Precise Table of Advanced Tests

Advanced tests are not advanced enough. The best case is that there are a few rules of thumb in the rule book but they do not take into account a number of critical factors.

First factor is the absence of "difficulty" related to the target number and only relying on threshold to convey loose adjective of difficulty. "Average" and "Formidable" are not sufficient and instead target numbers and number or rolls or rounds needs to be established.

Second factor is the suggestion that for each roll in an advanced test that you can design about 3 degrees of success. This is inaccurate as explained in a previous blog post - adventure-game-engine-stunt-die-and-advanced-tests. Due to the correlation between overall success and the stunt die you get smaller average successes with easy tests and larger average successes with hard tests. This is offset a bit as the hard tests fail more often. However the rules prescribe the number 3 regardless of target number. A TN 9 happens to line up (average of 2.91) which is the right number for a TN11 being performed by a player with +2 modifier. That would be a common low level test, so accidentally works. For harder tests like a TN 13 with an average of 1.23 (overall including chance to fail), the design number of 3 is going to over estimate what that advanced test should be.

There is another problem to using the average, even if you are using a better average for design. The average represents the 50% mark of probability. Using that average for design is still only going to give you something that can be achieved half of the time.

The solution is to model the series of dice rolls and the sum of degrees success and build the thresholds from that table. We can use https://anydice.com/ and create a function to help evaluate how a roll produces a degree, and all the intended rolls combined.

https://anydice.com/program/33d74

We use the "at least" graph and table to determine the various thresholds. Lets use the example from page 182 of the second edition rule book.

• TN 11
• Threshold of 8
• 3 rolls allowed
  

Looking at the "three" group of rolls, and the row for "8" we can see that it has a 38.57% chance of success. That sounds pretty bad, and is better described by TN 13 test for overall difficulty. Now we should factor in that the player in that example has a +2 modifier which will reduce the difficulty of the test from TN 11 to TN 9. In the program change the variable "T: 11" to "T: 9" and press calculate. Look for the "8" row again and we see the true probability of that advanced test was 62.25% or more like a TN10 test. This really shows how arbitrary the design guidelines are and we are developing a precise idea of the true chance.

What we really want is to take a target number and find the right threshold that matches it the best. By changing the "T" value to go through all the target numbers we can build the following chart. It finds the threshold for each target number and number of rolls that equals the single roll target number chance or the next easiest number.

Looking at the row for TN 11, each threshold represents an overall 50% chance of success or slightly higher when needed. So rolling 10 times to get a 23 has the same chance as rolling 3 times to get a 6. The TN 9 preserves a 74.4% chance across all number of rolls as well. A GM can certainly use the anydice program and find something different, but it seems natural to reuse and mirror the same chance of success between all number of rolls. It is simpler but makes a readable table.

This table factors in failures so you are designing tests with an accurate representation of attempts. With TN being an accurate description of difficulty now you can ignore the table on page 182 for adjectives and use page 43 which is much more common as they represent the single roll tests.

Between the above table and the anydice program, as a GM you should be able to craft the exact experience you are looking for in an advanced test.

PS: In the program, you can set the A variable to "A: 2d6" and you have a simulation of how much damage a basic roll does... Future post for sure :)