:1, 2:2, 3:3, and 4:4. For d4 vs. d4, this is 25% of the total rolls possible (16). To check my math, I then inverted the first table…
so the defender is down the left and the attacker is across the top. Then I added all three tables together, yielding this:
Except for one cell (it looks like two, but this table is symmetrical about its diagonal) at 99%, all the math adds up. I rechecked all the math and didn’t find an error, so I’m chalking it up to round-off errors.
So, if anyone has stayed with me this far, I think the math shows that from a probability standpoint, the die progression mechanic is viable.
I am planning to implement this with something melee heavy so that weapons get a base attack die and skill and circumstances modify the die. The defender’s armor gets a base defense die, with skill and circumstances modifying it. I may try this in a couple of weeks with some Robin Hood figures.
from Buck’s Blog http://ift.tt/1FMHWA7
from Tumblr http://ift.tt/19V6Ss4
Chris Palmer This past week I completed some more units for my planned 10mm Lizardman Army for “Bear Yourselves Valiantly” mass combat fantasy rules. Some of my readers will remember that a few weeks ago I posted the Giant Turtles that were the first Lizardman units I painted.
So far, I did three stands of spear-armed troops, one of archers, and a Battlegroup leader, Wing Commander, and a Shaman. Next up I hope to finish some cavalry and other assorted troops.
|Three spear wielding Warbands and one of archers|
|The Wing Commander on his personal war-turtle “Pooky”, a Battlegroup leader with banner, and a wise old shaman|
|A close up of the regal Wing Commander|
This week I also completed the blue translucent Water Weird figure from Bones II. I prepped the figure in the usual way; soaking it in a dish of water with a couple drops of dish- soap added, then giving it a light scrub with a soft toothbrush, and then rinsing and drying. I then glued it to a 1” black-primed fender washer with Aleene’s Tacky glue, and glued the washers to a tongue depressor with a couple drops of Elmer’s White Glue.
First, I gave the “creature” part of the figure a heavy wash with Iron Wind Metals “Dark Blue” ink. I used a brush I had dipped in water, to help thin the ink slightly.
When the ink was good and dry, I drybrushed the figure with plain white. I then painted the vessel and washer with Apple Barrel “Rock Grey”.
When the grey paint was thoroughly dry, I gave the vessel a wash with thinned Black ink. When the ink was dry, I gave the vessel a good drybrushing with the base “Rock Grey”, and then some lighter highlights with Americana “Dove Grey”.
The next morning I gave the figure a coat of Ceramcoat “Mate Varnish”. The following day, I sprayed the figure with “Testor’s Dullcote”. After the Dullcote had had a day to dry, I painted the “water” part with Americana “DuraClear Gloss Varnish”.
I’m really pleased with how this figure turned out. I really like the texture juxtaposition between the wet water and the gritty old vessel.